Investment planning

3.3.5. Effect of Diversification on Portfolio Risk and Return If the prior expectations of the returns on all assets in the portfolio are identical, the expected return on a diversified portfolio will be identical to that on an undiversified portfolio. Some assets will do better than others; but since one does not know in advance which assets will perform better, this fact cannot be exploited in advance. The return on a diversified portfolio can never exceed that of the top-performing investment, and indeed will always be lower than the highest return (unless all returns are ex post identical). Conversely, the diversified portfolio's return will always be higher than that of the worst- performing investment. So by diversifying, one loses the chance of having invested solely in the single asset that comes out best, but one also avoids having invested solely in the asset that comes out worst. That is the role of diversification: it narrows the range of possible outcomes. Diversification need not either help or hurt expected returns, unless the alternative non-diversified portfolio has a higher expected return. One simple measure of financial risk is variance. Diversification can lower the variance of a portfolio's return below what it would be if the entire portfolio were invested in the asset with the lowest variance of return, even if the assets' returns are uncorrelated. 3.3.6. Hedging A hedge is an investment position intended to offset potential losses/gains that may be incurred by a companion investment. In simple language, a hedge is used to reduce any substantial losses/gains suffered by an individual or an organization. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of over- the-counter and derivative products, and futures contracts. Public futures markets were established in the 19th century to allow transparent, standardized, and efficient hedging of agricultural commodity prices; they have since expanded to include futures contracts for hedging the values of energy, precious metals, foreign currency, and interest rate fluctuations. Hedging is the practice of taking a position in one market to offset and balance against the risk adopted by assuming a position in a contrary or opposing market or investment. 191

Sub-Section 3.4 Analysis of Returns Learning Outcome The objectives of the topic 3.4 – Analysis of Returns are as follows: 1. To understand the power of compounding in investing. 2. To learn the difference between Time weighted & Rupee weighted return concepts. 3. To learn the difference between Inflation adjusted Real return & Nominal Rate of return. 4. To learn the difference between Effective rate of return & Nominal rate of return. 5. To understand the concept of Holding Period return. 6. To understand the relative difference between Compounded Annual Growth Rate (CAGR) and Internal Rate of Return (IRR). 7. To understand the concept, difference & methodology of calculating the Yield to maturity & Current Yield in debt instruments. 8. To learn to analyse stocks through some performance and valuation measures such as Dividend Yield & Earnings Per Share. 9. To learn to analyse stocks valuation through measures such as Price to Earnings & Price to Book Value. 10. To judge under valuation and over valuation of stocks based on financial ratio like Price to Earnings. 11. To learn to value stocks based on their intrinsic value calculated via the Dividend discounting mode. 12. To learn to differentiate between Growth, Dividend & Dividend Reinvestments amongst Mutual Fund schemes. 13. To measure and evaluate the performance of mutual fund schemes on various parameters. 192

3.4.1. Power of Compounding Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with 1000 initial principal and 20% interest per year would have a balance of 1200 at the end of the first year, 1440 at the end of the second year, 1728 at the end of the third year, and so on. To define an interest rate fully, allowing comparisons with other interest rates, both the interest rate and the compounding frequency must be disclosed. Since most people prefer to think of rates as a yearly percentage, many governments require financial institutions to disclose the equivalent yearly compounded interest rate on deposits or advances. For instance, the yearly rate for a loan with 1% interest per month is approximately 12.68% per annum (1.0112 − 1). This equivalent yearly rate may be referred to as annual percentage rate (APR), annual equivalent rate (AER), effective interest rate, effective annual rate, and other terms. When a fee is charged up front to obtain a loan, APR usually counts that cost as well as the compound interest in converting to the equivalent rate. These government requirements assist consumers in comparing the actual costs of borrowing more easily. For any given interest rate and compounding frequency, an equivalent rate for any different compounding frequency exists. Compound interest may be contrasted with simple interest, where interest is not added to the principal (there is no compounding). Compound interest is standard in finance and economics, and simple interest is used infrequently (although certain financial products may contain elements of simple interest). A formula for calculating annual compound interest is as follows: S  P  1  j nt  n  where S = value after t periods P = principal amount (initial investment) j = annual nominal interest rate (not reflecting the compounding) n = number of times the interest is compounded per year t = number of years the money is borrowed for As an example, suppose an amount of 1500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Then the balance after 6 years is found by using the formula above, with P = 1500, j = 0.043 (4.3%), n = 4, and t = 6: S  1500  1  0.043 4x6  1938.84  4  193

So, the balance after 6 years is approximately 1938.84. The amount of interest received can be calculated by subtracting the principal from this amount. The amount function for compound interest is an exponential function in terms of time. A(t)  A0  1  r nt  n  t = Total time in years n = Number of compounding periods per year (note that the total number of compounding periods is n.t) r = Nominal annual interest rate expressed as a decimal. e.g.: 6% = 0.06 nt means that nt is rounded down to the nearest integer. As n, the number of compounding periods per year, increases without limit, we have the case known as continuous compounding, in which case the effective annual rate approaches an upper limit of er − 1. Since the principal A(0) is simply a coefficient, it is often dropped for simplicity, and the resulting accumulation function is used in interest theory instead. Accumulation functions for simple and compound interest are listed below: a(t)  1  tr a(t)   1  r nt  n  Note: A(t) is the amount function and a(t) is the accumulation function. Continuous compounding can be thought of as making the compounding period infinitesimally small, achieved by taking the limit as n goes to infinity. See definitions of the exponential function for the mathematical proof of this limit. The amount after t periods of continuous compounding can be expressed in terms of the initial amount A0 as a(t)  A0ert It has been shown that the mathematics of continuous compounding is not limited to the valuation of continuously compounded financial instruments and flow annuities, but rather that the exponential equation is a versatile model that may be used for valuation of all financial contracts normally encountered. In particular, any given interest rate (r) and compounding frequency (n) can be expressed in terms of a continuously compounded rate r0: r0  n ln(1  r) which will also hold true for any other interest rate and compounding frequency. All formulas involving specific interest rates and compounding frequencies may be expressed in terms of the continuous interest rate and the compounding frequencies. 194

3.4.2. Time Weighted Return vs. Money Weighted Return Time-Weighted Rate of Return The time-weighted rate of return is the preferred industry standard as it is not sensitive to contributions or withdrawals. It is defined as the compounded growth rate of ₹1 over the period being measured. The time- weighted formula is essentially a geometric mean of a number of holding-period returns that are linked together or compounded over time (thus, time-weighted). The holding-period return, or HPR, (rate of return for one period) is computed using this formula: Formula Where: MV0 = beginning market value, MV1 = ending market value, D1 = dividend/interest inflows, HPR = ((MV1 - MV0 + D1 - CF1)/MV0) CF1 = cash flow received at period end (deposits subtracted, withdrawals added back) For time-weighted performance measurement, the total period to be measured is broken into many sub-periods, with a sub-period ending (and portfolio priced) on any day with significant contribution or withdrawal activity, or at the end of the month or quarter. Sub- periods can cover any length of time chosen by the manager and need not be uniform. A holding-period return is computed using the above formula for all sub-periods. Linking (or compounding) HPRs is done by (a) adding 1 to each sub-period HPR, then (b) multiplying all 1 + HPR terms together, then (c) subtracting 1 from the product: Compounded time-weighted rate of return, for N holding periods = [(1 + HPR1)*(1 + HPR2)*(1 + HPR3) ... *(1 + HPRN)] - 1 The annualized rate of return takes the compounded time-weighted rate and standardizes it by computing a geometric average of the linked holding-period returns. Formula Annualized rate of return = (1 + compounded rate)1/Y - 1 Where: Y = total time in years Time-weighted rate of return (TWROR) is a measure of the historical performance of an investment portfolio which compensates for external flows. (External flows are net movements of value which result from transfers of cash, securities or other instruments, into or out of the portfolio, with no equal and opposite movement of value in the opposite direction, and which are not income from the investments in the portfolio, such as interest, 195

coupons or dividends.) To compensate for external flows, the overall time interval under analysis is divided into contiguous sub-periods at each point in time within the overall time period whenever there is an external flow. The returns over the sub-periods between external flows are linked geometrically (compounded) together, i.e. by multiplying together the growth factors in all the sub-periods. (The growth factor in each sub-period is equal to 1 plus the return over the sub-period.) Investment managers are judged on investment activity which is under their control. If they have no control over the timing of flows, then compensating for the timing of flows using the true time-weighted return method is a superior measure of the performance of the investment manager Money-Weighted Rate of Return A money-weighted rate of return is identical in concept to an internal rate of return: it is the discount rate on which the NPV = 0 or the present value of inflows = present value of outflows. Recall that for the IRR method, we start by identifying all cash inflows and outflows. When applied to an investment portfolio: Outflows 1. The cost of any investment purchased 2. Reinvested dividends or interest 3. Withdrawals Inflows 1. The proceeds from any investment sold 2. Dividends or interest received 3. Contributions Example: Each inflow or outflow must be discounted back to the present using a rate (r) that will make PV (inflows) = PV (outflows). For example, take a case where we buy one share of a stock for ₹50 that pays an annual ₹2 dividend, and sell it after two years for ₹65. Our money-weighted rate of return will be a rate that satisfies the following equation: PV Outflows = PV Inflows = 2/(1 + r) + 2/(1 + r)2 + 65/(1 + r)2 = 50 Example 1 Assume an investor makes the following investments:  Today, she purchases a share of stock in Redwood Alternatives for Rs. 50.00.  After one year, she purchases an additional share for Rs. 75.00.  After one more year, she sells both shares for Rs. 100.00 each. There are no transaction costs or taxes. The investor's required return is 35.0%. During year one, the stock paid a Rs. 5.00 per share dividend. In year two, the stock paid a Rs. 7.50 per share dividend. 196

Caculate the time weighted return: SOLUTION : To calculate the time weighted return: Step 1: Separate the time periods into holding periods and calculate the return over that period: Holding period 1: P = Rs. 50.00 D = Rs. 5.00 P = Rs. 75.00 (from information on se cond stock purchase) HPR = (75 − 50 + 5) / 50 = 0.60, or 60% Holding period 2: P = Rs. 75.00 D = Rs. 7.50 P = Rs. 100.00 HPR = (100 − 75 + 7.50) / 75 = 0.433, or 43.3%. Step 2: Use the geometric mean to calculate the return over both periods Return = [(1 + HPR ) × (1 + HPR )] − 1 = [(1.60) × (1.433)] − 1 = 0.5142, or 51.4%. Example 2 An investor makes the following investments:  She purchases a share of stock for Rs. 50.00.  After one year, she purchases an additional share for Rs. 75.00.  After one more year, she sells both shares for Rs. 100.00 each.  There are no transaction costs or taxes. During year one, the stock paid a Rs. 5.00 per share dividend. In year 2, the stock paid a Rs. 7.50 per share dividend. The investor's required return is 35%. Calculate the money - weighted return. To determine the money weighted rate of return, use your calculator's cash flow and IRR functions. The cash flows are as follows: CF0: initial cash outflow for purchase = Rs. 50 CF1: dividend inflow of Rs. 5 - cash outflow for additional purchase of Rs. 75 = net cash outflow of Rs. 70 CF2: dividend inflow (2 × Rs. 7.50 = Rs. 15) + cash inflow from sale (2 × Rs. 100 = Rs. 200) = net cash inflow of Rs. 215 Enter the cash flows and compute IRR: Use Cash Editor function in FC-200V 1 = -50; 2 = -70; 3 = +215; IRR (Solve) = 48.8607 197

3.4.3. Real (Inflation Adjusted) vs. Nominal Rate of Return In calculating return over a number of years, we have seen that you must consider the stream of income over time. When investment is made, the investor postpones his/her current consumption for future income. If during, the period of investment, the prices of goods or services rise, the investor requires more money to acquire the same. Goods or services Prices of goods and services rise during the period of inflation and reduces the purchasing power of an investor. It is, therefore, essential to adjust the total return on investment for inflation. Such inflation adjusted returns are known as ‗real‘ rate of return. In times of changing prices, nominal returns of an investment may be a poor indicator of real returns (Real rate). Fisher Effect: Fisher method calculates the exact real return as follows = 1  Nominal Return  1 -1 1  Inflation Rate To illustrate, you consider the following information: Value of an investment in the beginning period ₹100000 Income received during the year: Dividends 8000 Capital Appreciation 12000 Inflation Rate 5% Total return on this investment is (8000+12000)/100000 = 20% whereas real rate of return after adjusting for inflation would be 15% (20% minus 5%) This method of calculating the Real Return is simplistic and approximate. The Actual calculation is known as fisher effect. Real rate of return = (interest rate - inflation) / (1+inflation rate) = (20-5)/(1+5%)=15/1.05=14.28% Example 1 Harish invested in an instrument for three years which gives a return of 11%, 15% and 12% in three years respectively. You as Harish‘s advisor have observed that the ruling inflation in these three years respectively was 4%, 7% and 8%. Calculate the real rate of return which Harish has received from this instrument. • If the amount invested is Rs. 1,000 • Real rate of return (at the end of year 1) =(11-4)/1.04 = 6.7308% • Real Value of the investment at the end of year 1 = 1000*1.067308 = 1067.308 • Real rate of return at the end of year 2 = (15-7)/1.07 = 7.4766% • Real Value of the investment at the end of year 2 = 1067.308 * 1.074766 = 1147.10635 198

• Real rate of return at the end of year 3 = (12-8)/1.08 = 3.7037% • Real Value of the investment at the end of year 3 = 1189.5918 • Real rate of return earned from the investment = 5.9577% (using rate function in excel, nper=3, pmt=0, pv=-1000; FV = 1189.5918) 3.4.4. Effective vs. Nominal Rate of Return Nominal Interest Rate It refers to the annual rate of interest calculated without taking into consideration the effect of compounding. It is the (stated) annual rate of interest that an investment product is offering at the face value. Method of Calculation: Formulae: Nominal Interest Rate (APR) = n*{(1+EFF)(1/n)-1} Where n is the number of compounding in a year. Calculator: Conversion (CNVR) mode – Solve for APR Effective Interest Rate It refers to the annual rate of interest calculated after taking into consideration the effect of compounding. It is the (gross) annual rate of interest that an investor is actually earning from an investment product. Method of Calculation: Formulae: Effective Interest Rate (EFF) = {1+(APR/n)}n-1 Where n is the number of compounding in a year. Calculator: Conversion (CNVR) mode – Solve for EFF Nominal Versus Effective Interest Rate The nominal interest rate (also known as an Annualised Percentage Rate or APR) is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding (this immediately follows from elementary algebraic manipulations of the formula for compound interest). Note that a nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate. 199

Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rates correct for this by \"converting\" nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual rate. Confusingly, in the context of inflation, 'nominal' has a different meaning. A nominal rate can mean a rate before adjusting for inflation, and a real rate is a constant-prices rate. The Fisher equation is used to convert between real and nominal rates. To avoid confusion about the term nominal which has these different meanings, some finance textbooks use the term 'Annualised Percentage Rate' or APR rather than 'nominal rate' when they are discussing the difference between effective rates and APR's. The term should not be confused with simple interest (as opposed to compound interest) which is not compounded. The effective interest rate is always calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective rate, i the nominal rate (as a decimal, e.g. 12% = 0.12), and n the number of compounding periods per year (for example, 12 for monthly compounding): r  (1  i /n)n  1 Significance: Effective and nominal interest rates allow banks to use the number that looks most advantageous to the consumer. When banks are charging interest, they advertise the nominal rate, which is lower and does not reflect how much interest the consumer would owe on the balance after a full year of compounding. On the other hand, with deposit accounts where banks are paying interest, they generally advertise the effective rate because it is higher than the nominal rate. Therefore, if you were to borrow money at 8 percent APR and immediately deposit it in an account at 8 percent APY, the deposit account will have 200

less money at the end of the year than you owe on the debt Example 1 For a nominal interest rate of 10% per annum compounded monthly, quarterly, and semi- annually, the respective annual effective rates would be ______. Using FC 200V calculator CNVR function N=12, I%=10, EFF (solve) = 10.4713% N=4, I%=10, EFF (solve) = 10.3813% N= 2, I=10, EFF (solve) = 10.25% Example 2 Given r = 9% per year compounded monthly, find the Effective Monthly Rate (effective rate per compounding period). Solution: m = 12 compounding periods within a year (T). Effective Monthly Rate (effective rate per CP): 0.09/12 = 0.0075 = 0.75%/month Example 3 The nominal rate is 1% per month and compounding occurs monthly, what is the effective rate for 12 months. I = (1 + .12/12)12 = 1.1268 – 1 = 12.68% Example 4 If the effective rate of interest compounded quarterly is 16%, then the nominal rate of interest is Using FC 200V calculator CNVR function N=4, I%=16, APR (solve) = 15.1208% 201

3.4.5. Total Return / Holding Period Return (HPR) The period during which you own an investment is known as its holding period and the return for that period is known as Holding Period Return (HPR). In other words, this is the total return earned by the investor by holding an investment for a given period of time. In the case of equity shares, return arises in the form of dividends and capital growth. Let us say, a share in a company is purchased for ₹20. It pays a dividend of ₹2 per annum. Return in this case is 2/20, or 10 per cent p.a. this return is known as dividend yield If the price of the share increases in the course of the year and it is sold for Rs.30, the investor‘s return would be ₹2 + Rs.10. The return in this case is 12/20, or 60 per cent. However, until the share is sold, the ₹10 increase in value remains unrealised. (Taxation must be taken into account, but we will deal with this issue later.) If, for some reason, the value of the share goes down to ₹15 and the investor sells it at the end of the year, he or she will have a negative return, of the stock has paid its dividend of ₹2 p.a. The general formula for holding period return (HPR) is: R  (p1  p0 )  i x100  15% p0 Where: P0 = initial value P1= final value i =interest or dividend The HPR above 1 unity indicates that the investment has grown positively while HPR below 1 unity shows that the investor has incurred a loss. In the case of our example, R  (30)  2  1.60 20 So far, we have considered how the holding period returns on a single investment are computed. Let us now see the calculation of return on a portfolio of investments. This is measured as a weighted average of the returns for the individual investments in a portfolio. The weights are calculated by considering the beginning values of each investment in the portfolio. Investment Market value Market value at Weights HPR in the end of the year of the year 0.15 The Beginning 115000 0.10 0.20 300000 0.25 0.10 A 100000 715000 0.65 B 250000 C 650000 202

Return on the portfolio is (0.10*0.15 +0.25*0.20+0.65*.10) = 0.13 i.e., 13% Example 1 You purchase 500 shares of a company at Rs 205 per share on 1st July 2011. The dividend of Rs 1100 and Rs 1300 were received respectively in August 2011 and September 2012. On 1st January 2013 the share were sold for Rs 1.15 lakh. Your holding period return comes to? Holding Period Return = Ending Price – Initial Price + Dividend Initial Price Initial Price = 500*205 = 102500 Ending Price = 1,15,000 Dividend Income = 1100 + 1300 = 2400 Holding Period Return = 115000 – 102500 + 2400 = 14.5366% = 14.54% Example 2 Calculate Total Return / Holding Period Return Price at the beginning of the year = Rs. 60 Price at the end of the year = Rs. 70 Dividend received during the year = Rs. 5 (Answer; Total Return 25%) Solution: Total Return = { ((P1 - P0) + D1) / P0 }*100 {(70-60+5) / 60 } *100 3.4.6. Compounded Annual Growth Rate (CAGR) and Internal Rate of Return (IRR) Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. Let us now consider an equity investment worth ₹250 two years ago and is worth ₹300 today. The dividend received is ₹25 each year. The HPR on this equity investment can be calculated by applying the above formula. 203

HPR  300  50  1.40 250 Note that this 40% return is for a period of two years. Investors generally prefer to evaluate the returns in annual terms so that comparison of alternate investments is possible. How to convert the HPR that we have calculated in annual percentage? Annual HPR = HPR 1/n = {1.40}1/2 or 1.1832 Thus, the CAGR of the investment is 18.32%. (1.1832 -1.0) = 18.32% annually The internal rate of return (IRR) is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return (DCFROR). The internal rate of return on an investment or project is the \"annualized effective compounded return rate\" or rate of return that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero. It can also be defined as the discount rate at which the present value of all future cash flow is equal to the initial investment or in other words the rate at which an investment breaks even. In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment. Given the (period, cash flow) pairs (n, Cn) where is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by in: NPV  N Cn 0 n0 (1  r)n The period is usually given in years, but the calculation may be made simpler if r is calculated using the period in which the majority of the problem is defined (e.g., using months if most of the cash flows occur at monthly intervals) and converted to a yearly period thereafter. Example 1 You invest Rs. 15000 at the end of year 1, Rs 20,000 at the end of year 2 and Rs 50,000 at the end of each year from 3rd year to 10th. Calculate the PV of this stream if the discount rate is 10%. Using cash editor function in Casio FC 200V 10 2 15000 3 20000 4 50000 5 50000 204

6 50000 7 50000 8 50000 9 50000 10 50000 11 50000 I = 10 NPV (solve) = Rs. 250616.765 Example 2: You are investing Rs. 20,000 and you will get Rs. Rs. 6000 at the end of first year, Rs. 8,000 at the end of second year, Rs. 10,000 at the end of third year. How much rate of return you have earned on your investment? Using cash editor function in Casio FC 200V 1 -20000 2 6000 3 8000 4 10000 IRR:Solve = 8.8963% 3.4.7. Yield to Maturity (YTM), Yield to Call and Current Yield Influences on Return from Fixed Interest Securities: The return (yield) from investing in interest-bearing securities takes two forms: an interest flow and capital appreciation. Interest is normally fully assessable and the capital appreciation is usually taxed as income as well. A more detailed coverage is given later in the topic on the taxation of interest-bearing securities. There are many influences affecting the yield of interest-bearing securities. These are liquidity, risk, economic factors and maturity. Each is linked with the other. 1) Liquidity Liquidity is an important consideration. Investors will at some time hold cash or funds in current accounts or savings accounts. It is important that funds held for a reason by investors at call or for use within a year, earn as a high a return as possible. Financial 205

planners should ensure that such funds are invested and generate the highest possible returns. At call funds and short term funds could be held in MMMFs earning a higher interest compared with zero interest on current accounts or 3–4 per cent on savings accounts and in other forms of money market investments. The need for funds in the short term determines that interest-bearing investments are the only options. Shares and property are long-term investments, normally for a minimum of five years. Conversely, when investing for the long term, investors are reducing the liquidity of their portfolio and this reduction needs compensation in terms of increased earnings. 2) Risk Risk is another major factor. This risk is borne by the investor. It is the risk of possible default in terms of interest payments and redemption by the issuer. Here the risk is the possibility that the return earned will not be the same as the return expected at the time of investment. The higher the quality or credit worthiness of the issuer of the security, the lower the risk of default associated with the security and the lower the interest rate needed. The greater the risk, the greater the interest that should be paid to compensate the investor for the risk undertaken. Therefore, issuers with lower quality credit worthiness will have to pay a higher interest to compensate for the additional risk the investor will bear. Professional credit rating organisations, such as CRISIL and ICRA, provide information about the credit quality of security issuers in India, spread between AAA-rated corporate bonds and government securities. Standard & Poor‘s and Moody‘s ratings provide international capital markets with a global framework for comparing credit quality of rated debt securities. The rating system permits a comparison of rated debt obligations incorporating the currency and the industry in which the issuer operates. When selecting investments into a client‘s portfolio, the organisation with an investment grade of Aaa would be the best quality issuer with the smallest level of risk and lower yields. In contrast, one with an investment grade of Aa3 is of a lower grade and its bonds would need a higher yield to attract the risk-averse investor As well as the credit worthiness of the issuer, the ranking of the security in the event of the issuer of the security going into default must also be considered. Securities may be secured or unsecured. The higher the ranking, the lower the risk and the lower the expected return. Again a financial planner is responsible for matching this risk/return trade off. For example, if a company issues debentures and unsecured bonds of a similar maturity, the debentures would normally carry a lower interest rate because the unsecured bonds are subordinated to the debentures in an instance of financial distress and therefore carry a higher risk. However, if the company is credit rated as ‗secure‘, a decision might be made that the additional risk is minimal and the extra return worth the risk. The price at which the security is bought or sold will reflect current market interest rates plus a risk premium. The trick is to anticipate the direction of movement in yields, because the value of the security is determined by the discount rate prevailing when the security is sold. If an investor anticipates a fall in interest rates, then locking up for a long term in a fixed interest security is more attractive than a short-term investment. Conversely, if a rise in interest rates is anticipated, it is more attractive to invest short term and allow a release of funds to be invested in the future at a higher rate. 206

The key to a successful investment strategy in interest-bearing investments is to predict the direction of interest rate movements. Expressed more formally, the financial planner needs to understand the ‗determination of investor expectations‘. This is not easy to do, but it is important. While many clients invest collectively using fund managers to maximise investment value, planners need to be aware of any factor that might impinge on interest rates and, in turn, this is why it is essential for the planner to carefully read the latest financial news. The first step is to realise that investor expectations are affected by both economic and political (or non-economic) factors. 3) Economic Factors Some economic factors influencing interest rates are expected inflation, expected current account deficit, macro- economic policy, international influences and currency movements. A. Expected Inflation Rate Expectation about inflation is a powerful influence on interest rates. Inflation lowers the real value of an interest rate security. The higher the inflation rate (specifically, the expected inflation rate), the greater the need for interest rates to be raised to restore the real value of an interest rate security. Increasing inflation pulls interest rates higher and declining inflation allows interest rates to decline. A higher than expected inflation rate brings with it rising interest rates, to compensate lenders for the decline in the purchasing power of the interest received from borrowers in the money markets. In times of low inflation and price stability, the investor is better off earning positive real returns in comparison with years when the inflation rate exceeded the prevailing interest rates. Inflation risk is another risk faced by investors. This risk relates to the underlying rate of inflation relative to nominal yields. Ultimately investors are concerned with inflation-adjusted returns (i.e. real returns). Hence the larger the relative rate of inflation, irrespective of the nominal yields, the smaller the real rate of return. This is often called the Fisher effect and is defined as follows: (1+y) = (1+e) (1+r) where y = nominal yield e = expected inflation rate r = real yield This can be rearranged to give a definition of the real rate of return: r = [(1 + y) / (1 + e)]–1 For example, if a Treasury bond returns a rate of 6 per cent p.a. and the inflation rate is 7 per cent p.a., the real return can be estimated as: 1.06 / 1.07–1 = – 0.93% p.a. B. Current Account Deficit Deterioration in the country‘s balance of payments, usually brought about by a higher 207

current account deficit, invariably means a weaker exchange rate. This has the effect of inducing a tighter monetary policy, driving up interest rates to attract overseas funds and so fund the deficit. The capital inflow will then (hopefully) offset the bad current account figures. As long as the overseas funds remain in this country, this serves to prop up the value of the local currency (say Indian rupee) on international currency markets. Note that the slide in the value of the currency requires higher real interest rates than those in other countries with which local country trades. This is why balance of payments figures are given such prominence in the financial press. C. Macro-economic Policy Government monetary policy has a major impact through the sale or purchase of securities which is known as ‗open market operations‘. Fiscal policy is implemented through changing taxation and government spending, which have a flow-through effect on economic activity and interest rates. As a rule, every additional dollar spent causes a multiplier effect on total demand. As economic activity increases, this normally drives up interest rates as the transactions‘ demand for money increases. A close eye should therefore be kept on government macro-economic policy. D. International Economics Interest rates are influenced by a number of international factors. The level of world growth: High levels of activity in the major world economies will result in strong manufacturing demand for commodities. The resulting higher commodity prices can improve our balance of payments and therefore ease the pressure on interest rates. Off-shore interest rates: India has consistently run a balance of payments deficit, forcing it to borrow funds offshore. To win funds, India needs to offer interest rates that are attractive relative to those offered offshore. This means that generally if offshore interest rates rise then domestic interest rates also tend to increase to continue to attract offshore investors to India. E. Currency Movements The prices of Indian exports and imports are affected by the value of the Indian Rupee (INR) against the currencies of our trading partners and competitors. A strong INR results in our exports being more expensive purchases for our trading partners and so decreases their competitiveness, while it reduces the cost of importing the competitors‘ goods. This has a negative effect on India‘s balance of payments and puts upward pressure on interest rates. A weak INR produces the opposite effect. 4) Non-economic Factors Non-economic factors influencing interest rates include what is known in the industry as ‗market sentiment‘. An impending election, for example, will materially affect financial markets. Notice that this is not directly an economic factor, but nevertheless it does have financial repercussions. It must therefore be factored into an investor‘s perspective. Marketability and yield are two other very important influences that must be understood by a financial planner. 208

A. Marketability Marketability refers to the ease and cost of resale of issued securities. A security which can be sold on a market where all buyers and sellers congregate, (e.g. a stock market) is more marketable than one where no such market exists and a specific buyer must be found before a security can be sold. Due to the greater flexibility of tradable over non- tradable securities, investors are prepared to pay a premium price for them, providing a lower interest rate. The more marketable the security, the greater the premium. Of late, some financial institutions ‗securitised‘ debt to make claims more marketable. Securitisation repackages IOUs into more easily transferable paper, which has the effect of improving the return for an investor holding the same amount of debt. Marketability depends on many factors, including credit assessment, depth of the market, extent and size of the parcel:  Credit risk: Refers to the quality of the issuer. The Central Government is the lowest credit risk, followed by State governments and large established companies.  Depth of the market: This is the volume of securities on issue and the number of holders. Understandably, greater activity is likely in a security if there is for example ₹50 crore on issue and more than 1000 holders of the security, than if there is only ₹5 crore on issue and only one holder.  Extent of re-issues: If a borrower is issuing in the primary market on a frequent basis, and re-issuing the same securities later, the issue will be an attractive asset to hold because it is known among professional traders.  Size of parcel: Securities trading in the professional markets take place in discrete, large parcels. A smaller, odd parcel would be awkward to handle and so requires a greater sacrifice in price compared to a larger, standard size parcel. B. Maturity Maturity is the term for which a security is issued. Money market instruments have a maturity of less than a year and capital market instruments have a maturity of more than 1 year. The longer the term normally the greater the return as the longer the term the greater the risk assumed by the investor that the interest will move higher. Security prices are influenced by the outlook for interest rates (or what amounts to the same thing, the yield expected) for that class of security. The expected interest rates is a crucial factor in the valuation of fixed interest securities. The price of a discount security of any particular risk class will be determined by the prevailing interest rates. But interest rates vary. From the late 1980s through mid ‗90s in India, interest rates shot up from 10 per cent to 16-18 per cent p.a., catching many investors unaware. In recent years, interest rates fell to close to 5%. Anticipating interest rate movements is a prime concern for the financial planner. C. Yield to Maturity (YTM) The yield to maturity critically affects the demand for a fixed interest security. In evaluating returns of securities with varying maturities, professional traders refer to the ‗term structure‘ of interest rates, represented by a yield curve. Using this curve to 209

value a security is called yield curve analysis. The yield curve shows the return or holding period yield (interest plus capital growth returns) at any point in time for a particular security according to its maturity. A positive yield curve slopes upwards and is the norm. The general rule that applies is that the longer the maturity, the higher the yield. In general, investors demand a premium for tying funds up for a longer period of time. It is also possible for the curve to be flat or even negative, depending on expectations of underlying economic trends and interest rates. Many factors determine the slope and position of the yield curve. Foremost among these factors is the supply and demand for loanable funds at any given time. The supply of funds is determined by government monetary policy and by overseas capital inflows. The other side of the coin, the demand side, is determined to a very large extent by the total demand for funds from the corporate sector (to fund investment in capital projects), the household sector (for consumption purposes), and the government sector. While the corporate and household sectors‘ demand for funds is reasonably stable, the public sector‘s demand for funds can be unexpectedly volatile at times. This volatility impacts directly on the yields in the money markets, and therein lies the challenge for investors. An investor can always read yield curves by closely following the interest rates on offer by following the reports in the financial press. Suppose that today‘s rate, for example: 5 per cent at call; 6 per cent for three months; 6.5 per cent for six months; and 7 per cent for 12 months. Tomorrow, it might read 5.5 per cent at call; 6.5 per cent for three months; 7 per cent for six months; and 7.5 per cent for 12 months. In this case, interest rates have risen overnight. The yield curves on both days were upward sloping, but have shifted upwards overnight so that the same investment outlay yesterday would yield less than if the funds had been invested today. In the money markets, the price of yesterday‘s IOU would fall to reflect this, producing a capital loss to all investors who had purchased yesterday. Conversely, if the investor passed a bank that offered interest terms lower than yesterday, the price of all yesterday‘s securities would rise, producing a capital gain. Central government bonds form the benchmark for all yields in the fixed interest markets because of their minimal credit risk and high level of marketability. All other securities trade at a certain risk margin above this reference point. The difference between this and the benchmark yield is called the basis point differential, where one basis point is 1/100th of one per cent. Zero Coupon Yield Curve depicts the relationship between interest rate and maturity for a set of non-interest paying bonds as on a given date, Government securities do differ by coupon rates; however, because of its low risk characteristics and large amount of trading in the market, ZCYC is estimated and widely used for bond valuation in developed countries. Moreover, this can be taken as the benchmark yield for risk free securities and yields on other instruments may be estimated according to the level of credit risk. Given below is ZCYC as on October 24, 2002. You can see that the securities with the longer term to maturity demand a high interest than the instruments having shorter maturity. Investors will seek to earn a yield in line with other interest rates available in the market. Note that it is interest rates that dictate prices, not the other way around. Any 210

new issues must compete with yields then prevailing in the secondary market. Because of the overwhelming preponderance of securities available in the secondary market, any new borrower coming on the scene must accept the terms and conditions established by this market. The debt certificates might be hot off the press, but all new borrowers entering the primary market are price takers, not price makers. The relationship between price and yield is one of the most fundamental relationships in the fixed interest markets. Basically it is an inverse relationship, that is, as yield increases, the price falls, and vice versa. The gap between face value and market value gives rise to some odd expressions unique to the fixed interest market. New and existing securities may be traded:  at par, where the purchase price is equal to the face (or maturity) value of the security, meaning no capital gain or loss is incurred by the seller;  below par, or at a discount, where the purchase price is less than face value, meaning the yield exceeds the return from the coupon payment alone; or  above par, or at a premium, where the price is above the face value, meaning the yield is lower than the return obtained from the coupons alone. Valuing Money Market Securities How is the market price of a discount security determined? If we take a security issued at ₹100 000 to be redeemed at ₹105 000 when it matures in six months time, its annual yield or return, if held to maturity, would be approximately 10 per cent per annum, ₹5000 + ₹5000 = ₹10 000, which is 10 per cent of ₹100000. If the security is sold before it matures, its price should reflect the portion of return accrued to date. By pro-rating the time left to maturity, expressed as a portion of the annual interest rate, we can determine its exact value using the time value of money formula: PV = FV / (1 + i) Indeed, we may determine the market value or appropriate price for discount securities at any time before maturity as: PV = FV / [1 + (i x n/365)] Where: PV = price (or present) value (₹100 000 in our case) FV = face (or future) value (price to be paid at maturity, i.e. ₹105 000 in our example) n = number of days to maturity (in this example, six months or 182.5 days) i = yield p.a. (in this example, 10 per cent) Note that in the formula the interest rate is split up according to the proportion of a year left before the security matures. In Europe and Australia, a ‗year‘ is defined as 365 days, whereas in the USA the convention is that it has only 360 days, which simplifies the mathematics involved in valuing discount securities. Continuing with our example above, when the security was first issued, it had 182.5 days to maturity, and a face (or future) value of ₹105 000. The appropriate market price using a yield of 10 per cent per annum is consequently: 211

PV = ₹105 000 / [ 1+ (0.1 x 182.5/365) ] = ₹105 000 / 1.05 = ₹100 000 Which is as it should be, since the whole six-month term to maturity remains. Later, when the same security has only 90 days remaining before maturity, assuming the yield is still 10 per cent, the price would adjust to ₹102 473.26: PV = ₹105 000 / [1+ (0.1 x 90/365)] = ₹105 000 / 1.02465753 = ₹102 473.26 Any buyer would expect to receive the full ₹105 000 for the security when it is redeemed. For something to be in it for the buyer, the price must be less than this. Both the original buyer and any subsequent buyer receive a small reward for whatever length of time the security is in their possession. The original investor would have bought the security for ₹100 000 but can sell it for ₹102 473.26 in the secondary market three months later, or any time up to the maturity date. The price adjusts and comes closer to the face value as the time to maturity approaches. A very useful rearrangement of this valuation formula is to calculate the yield, if we already know the purchase price. Remember, the interest rate (i) is the yield: Therefore: PV = FV / [1 + (i x n/365)] 1 + ( i x n / 365 ) = FV / PV i = (FV / PV) – 1 x (365/n) If our security has only 90 days remaining before maturity, the appropriate selling price would be ₹102473.22. The yield can then be determined by using the above formula: I = ((FV / PV ) – 1) x (365/n) = ((₹105 000 / ₹102 473.22) – 1) x (365/90) = (1.0247 – 1) x (4.0555555) = .10 or 10% This 10 per cent yield can be compared to other investments to see which gives the best return. Question 4.4 A treasury bill has a face value of ₹100 000. It has 90 days to maturity, and sells in the market today for ₹97 242. What is the yield? Valuing Fixed Interest Securities Unlike the short-term money market, where the maturity date is less than one year, for longer-term securities, the time between receipts of interest income becomes a significant factor in valuing/pricing the security. For short-dated paper no explicit interest payments 212

are made, and effectively the interest payment is built into the price the investor pays up front for that security. However, for securities with maturity dates exceeding one year, explicit interest payments are made at stipulated times for a fixed amount. The amount and timing of these interest payments will materially affect the price at which the security will be traded on the open market. To be precise, four factors will determine the appropriate price for a fixed interest security:  The face (or maturity) value: This is the amount of the loan, printed on the face of the security itself, which must be paid on maturity.  The maturity date: This establishes when the principal repayment is due.  The coupon or interest payment: This is the interest rate, almost always expressed as an annual equivalent, fixed at the time of issue as a coupon which may be detachable if the loan is a non-inscribed (or bearer) security.  The yield: Yield is the return an investor will receive by holding a bond. Two types of yields must be distinguished. The current yield includes both the coupon and capital gain or loss if the security were sold immediately. The current yield will vary depending on interest rates prevailing when the security is sold. The yield to maturity (YTM) is the return an investor would receive if the security were held to maturity. That is, the YTM means the security not sold prematurely on the secondary market. Both yields are normally expressed as an annual percentage rate. Current is the ratio of the annual interest payment to the bond‘s current price. Current yield = Annual coupon payment x 100 Market price of the Bond Example: You purchased a bond with a par value of ₹100/- for ₹95/- and it paid a coupon rate of 5% then calculate the current yield. (0.05x100) x100  5.26% 95 It is important to note that if the market price of the bond is equal to its par value then: Current yeild = nominal yield Yield to Maturity YTM is then annual % rate of return that will be earned if the bond is purchased today at the current market price and is held by the investor till maturity. YTM is calculated as the rate of discount that makes the present value of a bond‘s cash flows equal to its current market price. n Int  RV (1  YTM)p (1  YTM)n i1 YTM = yield to maturity RV = Redemption value 213

n = Number of years Question: Suppose a bond is selling for ₹950/- and has a coupon rate of 7%, paid annually it matures in 4 years and the par value is ₹1000/-. What is the YTM? 950  70  70  70  70 (1  r)1 (1  r)2 (1  r)3 (1  r)4 = 8.53% (Using Casio FC 200V) Set: End n = 4 PV = –950 Pmt = 70 FV = 1000 P/Y = 1 C/Y = 1 Solve i = 8.53 Take care with your use of the terminology here. Once a security has been issued, the face value, coupon and maturity have been pre-determined. Price is affected by market judgement of the appropriate yield prevailing on the day a security is sold. It would constitute a case of fraud if the holder changed any figures in any way on the original certificate, so the only thing that can adapt to market realities is the price at which the security changes hands. By law, the original figures inscribed on the parchment must remain unaltered. This is often a source of confusion for the uninitiated, because there are really two prices for a fixed interest security: that which is written on the IOU (the face value), and the price at which this already priced IOU changes hands (the market value). The selling price of the security is then determined by the market, based on the yield sought by investors from similar securities on offer at that time. The pricing of a long-term fixed interest security is carried out using the same discounted cash flow techniques that are used to calculate the price of discount securities in the short- term money market. All future cash flows consisting of the coupon interest payments and maturity payment, are discounted back to the present, using the market yield as the discount rate. While the pricing formula can become complicated, especially for longer-term securities, dedicated calculators and pre-programmed computers now handle most of the number- crunching mechanics. As a financial planner, you should nevertheless understand the reasoning behind how prices are determined. Present value (PV) is equal to future value (FV) discounted at an appropriate rate (i). PV = FV / (1 + i) Note that this elementary formula assumes annual interest and the future value amount is after one year. Expressed in half-yearly terms, the formula can be adjusted easily enough: PV = FV / (1 + i/2) The FV is the future value in six months, and the interest rate is simply cut in half. If the 214

future value promised in six months is the ₹100 principal plus a ₹5 coupon payment (equivalent to 10 per cent annual interest and represented as g), then the PV will be: PV = (₹100 + g) / (1 + i/2) = (₹100 + Rs.5) / (1 + 0.05) = ₹100 Which is as it should be. If interest rates rise to 20 per cent before the loan matures, the amount received will still be the ₹100 principal plus the ₹5 coupon payment or ₹105 (since this was the amount contracted at the time the security was issued). The (full year) discount rate will be 20 per cent p.a. instead of 10 per cent p.a., or 10 per cent instead of 5 per cent expressed in half-year terms, so the security will be valued at: PV = ₹105 / (1 + 0.10) = ₹95.45 Notice that a rise in interest rates will cause a fall in the price of the security. Had interest rates fallen to say 8 per cent p.a., or 4 per cent half-yearly, the price would have risen to Rs.100.96: PV = ₹105 / (1 + 0.04) = ₹100.96 The Price of Bonds Moves in Opposite Direction of Interest Rates. You buy a bond when it is issued for ₹1000/- that pays 8% interest. Suppose you want to sell the bond but the interest rate rises to 10%. You will have to sell the bond at lower price than the price you paid because why someone will pay you ₹1000/- for a bond that pays 8% when they can buy similar bond at prevailing market rate of 10%. Relationship between Bond prices, YTM and time to maturity (Malkiel‘s properties of Bond Values) 1. Bond prices are inversely related to interest rates (or YTM). 2. Prices of long term bonds are more sensitive to interest rate changes than the price of short term bonds. 3. Prices of high coupon rate bonds are less sensitive to changes in interest rates then prices of low coupon rate bonds. 4. Increase in ATM results in a smaller price change than a decrease in YTM of same magnitude. Yield to Call A bond may have a call provision that entitles the issuer to call (buy back) the bond prior to the stated maturity date. The issuer would generally exercise the call option when interest rate decline. For such bonds which have callable option, it is practice to calculate ―Yield to Call‖. YTC is the value of ‗r‘ in the following equation: Price of the Bond =nC  (1 M i1 (1  r)n  r)n 215

C = coupon M = call price i=1 (1 + r) (1 + r)n n = number of years until call date YTC is the interest rate that investor would receive if they held the bond until the call date. Yield to Put It is same as YTC with the only difference that here the bond holder has the option to sell the bond back to the issuer at a fixed price on a specified dae. YTP (Yield to Put) is the interest rate that investor would get if he held the bond until its put date. Question 4.5 Perrira is considering an investment in a corporate bond with two years to maturity. Its current market price is ₹1000, which is its face value as the current yield to maturity on a bond with this risk level, and term to maturity is the same as its coupon rate, 5 per cent. (a) What impact would there be on the market price of Perry‘s bond if interest rates rose by 1 per cent to 6 per cent almost immediately after acquiring the bond? (b) In (a) what would be the impact on market value, if the maturity of the bond was three years instead of two? (c) What can you deduce from the movement in market price calculated in (a) and (b)? (d) Back to the original data, assume that the coupon rate is 15 per cent. What impact would there be on that two-year bond if the yield to maturity went up another 1 per cent to 6 per cent? (e) Again what can you deduce from the movement in market price in (a) and (d)? Conventions The normal practice in bond pricing is to initially assume the bond has a face value of ₹100 and then apply the appropriate multiplier to the denomination in question. For example, to value a ₹100 000 bond, the appropriate price will be calculated assuming we will have a ₹100 bond, and once this price is calculated, we will simply multiply the answer by 1000. This is why ₹100 bonds are often used in examples to illustrate valuation principles. The convention is that for domestic bonds with six months and 14 days or less to maturity, with the next interest payment to be received at maturity, the gross price is calculated through an adjustment of the exact number of days to the next interest payment. The number of days to the next interest payment is denoted f, and the number is expressed as a proportion of a 365-day year: Gross price = (₹100 + g) / [1 + (i × f/365 )] Where: I = annual yield to maturity g = half-yearly coupon payment per ₹100 face value 216

f= number of days to maturity If the number of days to the next interest payment were 182.5 days (i.e. exactly half a year), then we would be back to the previous simple half-year formula: Gross price = (₹100 + g) / [1 + (i × 182.5/365 )] = (₹100 + g) / [(1 + (i × 1/2)] = (₹100 + g) / (1 + i /2) It is easy to see how this formula can assist an investor in correctly pricing any fixed interest security given the number of days to maturity. If a six per cent ₹100 000 one-year fixed interest security has 40 days to go to maturity, and market yields are currently five per cent p.a., the price that should be quoted (assuming interest is paid annually) would be: Gross price = (₹100 + 6) / [1 + (0.05 × 40/365 )] = (₹106) / [1 + (0.05 × 0.1096 )] = ₹106 / [1.00548] = ₹105.42 per ₹100, or ₹105 422 This formula is very similar to the pricing equation we used to determine the price of a short-term discount security, but note the difference. In our discounted security examples, the maturity amount would have been a round number, ₹100 000, because there would have been no explicit interest payment. Note also the subtle but important difference regarding the timing as to when the interest payments are made. We simplified our mathematics in the previous example by assuming the payment occurred only once, and on the redemption date. Had the interest payments been made semi-annually, we would have had to split our calculations into two components: the ₹3 at the end of the first six months, and then another ₹3 at the end of the second six months. We would then have had to discount each of these back to the present at the prevailing market rate. Finally, we would then have had to do the same for the principal payment received at the end of the 12 months. As you can see, pricing fixed interest securities is more complicated than pricing discount securities! To illustrate this with a very simple example, consider a security with a face value of Rs.100, coupon of 12 per cent (payable annually) and maturity of two years. If the current yield is 12 per cent the market price is ₹100 (or multiples thereof): Value / market price = c / [1 + i] + (c +₹100) / (1 + i)2 = 12 / [1 + .12] + (12 +₹100) / (1 + .12)2 = ₹100 where: c = annual coupon interest i = yield to maturity or prevailing interest rate Now if the yield increases to 13 per cent, the market price would fall to ₹98.33: Value / market price = c / [1 + i] + (c +₹100) / (1 + i)2 = 12 / [1 + .13] + (12 +₹100) / (1 + .13)2 = ₹98.33 An idiosyncrasy is that prices are first calculated on a maturity value of ₹100 and rounded 217

to three decimal places. The price of a ₹100 bond at a given date and interest rate might be ₹95.64237, but this is rounded to ₹95.642. If the maturity value of the bond in question is Rs.1 million, the consideration received would be ₹956420. One convention is that Central Government and semi-government bonds pay coupon interest semi-annually, which is normally also the case for corporate securities. Incidentally, in all our examples, our assumption was that the coupon interest rate was to be paid annually (to simplify the mathematics). In practice, however, in this country, coupon interest is normally paid semi-annually (as in the United States, United Kingdom and New Zealand) and only rarely yearly, quarterly or monthly. This may be contrasted with the situation in Europe, where coupon interest is usually paid annually. Question 4.6 Nivedita Gupte, being a conservative investor and wanting to invest in fixed interest bearing securities, realises that because the yield curve is upwards sloping she can get a much better return investing for five years than she can if she invests for one year. She wants to take advantage of the higher return but is concerned about the risk of interest rates rising when she is locked in for five years. What can she do to reduce the interest rate risk and improve her return over that offered by one year bonds? Bond A Bond is a long term debt instrument or security. Bonds issued by the Govt. don‘t have any risk of default. We government will always honor obligations on its bonds. Bonds of public sector companies in India are generally secured but they are not free from the risk of default. The private sector companies also issue bonds, which are also called Debenture in India. Duration We have discussed that bond price are sensitive to changes in the interest rates, and they are inversely related to the interest rates. The intensity of the price sensitivity depends on a bond‘s maturity and the coupon rate of interest. The longer the maturity of a bond, the higher will be its sensitivity to the interest rate changes. Similarly, the price of a bond with low coupon rate will be more sensitive to the interest rate changes. ―Duration is a measure of the ―average maturity‖ of the stream of payments associated with a bond.‖ A bond‘s maturity and coupon rate provide a general idea of its price sensitivity to interest rate changes. However, the bond‘s price sensitivity can be more accurately estimated by its duration. A bond‘s duration is measured as the weighted average of time to each cash flow (interest payment or repayment of principal). Duration calculation gives importance to the timings of cash flows; the weight is determined as the present value of cash flows to the bond value. Hence two bonds with similar maturity but different coupon rate and cash flow patterns will have different durations. Let us consider two bonds with 5 years maturity. The 8.5% rate bond of ₹1000 face value has current market value of ₹954.74 and YTM of 10%, and the 11.5% rate bond of ₹1000 face value has a current market value of ₹1044.57 and YTM of 10.6%. 218

The duration of the bond is calculated as the weighted average of times to the proportion of the present value of cash flows. Duration of Bonds 8.5 Per Cent Bond Year Cash Flow Present Proportion Price Price * Value at of Bond Proportion Time 1 85 2 85 10% 0.062 of Bond 0.082 3 85 77.27 0.149 4 8558.06 70.25 0.082 0.203 5 1,085 63.86 0.074 3.572 673.70 943.14 0.068 4.086 (Duration) 0.246 0.714 1.000 11.5 Per Cent Bond Year Cash Flow Present Proportion Price Price * Value at of Bond Proportion Time 1 115 2 115 10.6% 0.101 of Bond 0 3 115 0.182 4 115 103.98 0.101 0.247 5 1,115 0.297 94.01 0.091 3.259 85.00 0.082 76.86 0.074 673.75 0.652 1,033.60 1.000 4.086 (Duration) Year Cash Flow Present Value at 10.6% Proportion of Bond Price Proportion of Bond Price * Time We can notice that the duration of 8.5% bond (the lower coupon bond) is higher than the duration of 11.5% bond (the higher coupon bond). The volatility or the interest rate sensitivity of a bond is given by its duration and YTM. A bond‘s volatility, referred to as its modified duration, is given as follows: Volatility of bond = Duration/ (1+YTM) The volatilities of the 8.5% and 11.5% bonds are as follows: Volatility of 8.5% bond = 4.252/(1.100) =3.87 219

Volatility of 11.5% bond = 4.086/ (1.106) = 3.69 The 8.5% bond has higher volatility. If YTM increases by 1%, this will result in 3.87% decrease in the price of the 8.5% bond and a 3.69% decrease in the price of the 11.5% bond. Properties of duration 1. For all bonds which pay periodic coupons, the duration is less than the term to maturity. This is because investor recovers a part of his investment every year. When due weight age is given to the recoveries made in the intermediate periods, the bonds duration will be shorter than the term to maturity. 2. A bond‘s duration will be equal to its term to maturity if and only if it is a zero coupon bond. When no intermediate recoveries are made by an investor, the duration will equal the term to maturity. 3. The duration of a perpetual bond is equal to (1+r)/r, where r=yield to maturity of the bond. 4. As the maturity of coupon-bearing bond lengthened, the duration also increases, albeit at a slower rate. 5. Longer the coupon-paying bond‘s term to maturity, the greater the difference between its term to maturity and duration. 6. Duration and YTM are inversely related. As increase in YTM would reduce the present values of all the cash flows, and the cash flows that are further away would be reduced the most. 7. Duration of a level annuity is : Duration  1  yield  No. of Payments yield  yield)No. of Payments1 (1 Credit Rating Credit rating is primarily intended to systematically measure credit risk arising from transactions between lender and borrower. Credit risk is the risk of a financial loss arising from the inability (known in credit parlance as default) of the borrower to meet the financial obligations towards its creditor. The ability of a borrower to meet its obligations fluctuates according to the behaviour of risk factors, both internal and external, that impact the performance of a business enterprise. Credit rating is a well established enterprise in most economies, including India, where specialized agencies have evolved to create extensive methods of analysis of information, and provide ratings to borrowers. The acceptance of these ratings by lenders crucially hinges on the independence of the rating agency, and the expertise it brings to bear on the process of credit rating. In India, it is mandatory for credit rating agencies to register themselves with SEBI and abide by the SEBI (Credit Rating) Regulations, 1999. There are 5 SEBI registered credit rating agencies in India, namely, CRISIL, ICRA, CARE etc, which provide a rating on various categories of debt instruments. Credit rating agencies assess the credit quality of debt issuers, on the basis of a number of 220

quantitative and qualitative factors, employing specialized analysts, who focus on industry categories in which they have specialized knowledge. Apart from information provided by the borrower, these analysts independently collect and assess information, about the industry and company variables, and performance of peer group companies, and collate such data. Most rating agencies follow a committee approach, where a rating committee examines the information on the company, and judges the rating that should be assigned to the instrument on offer. Rating essentially involves the translation of information variables into a ranking, which places the company in a slot that describes the ability and willingness of the company to service the instrument proposed to be issued. Rating Symbols The ranking of credit quality is usually done with the help of rating symbols, which broadly classify instruments into investment grade, and speculative grade. An illustrative rating list is provided below (representing CRISIL‘s rating symbols). CRISIL assigns ratings to only rupee denominated debt instruments. CRISIL‘s rating is assigned to the issue or instrument alone and not to the issuer. Instruments which have the same rating are of similar but not identical investment quality. This is because the number of rating categories is limited and hence cannot reflect small differences in the degree of risks. CRISIL‘s credit ratings fall under three categories: long term, short term and fixed deposit ratings. Long term ratings categories range from AAA to D; CRISIL may apply ‗+‘ or ‗-‘ signs as suffixes for ratings from ‗AA‘ to ‗C‘ to reflect comparative standings within the category. In the case of preference shares, the letters ―pf‖ are prefixed to the debenture rating symbols. The fixed deposit rating symbols commence with ―F‖ and the short-term instruments categories range from P1 to P5; CRISIL may apply ‗+‘ or ‗-‘ sign for ratting from P1 to P3. use the letter ―P‖ from the concept of ‗prime‘. High Investment Grades AAA – (Triple A) Highest Safety Debentures rated ‗AAA‘ are judged to offer highest safety of timely payment of interest and principal. Though the circumstances providing this degree of safety is likely to change, such changes as can be envisaged are most unlikely to affect adversely the fundamentally strong position of such issues. AA – (Double A) High Safety Debentures rated ‗AA‘ are judged to offer high safety of timely payment of interest and principal. They differ in safety from ‗AAA‘ issues only marginally. Investment Grades A – Adequate Safety Debentures rated ‗A‘ are judged to offer adequate safety of timely payment of interest and principal. However, changes in circumstances can adversely affect such issues more than those in the higher rated categories. BBB (Triple B) Moderate Safety Debentures rated ‗BBB‘ are judged to offer moderate safety of timely payment of interest and principal for the present; however, changing circumstances are more likely to lead to a 221

weakened capacity to pay interest and repay principal than for debentures in higher rated categories. Speculative Grades BB (Double B) Inadequate Safety Debentures rated ‗BB‘ are judged to carry inadequate safety and principal, while they are less susceptible to default than other speculative grade debentures in the immediate future; the uncertainties that the issuer faces could lead to inadequate capacity to make timely interest and principal payments. B - High Risk Debentures rated ‗B‘ are judged to have greater susceptibility to default; while currently interest and principal payments are met, adverse business of economic conditions would lead to lack of ability or willingness to pay, interest or principal. C – Substantial Risk Debentures rated ‗C‘ are judged to have factors present that make them vulnerable to default; timely payment of interest and principal is possible only if favourable circumstances continue. D – Default Debentures rated ‗D‘ are in default and in arrears of interest or principal payments or are expected to default on maturity. Such debentures are extremely speculative and return from these debentures may be realized only on reorganization or liquidation. Rating agencies may apply ‗+‘ (plus) or ‗?‘ (minus) signs for ratings from AA to C to reflect comparative standing within the categories. Bond Investment Management: Active and Passive Approaches Investors may follow different active or passive strategies which are built around different perceptions about bond values. Passive Bond Management Many investors believe that securities are fairly price that expected return are commensurate with level of risk. Such investors follows passive strategies and does‘nt actively try to outperform the market. Investors ―buy and hold‖ the bonds whose maturity period match with their investment period so as to reduce the price risk and reinvestment risk. He does‘nt actively churn his bond portfolio to improve returns or to reduce risk. The technique is called as ―immunization‖. Another method of passive strategy is ―Indexing Strategy‖. Such strategy calls for building a portfolio that replicates a well known bond index. Active Bond Management These strategies identifies mispricing of bonds in the market and helps in finding out the 222

over priced/under priced bond. As interest rates and bond values are inversely related, this relationship can be used in building up of bond portfolio. Horizontal analysis is one type of interest rate forecasting wherein bond yield is calculated over a particular time period. Immunization Immunization attempts at return of bond portfolio in such a way that the effects of two components (price risk and reinvestment risk) of risk can let out each other exactly. It refers to the investment strategy adopted by an investor to protect his investment from the interest rate risk exposure. This can be achieved by selecting the bonds whose duration is equal to the investment horizon. For example, if the investment horizon is 4 years, he should select bonds that have duration of 4 years. Whenever there is a change in interest rate, the loss or gain on capital value will be exactly offset by the gain or loss on reinvestment risk. 3.4.8. Performance Analysis of Stocks - Dividend Yield, Earning per Share (EPS) Dividend yield is a financial ratio that shows how much a company pays out in dividends each year relative to its share price. Dividend yield is calculated as Annual Dividends per share divided by price per share. In the absence of any capital gains, the dividend yield is the return on investment for a stock. Lower the dividend yield, greater the growth potential & Vice Versa. Earnings per share (EPS) is the monetary value of earnings per outstanding share of common stock for a company. () 3.4.9. Market Valuation Ratios – Price to Earnings Ratio (P/E), Price to Book Value (P/B) Evaluating Share Investment We look now at some areas covering the evaluation of shares. You can make more informed decisions on which shares to buy or sell by consulting the financial press. In this section, we look at a typical newspaper report. The discussion also enables us to revisit the most common ratios used to measure various aspects of dividend earnings. Newspapers and financial magazines regularly report the trading and financial details of the shares listed on the stock exchange. It is also possible to download the stock quotes from the websites of some investment magazines as well. In addition to these details, newspapers 223

give details such as P/E, 52-week high/low, dividend yield etc., The 52-week high and low show the highest and lowest price at which the particular share traded during the year. Similarly, the Day’s high and low show the highest and lowest price at which the share traded during the day. The price earnings (P/E) ratio is calculated by dividing the market price of an ordinary share by the earnings per share. Price Earnings Ratio = Market Price Earnings per share This ratio is most often used as a relative measure, with investment decisions being made according to the level of a company‘s P/E ratio relative to that of other companies in the same sector or market. Price earnings ratios are also useful determinants of overall value when considered alongside historical evidence for the same stock, sector or market. If the price earnings ratio of a company is above its historical average, the price may be considered too high unless a substantial increase in earnings is likely in subsequent years and the market has already adjusted for that expectation. It is a valuation ratio of a company's current share price and its per share earnings. It is also known as \"price multiple\" or \"earnings multiple\". EPS may be calculated based on: Historic data (generally from the last four quarters) i.e. Trailing P/E or Expected data (generally estimates of earnings expected in the next four quarters) i.e. Projected or Forward P/E. Higher the P/E, greater the growth potential & Vice Versa. 3.4.10. Market P/E Ratios - Undervalued or Overvalued Markets The price-earnings, or P-E, multiple is one of the most common indicators we use to judge the worth of a company‘s shares. Most commonly, people watch stock market indices such as the Sensex or Nifty to understand whether the market is rising or falling. But, stock indices do not tell the full story. That is why investors also keep a watch on the P-E multiples to understand whether the rise or fall is justified by the earning prospects of the company. The P-E multiple tells us how many times the earnings per share we are paying for purchasing the shares at the present market price. So, for calculating P-E multiples, we need to know two things—the present market price of the shares and the earnings per share, or EPS. Getting the present market price quoted at the stock exchanges is easy, but calculating EPS requires some exercise. For calculating EPS, you first need to know the net earnings of the company. Analysts generally take the net earnings from the most recent four quarters, or 12 months, to calculate what is known as trailing EPS. However, some analysts use the projected earnings to calculate what is known as forward 224

EPS. Trailing and forward P-E multiples can be calculated by using trailing and forward EPS, respectively. For the sake of simplicity, here we are referring to past earnings only. Once you have the net earnings figure, you need to subtract the dividend that is payable to preference shareholders and divide the result with the number of outstanding equity shares to get EPS. For instance, if the net earnings of a company after paying preference dividend is ₹1 lakh, and the total number of equity shares is 10,000, then EPS would be 10. Companies report the EPS figure in their income statements. Once you know EPS, you can calculate the P-E multiples. You need to just divide the present market price of the shares with EPS. If the present market price is ₹200 and EPS is 10, then the P-E multiple would be 20. That‘s it. But, what does it tell you? If you look at the P-E multiples like an investor, you will understand that for purchasing a share that is earning ₹10 every year, you‘re paying a price that is 20 times its earning. So, the higher the gap between the price and the earnings, the higher the P/E multiple. That‘s why people call stocks that have higher P-E multiples overvalued, and those with lower P-E multiples, undervalued. But big question is what level of P-E multiple is a stock neither overvalued nor undervalued? Now, that‘s a tricky issue. Some shares with higher P-E multiples may still be undervalued and some at even low levels may be overvalued. It all depends upon the company you are looking at. The companies with higher P/E multiples may be considered undervalued of the growth in the company is higher than the P/E multiples. As a thumb rule, you need to compare the P-E multiple of the company with that of peer group companies in the same sector or industry. But, this may also not give you the true picture if the sector, as a whole, has been overpriced by the market. In case the present looks surreal, you can look at the historic figures of the P-E multiples of the same company to see whether the present is in sync with the past. If you are still not sure about the true level, then learning a little bit of stock market Greek may help you understand the market talk of experts about true levels. Summary: The P-E multiple is one of the indicators of valuation of shares being traded in stock markets. The P-E multiple is calculated by dividing the market price of the share by the value of the earnings per share. In general, higher P-E multiples may indicate overvaluation and lower P-E multiples, undervaluation. Earnings per share (EPS) are the after-tax profit earned on behalf of the ordinary shareholders by the company, divided by the number of ordinary shares on issue at the time. Preference share dividends will be left out of the profit calculation, as are extraordinary or non- recurring items in most cases (although it is often instructive to consider the effects of the latter on share prices). The profit thus calculated is divided by the number of ordinary shares on issue by the company. The equation is: Earnings Per Share = After tax profit  Preference Dividends Number of Equity shares In cases where there has been a bonus or rights issue during the period under consideration, 225

the number of equity shares most commonly used is the average number of shares for that period. 1. Calculation of Future P/E: The price to earnings ratio is one of the most widely followed statistics by the investors. There are two versions of the P/E ratio. A trailing P/E is the current market price divided by the company‘s reported earnings per share gathered from the recent annual results. However, the investors are more interested in future, concerned about what will happen in next 1 or 2 years than what had happened in the past period. They prefer to compute P/E based on expected earnings rather than on actual, realized earnings. This P/E based on expected earnings are sometimes referred to as Future P/E. This is indicated by analysts as ―ABC share sells at 20 times future or estimated earnings‖. Investors have to devise an approach to make estimation about the future earnings of a company. There are two widely used approaches under fundamental analysis. They are 1) Top- down approach and B) Bottom up approach. In the former, the analyst tries to figure out the prospects of the economy and the industry for a period in future and makes estimation about the turnover that a company is likely to achieve, considering its strengths and weaknesses. This is followed by the estimation of gross and net profit, based on the profit margins experienced by the company. In the latter approach, the analyst tries to estimate the bottom line (net profit) that the company likely to achieve in the future period and then finds out the sales figures. Any standard book on fundamental analysis of investments will give a detailed description of these approaches and the estimation of future earnings. 2. Evaluation of the Shares of a Turnaround Company: A turnaround share is one which is either cutting down its losses or have started making token profits. Though the company undergoes a bad batch, its future prospects are expected to be bright. The turnaround may be on account of restructuring of business operations, takeover of an ailing company by a successful entrepreneur, surge in demand for the company‘s products etc., These shares, when identified and purchased at lower prices turn out to be the big gainers when the company starts making profits and pays dividend after wiping out the accumulated losses, if any. An example of a turnaround stock in recent times is Steel Authority of India Ltd (SAIL). With the economic recovery and the surge in demand, the steel industry‘s fortunes have looked up and the share prices have gone up many fold. Due to inadequate profits and/ or accumulated losses, these companies do not pay any dividend. Thus, Dividend discount model cannot be applied to value the share. Some analysts use cash flow per share (net profit/ loss plus non-cash expenses like depreciation) in lieu of dividend per share to value the turnaround stocks. 3. Evaluation of the Shares of a Highly Growth Oriented Company: Shares of companies whose assets, sales and profits grow rapidly come under this category. The growth may be due to profitable expansion, diversification, modernization or mergers and acquisitions. These companies generally have the following characteristics: Good market share, competitive advantages, strong financial position, research and development activities and good management. Sound financials coupled with strong management makes the stock price shoot up in the market and the liquidity of the high growth stock is generally high. Institutional holding in the company is also substantial. The valuation model based on dividends cannot be applied for evaluating 226

the shares of a highly growth oriented company. That is, if the expected growth rate in dividend is higher than the discount rate, the mathematical model simply fails. Regression model, which establishes the relationship of some key fundamental factors with return or price, may be useful in finding the value. Besides, the investor has to analyses the risk and return characteristics of the firm, outlook for the industry and management abilities for evaluating the shares of a highly growth oriented firm‘s shares. 4. Evaluation of the Shares of a Dying Company: It is not uncommon to find that blue chips of yesteryears have become sick companies today. The investors should periodically evaluate the shares in terms of returns and if they are not getting returns which are not equal to the risk free rate or opportunity cost, the share is due for disinvestment. The characteristics of these dying companies include consistent decline in growth rates of sales and profits, reduction in dividend rates, unrelated diversification, fierce competition and bleak industry prospects. If the company pays dividend, by applying dividend discount model, one can find out whether the shares are overpriced and disinvest the shares in the market. (Of course, the estimates needed for the model are to be carefully estimated). But the investors should watch out for indicators like declining institutional investment, low liquidity and deterioration in fundamental factors and take a decision to sell the share by keeping the sentiments away. 5. Private Placement of Shares: When the shares are offered to select few individuals or institutions rather than to the public in general, the issue is said to be privately placed. 3.4.11. Security Valuation- Dividend Discount Model (DDM) Valuation of a Share How is the value of a share determined? Valuation of shares is not as straight forward as the valuation of interest-bearing securities for three reasons: First, we do not know the size of the expected dividends as these are set yearly by the management of the company and that depends on many factors, such as the profitability of the company and the company‘s capital requirements. Secondly, shares have no maturity date. Thirdly, there is no easy way to observe the rate that is required by the market, as each share has risk characteristics unique to itself so rates required will differ. So what determines the value of a share? Note that the purpose of the following consideration of valuation is not to arrive at a figure, for example, a market price. The purpose is to gain an understanding of what determines the value of a share so that an investor can concentrate on the relevant determinants of value and find out the intrinsic worth of a share. Consider These Alternatives The most obvious value of a share is the current market price of the share. However, other values may be based on the book value of the assets the company owns less its liabilities, that is, net tangible assets and perhaps also intangible assets such as goodwill. Asset valuations based on past rather than future data may be poor indicators of future performance of shares. Other valuations may be based on what would be received if the companies were liquidated and its debts paid. Alternatively, you could consider the value 227

(based on share prices or other measures) of similar companies in the same industry. This means substituting the value of one company (usually a listed company) is often used to estimate the value of an unlisted company that is seeking to raise capital on the stock exchange. Present value is the valuation method of valuing of a share with which we are most concerned. The best understanding of the value of a share is found by estimating the present value of the expected cash flows from that share. The expected cash flows are expected dividends. Investors should realise that the value of a share relies on the dividends that can be expected to be received from owning that share. Only the future pays, never the past. Cash today is worth more than cash tomorrow. As well, to take on more risk, investors need higher returns and this will be reflected in the discount rate. Market price should approximate present value in an efficient market. If it does not, an opportunity is available to take an arbitrage profit on the purchase and sale of that share. The best explanation of arbitrage profit is a profit made from inefficiencies in the market. If the market price of Rs. 100 share is far below the present value of Rs. 150/- it is worth buying. The present value method of determining a share‘s value is the best of all the previously mentioned methods. The approach provides a sound basis for understanding what factors influence the price of a share. Cash is king. For an investor who invests his/her cash in the expectation of future cash flows, it is the present value of those expected cash flows that determine where and how much should be invested. There are, however, practical problems in its implementation because it is difficult to predict growth rates of dividends. Dividend Discount Model Estimating present value of a share As has been said, the value of a share to its owner is the cash flow that it generates. This normally takes the form of cash dividends. Being received over time, these cash dividends can be evaluated using discounted cash flow (DCF) procedures. The stream of cash dividends into perpetuity will have a present value, which is found by discounting the dividends at an appropriate discount rate. This process can be represented in the following equation: Equation 2.1 P0  D1  D2  D3  ....... 1i (1  i)2 (1  i)3 Where P0 is the present value of the share D1, D2, D3 ... are the share‘s expected future dividends i is the discount rate, assumed constant in each future period, derived from a number of factors such as interest rates and inflation. It can be taken to represent the return on investment required by investors. This valuation process may seem relevant only when shares are acquired with the intention 228

of holding them forever since no amount of capital gain or loss is included in the cash flows. However, Equation 2.1 is still valid even where a share is purchased with the intention of selling it for a capital gain in the near future. For example, suppose a share is being evaluated as an investment for just one year. The cash flow from owning the share over this period will take the form of a cash dividend (assumed for convenience to be received at the end of the year) and the resale price of the share at the end of the year. Thus the present value of the share will be given by Equation 2.2. Equation 2.2 P0  D1  P1 i 1i 1 Where: P1 is the expected price of the share at the end of the first year. This would equal the present value of all expected dividends to be received from the end of year 2 onwards. Estimating Future Dividends In order to simplify the estimate of future dividends, the basic valuation formula has been adapted to assume a constant growth factor, (g). By assuming a constant growth factor, we can calculate future dividends in the following way: D1 = D0 (1 + g) D2 = D1 (1 + g) = Do (1 + g) D3 = D2 (1 + g) = Do (1 + g and so on. Hence Equation 2.1 can become: Equation 2.3 P0  D(1  g)  D0 (1  g)2  D0(1  g)3  ...... 1i (1  i)2 (1  i)3 Using the formula for the sum of geometric progression, Equation 2.3 can be reduced to a simplified equation: P0  D0(1  g) ig  D1 ig Example 1 Suppose ABC Ltd shares currently pay a dividend of ₹1.25. Let us assume a discount rate (i) of 15 per cent and a growth factor (g) of 11 per cent. Applying the growth factor of 11 per cent to the current dividend of ₹1.25 gives an expected dividend for the coming year of ₹1.3875. Then the appropriate price of a ABC Ltd share using this model and assumptions would be: 229

P0  1.3785  34.46 0.15  0.11 Unfortunately, however, the derived price is very sensitive to the estimates for the discount rate and growth rate. For example, if we estimate the growth rate at 8 percent instead of 11 percent, the share price would be: Hence, although the constant growth dividend model is useful in identifying the factors that influence the price of a share, it is very rarely used in the marketplace, most likely because of the difficulty of accurately estimating the growth rate and also the assumption of constant growth in perpetuity. If a company‘s dividend is not expected to grow at a constant rate, this makes the calculation of the price of the share much more difficult. To determine the value of a share it would be necessary to calculate an infinite number of present values for an infinite number of different dividends and sum them. This is sometimes made easier if we assume different dividends for the next ten years than a market price based on some conservative estimate of what the price would be if growth of the dividends became constant. The difficulties of the process of estimating present value of shares should not prevent an investor realising that the determination of the value of a share is based on expected dividends and the cash flow to be received from those expected dividends, and that evidence of a sound regular growth in dividends is one of the best indicators of a share‘s worth as an investment. Example 2 The equity stock of Carvy Limited is currently selling for Rs. 30 per share. The dividend expected next year is Rs. 2.00. The investors’ required rate of return on this stock is 15 per cent. If the constant growth model applies to Carvy Limited, what is the expected growth rate? Sol. According to the constant growth model, P0 = D1/(r-g) This means, g = r — D1 / P0 Hence, the expected growth rate (g) for Carvy Limied is: g = 0.15 – 2/30 = 0.83 or 8.3% 230

Example 3 XYZ company paid dividend 2, recently of common stock; dividend expected to grow by 20% for next 3 years, after which expect to stabilize at 10% growth. If required rate of return is 15%. How much maximum price would you pay today to buy stock? D0 D1 (Next D2 (2nd year) D3 (3rd year) D4 (4th Year onwards) (current) year) 2 paid 2*(1.20) 2*(1.20)^(2) 2*(1.20)^(3) 2*(1.20)^(3)*(1.10) (1.15) (1.15)^(2) (1.15)^(3) (0.15 – 0.10) = 2.08696(A) =2.1776937(B) =2.272376099(C) = 76.032, this dividend value represent as on beginning of 4th year which is nothing but end of 3rd year too. This dividend will be further discounted by 3 year to bring towards current value i.e.do 76.032/ (1.15) ^ (3) = 49.99227418 (D) Value of stock as on today’s date (Do) = 2.08696+2.1776937+2.272376099+49.99227418 = Rs. 56.5293 3.4.12. Analysis of Growth, Dividend Payout and Reinvestment Options (MF Schemes) Most Mutual Fund Scheme offers 3 options:- Parameter Dividend payout option Dividend Growth option Re-investment option NO Dividend YES received in 231 NO Bank Account

DDT YES (for non-equity YES (for non-equity NA Applicable schemes) schemes) NO Increase in NO YES Units NAV captures the portfolio Change in NAV declines to the extent NAV declines to the extent entirely NAV of dividend and DDT of dividend and DDT Important Points  The reduced NAV, after a dividend payout is called ex‐ Dividend NAV.  After a dividend is announced, and until it is paid out, it is referred to as cum‐ Dividend NAV.  In a dividend re‐investment option new units are issued on the basis of ex‐ Dividend NAV.  Automatic Reinvestment Plans (ARP): Reinvestment of amount of dividend made by fund in the same fund and receives additional units. It gives Benefit of Power of Compounding. 3.4.13. Measurement and Evaluation of Portfolio Performance Performance Measurement and Evaluation Investors are always interested in evaluating the performance of their portfolios. Investor will take efforts to find out whether he got reasonable returns on his investments in the funds selected, or whether he needs to switch to another fund. Similarly, the financial planner or advisor is expected to give proper advice on the funds and about their performance. The performance of a portfolio or fund manager is generally evaluated on two counts: a) The ability to record above – average returns and b) The ability to eliminate unsystematic risks through diversification. Some portfolio techniques consider only one of the requirements and some evaluation measures are composite considering both the return and risk. This section deals with how to measure and evaluate the performance of the different funds that are available to the investor. As there are many measures of fund performance, you must find the most suitable measure, depending on the type of fund you are looking at, the stated investment objective of the fund and more importantly based on the current financial market conditions. Return Measurement Following are the commonly used measures of return by fund managers and investors. Change in NAV If an investor wants to compute the return on his mutual fund investment between two dates, he can simply find out the percentage change of the Per Unit Net Asset Value during the period. The formula used for this purpose is (NAV at the end of the period / NAV at the beginning) -1*100 232

If period covered is not equal to one year, it would be better to annualise the returns by using the following formula: [change in NAV / months covered]* 12 Example: A fund‘s NAV was ₹10 at the beginning of the year and ₹11 at the end of the year, percentage change was + 10% (11-10 /10* 100). Now, let us assume that an investor purchases a unit in an open-end fund at ₹10, and its NAV after 10 months is ₹11, the annualised NAV Change is: 12%: (0.1/10}* 12)* 100. Change in NAV is the most commonly used performance measure by investors, and so is also most commonly published by the mutual fund managers. Whether the return in terms of NAV Growth is sufficient or not should be interpreted in light of the investment objective of the fund, current market conditions and alternative investment returns. Thus, a long-term growth fund or infrastructure fund will give low returns in the initial years. Equity funds may give lower returns when the markets are in a bearish phase. Debt funds may give lower returns when interest rates are rising. However, this measure does not consider the dividend distributed in the interim period. Therefore, it is suitable for evaluating growth funds and accumulation plans of debt and equity funds, but should be avoided for income funds and funds with withdrawal plans. Total Return This measure takes in to account of the dividends distributed by the fund between the two NAV dates, and adding them to the NAV change to arrive at the total return. The formula for computing total return is: [(Distributions + Change in NAV) / NAV at the beginning of the period] * 100 Example: Suppose that your client purchased an open-end equity fund unit at ₹20. The fund had an interim dividend distribution of ₹2 per unit. The NAV of the fund at year-end was ₹22. Thus, Total Return at the end of the year would be calculated as 20% [{2 + [22- 20]}/20*100. This measure is suitable for comparing the performance of different types of funds but the financial planner should be careful in interpreting the results which should be on the basis of market conditions and investment objective of the fund. A slight modification in the above formula to consider reinvestment of dividends in the fund itself at the NAV on the date of distribution (ex-dividend date) is possible. This modification would help in finding out the growth of an investor‘s mutual fund holdings and the return on Investment on a cumulative basis over a certain time period. Formula for computing Total Return with Reinvestment is: [{(Units Held + dividend/ex-dividend NAV)*end NAV} - beginning NAV]/beginning NAV* 100 Example: Let us assume that an investor purchased 1 unit of an open-end equity fund at ₹20. The fund had distributed interim dividend of ₹2 per unit, which is reinvested when the NAV was ₹21. increasing his holdings by 0.09 unit (2/21) in the fund, making his total holding 1.09 (original 1 unit + 0.09 through reinvestment). Now suppose that the NAV of the fund at year-end was ₹22. The value of the investor‘s holding at year end is ₹23.98 233

(22*1.09), giving the investor a Total Return with reinvestment of distributions of 19.9% ([23.98 -20]/20). Note that this is lower than the simple Total Return of 20% computed in the previous section. This measure is appropriate for measuring performance of accumulation plans, monthly/quarterly income schemes and debt funds that distribute interim dividends. Returns Since Inception In India, SEBI requires returns to be computed since the inception of a scheme using Rs.10 as the base amount. This method is correct as long as it is applied to no-load funds. Otherwise an adjustment for the loads paid has to be made as follows: As the investment amount will be lower because of an entry load charged by the fund, investor‘s return on amount invested has to be reduced by the initial load paid. This can be done by reducing the % cumulative NAV growth figure by the entry load paid. Suppose an investor gives ₹100 to a fund which invests ₹97, which grows to ₹194 in ten year time period. However ₹194 represents only 94% increase and not 100%. The average annualised rate of return will be 194 = 100*(1+R/100)10 = 6.85% While using the above measures care should be taken to compare only those funds for which performance data are available during the same period of time. Other Evaluation Measures Expense Ratio: The expense ratio is an indicator of the fund‘s efficiency and cost effectiveness. It is defined as the ratio of total expenses to average net assets of the fund. Offer Document discloses the past and estimated expense figures and ratios and the financial planner may compare these figures with that of the numbers given in the annual report of any fund to get an idea on the functioning. SEBI regulates this aspect for funds in India, Expense ratio must be evaluated in the light of fund size, average account size and portfolio composition- equity or fixed income. For example, funds with small corpus size will have a higher expense ratio affecting investor returns than a large corpus fund, It is important to note that brokerage commissions on the fund‘s transactions are not included in the fund expenses figure while computing this ratio. Income Ratio Income ratio is defined as fund‘s net investment income divided by its net assets for the period. This ratio is a useful measure for evaluating income-oriented funds, particularly debt funds. It should be used to supplement the analysis based on the expense ratio and total return. Portfolio Turnover Rate: Portfolio turnover rate measures the amount of buying and selling done by a fund. It measures how many times the fund manager turns over his portfolio by buying or selling in the market. A 100 percent turnover implies that the manager shuffled his entire portfolio during the period in question. High turnover ratio also indicates high transaction costs. 234

Turnover ratios would be most relevant to analyse the performance of funds which follow the active portfolio style of management. Cash Holdings: Mutual funds allocate their assets among equity shares, debt securities and cash/bank deposits. The percentage of a fund‘s portfolio held in cash equivalents is an important element in its successful performance. Large cash holding allows the fund to buy the required securities without liquidating its other portfolios and also allows the fund a cushion against large, consistent net redemptions, but maintaining large cash reserves would lower the return on the portfolio. Borrowing By Mutual Funds: In India, mutual funds are not allowed to borrow to increase their corpus. SEBI Regulations allow mutual funds to borrow only for the purpose of meeting temporary liquidity needs for a period not exceeding six months, and to the extent of 20% of its net assets. Hence, it would be uncommon to see fund schemes with borrowings on their balance sheets, and if borrowings are seen, caution may need to be exercised in evaluating the fund performance. We have seen so far the various measures, some are based on the rates of return and few other measures based on risk adjusted rates of return. An investor / advisor needs to look at the absolute measures of performance, and more importantly he needs to select the right benchmark to evaluate a fund‘s performance, so that he can compare the measured performance figures against the selected benchmark. For example, an investor‘s expectations of returns from an equity fund should be judged against how the overall stock market performed, in other words by how much the stock market index itself moved up or down, and whether the fund gave a return that was better or worse than the index movement. Based on the investment objective and the class of assets in which investments are made, investors have to choose a benchmark. 235

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SECTION–IV INVESTMENT STRATEGIES and PORTFOLIO MANAGEMENT SUB-SECTIONS 4.1 Active Investment Strategies 4.2 Passive Investment Strategies 4.3 Investment Portfolio Management 4.4 Revision of Portfolio Testing Objective Theoretical testing knowledge: ―Grade 1‟ Theoretical (predominantly) testing clarity of concepts or Numerical testing Total weight to Exam 3 basic skills: ―Grade 2‟ Numerical testing basic skill sets: ―Grade 3‟ Nature of Test Items Numerical testing analytical skills & synthesis: ‖Grade 4” 17.33% 4 items: 1 mark each 2 items: 2 marks each 2 items: 3 marks each 3 items: 4 marks each 237

Sub-section 4.1 Active Investment Strategies Learning Outcome The objectives of the topic 4.1 – Active Investment Strategies are as follows: 1. To educate the financial planner that one could implement active investment strategy by managing the portfolio in a dynamic manner across different asset classes via appropriate asset allocation. 2. To understand the impact of churning client‘s portfolio and booking profits/ losses through frequent churning. 3. To map the opportunities of investing in undervalued sectors and stocks to make significant gains. 4. To understand the difference between Speculation, Hedging & Arbitrage and the relevant strategies for traders & investors. 5. To understand the financial products – Futures & Options and their relevant features, pricing & payoffs. 6. To apprehend the concept of market timing and its effects on investment portfolio 7. To understand the process of selection of securities for investment. 8. To differentiate between the two popular style of investing vis-à-vis Value & Growth. 238

4.1.1. Dynamic Management of Asset Allocation Across Classes Characteristics of the major asset classes In our country the major investment asset classes, together with the major instruments traded therein, are as follows:  equities (shares listed on the exchanges—industrial and finance company shares);  bonds (including Government and PSU Bonds, corporate bonds.);  cash (short-term money market instruments especially commercial paper and Treasury bills); and  International investments 1. The Equity Class Shares offer the opportunity for highest long-term average compound return of any asset class, while attended by the highest short-term risk. Managers are keenly aware of these two attributes. Some of the risk may be eliminated by diversifying the share portfolio. This introduces a separate risk of including in the portfolio non-performing shares which reduce long-term performance. General Characteristics of Shares Ordinary capital represents a share in ownership of the firm. There are two implications here for the fund manager:  Shares reflect ownership in real assets. To some extent the relative immunity of real assets (property) to erosion by inflation carries over to shares. Equities are unique in that they offer clearly defined universe of securities, (i.e. those traded on the particular exchange). The number of different shares is limited (about 10000 on the Indian bourses), and all have the same maturity date (‗infinity‘). Also, there are different types of shares (in terms of sectors within the market). The continuous visibility of prices means that any investor, large or small, effectively has the benefit of all the research of the largest institutional research departments. The prices viewed on screens or appearing in the financial press may not with hindsight be very good estimates of where prices should be. Nevertheless, at any point in time they are the best estimates that money can buy. Liquidity Fund managers prefer their investments to be highly liquid so that they can rearrange their portfolios quickly and economically. Compared with investments such as property, securitised equities are usually highly liquid and divisible. It is generally easy to sell part or all of one‘s equity holdings for a standard brokerage fee. However, this (liquidity) advantage is not great when compared with that of fixed interest securities and may be absent altogether when compared with illiquid second line (non-blue chip) shares. Risk The risk inherent in holding shares derives from two sources: the pattern of cash flows and insolvency. The first is the uncertainty of dividend cash flows and capital gains, 239

which gives rise to the concern that investors may be forced in times of economic stringency to sell their shares at a time when share prices are depressed. The second source of risk is insolvency risk. Accounting standards are not sufficiently stringent to ensure that information disclosed by companies will clearly indicate their solvency status. The fact remains that many corporate failures are not signaled to the market, with the consequence that shareholders lose nearly the entire value of their holding in such companies. Yield The medium to long-term yield on a diversified portfolio of stocks, as measured for instance by taking a stock index, historically outperforms analogous indices in other asset classes. Various studies across a wide range of markets have revealed that the number of stocks in a portfolio required to provide adequate diversification is surprisingly small. Usually between 10 and 20 stocks afford sufficient diversification to reduce ‗non-systematic risk‘ to an insignificant level. This is another very good reason why fund managers may include shares in their portfolio. Taxation Sometimes, gains on investments by mutual funds offer tax advantages. (for details, see section on Taxation included in this Topic). Availability of Risk Management Instruments There are two classes of ongoing risk to which any equities portfolio is subject. They are non-systematic and systematic risk. Stock diversification is used to eliminate stock- specific risks or non-systematic risk. Derivatives, including options and futures on individual stocks, are also effective. Share Price Index futures and options can be used to help manage systematic risk, (i.e. risk deriving from shifts in overall market level). Preferred Economic Conditions The economic conditions which are conducive to high returns in the share market are high growth periods (i.e. ‗booms‘), in the business cycle. High inflation can destroy bond market returns, but it does not usually have a devastating effect on share market returns. Fund managers anticipating out-performance of shares as a class during ‗booms‘ can be expected to weight their equity holdings quite heavily in this class approaching and during peaks in the business cycle. 2. The Fixed Interest Class The fixed interest class consists of the capital market (‗bonds‘, securities with terms of maturity greater than one year), and the short-term money market (‗cash‘, cash equivalent securities of term no to greater than one year). Investors and fund managers usually consider the two as separate asset classes. For instance, different trading and dealing conventions apply in the two markets. General Characteristics of Bonds Bonds held to maturity usually provide superior investment returns to short-term money market (STMM) returns. For fund managers offering pension schemes, bonds represent a low-risk avenue of 240