Investment planning

SECTION II: ANSWERS TO SELF ASSESSMENT QUESTIONS 1. (D) 2. (C) Risk Profilers 3. (C) Zero coupon bonds 4. (C) ₹8,601 & ₹4,631 Funds to be accumulated after 10 years 2,500,000 Returns expected from equity funds 12.00% p.a Returns expected from debt funds 9.00% p.a Returns expected from liquid funds 5.00% p.a Amount required to be accumulated upto 9 years 2,380,952 (₹2500000/(1+5%)) Suppose, monthly investment made is: ₹100.00. Amount invested in equity funds for 9 years 65.00 ₹100*65% Amount invested in debt funds for 9 years 35.00 ₹100*35% Accumulation in equity funds after 9 years 12,261 (Set: Begin; n=9*12; i=12; PMT =65;P/y- =12,C/y=1; FV (solve) = 12261 Accumulation in debt funds after 9 years 5,732 (Set: Begin; n=9*12; i=9%; PMT =35; P/y- =12,C/y=1; FV (solve) = 5,732 Total funds accumulated in equity and debt funds 17,993 (12261+5732) Required cumulative investment per month 13,233 ₹(2380952/17993)*(100) Investments in equity per month 8,601 (13233*0.65) Investments in debt per month 4,631 (13233*0.35) 5. (A) Aggressive Portfolio 6. (B) Tactical Asset Allocation 7. (B) Moderate 8. (A) Primarily growth with some income-oriented assets 9. (D) Short-term fixed deposit, to ensure liquidity and some returns 10. (D) Unsystematic risk 141

142

SECTION–III GOAL-BASED INVESTMENT PLANNING, MEASURING and MANAGING RISK, ANALYSIS OF RETURNS SUB-SECTIONS 3.1 Investment Planning to Achieve Financial Goals 3.2 Measuring Risk 3.3 Diversification Strategies 3.4 Analysis of Returns Testing Objective Theoretical testing knowledge: ―Grade 1‟ Theoretical (predominantly) testing clarity of concepts or Numerical testing basic Total weight to Exam 3 skills: ―Grade 2‟ Numerical testing basic skill sets: ―Grade 3‟ Nature of Test Items Numerical testing analytical skills & synthesis: ―Grade 4‟ 25.33% 3 items: 1 mark each 2 items: 2 marks each 5 items: 3 marks each 4 items: 4 marks each 143

Learning Outcome The objectives of the topic 3.1 – Investment Planning to achieve Financial Goals are as follows: 1. To educate the financial planner that one could create investment portfolios towards each goal separately or create a common corpus. Also highlighting the differences between both the approaches. 2. To share insights to selection of investment products and selecting the appropriate product ensuring the benefits of portfolio diversification. 3. To educate the difference between Lump sum & Systematic investing and the right approach to investing to fulfill a financial goal. 4. To monitor the progress of investment portfolio and measure the pace of growth of investments towards goal achievement. 5. To educate a financial planner how to deal with risk aversion of clients. It is widely accepted that some amount of risky investments can help to boost the portfolio returns and generate positive real return. 6. To restrain one from speculation and focus more on investment for goal achievement. Also to keep the speculative portfolio and the investment portfolio separate. 7. To learn to protect an investment portfolio getting eroded. It is thus important to generate a positive real return on the investment portfolio on an continuous basis. 144

Sub-Section 3.1 Investment Planning to Achieve Financial Goals 3.1.1. Goal Specific Investment Portfolio vs. Common Investment Pool Financial and investment planning are terms that are interchangeably used in personal finance parlance. But nothing could be farther from the truth. Investment Planning (IP) has the ―rate of interest‖ factor at its core, thus making the approach a little myopic. The IP process involves several steps, ranging from setting investment goals and understanding the risk appetite to designing an investment portfolio after evaluating the markets and the investment landscape. IP refers to a commitment of funds to one or more assets that will be held over a specific period. Anything not consumed today and saved for future use can be considered an investment. Investment Planning is a Six-step Process Step 1- Set your financial goals. Step 2- Understand investment vehicles. Step 3- Understand financial markets and concepts. Step 4- Develop an investment strategy. Step 5- Implement your strategy. Step 6- Monitor the performance of your investments. Goal-based Investing (GBI) A relatively new approach to wealth management that emphasizes investing with the objective of attaining specific life goals. Goal-based investing (GBI) involves a wealth manager or investment firm‘s clients measuring their progress towards the specific life goals such as saving for children‘s education or building a retirement nest-egg, rather than focusing on generating the highest possible portfolio return or beating the market. Consider an investor who is looking forward to retirement within a year, and who therefore cannot afford to lose even 10% of his or her portfolio. If the stock market plunges 30% in a given year and the investor‘s portfolio is down ―only‖ 20%, the fact that the portfolio has outperformed the market by 10 percentage points would offer scant comfort. Goal-based investing aims to get around this drawback of the traditional investment approach, which generally focuses on outperforming the market while staying within the investor‘s threshold for risk. Instead, it uses individual asset pools with an investment strategy that is tailored to the client‘s specific goals. Thus, if a client‘s main goals are to save for imminent retirement and fund the college education of her young grandchildren, the investment strategy would be more conservative for the former and relatively aggressive for the latter. As an example, the asset allocation for the retirement assets might be 10% equities and 90% fixed-income, while the asset allocation for the education fund may be 50% equities and 50% fixed-income. The two biggest advantages of goal-based investing, according to their proponents, are - (i) it increases clients‘ commitments to their life goals by enabling them to gauge tangible 145

progress towards their goals, and (ii) it reduces negative behavioral biases such as impulsive decision-making and overreaction. Common Investment Pool An common investment pool is a way of investing money alongside other investors in order to benefit from the inherent advantages of working as part of a group. These advantages include ability to:  hire professional investment managers, which may potentially be able to offer better returns and more adequate risk management;  benefit from economies of scale, i.e., lower transaction costs;  increase the asset diversification to reduce some un-systemic risk. Terminology varies with country but common investment pool are often referred to as investment pools, collective investment vehicles, collective investment schemes, managed funds, or simply funds. An common investment pool may be held by the public, such as a mutual fund, exchange-traded fund, or closed-end fund,[1] or it may be sold only in a private placement, such as a hedge fund or private equity fund.[2] The term also includes specialized vehicles such as collective and common trust funds, which are unique bank- managed funds structured primarily to commingle assets from qualifying pension plans or trusts. Common investment pools are promoted with a wide range of investment aims either targeting specific geographic regions (e.g., emerging markets or Europe) or specified industry sectors (e.g., technology). Depending on the country there is normally a bias towards the domestic market due to familiarity, and the lack of currency risk. Funds are often selected on the basis of these specified investment aims, their past investment performance, and other factors such as fees. 3.1.2. Selection of Products and Product Diversification The Concept of ‘Portfolio’ A person‘s wealth portfolio includes: Assets: stocks, bonds, shares in unincorporated business, houses or apartments, pensions benefits, insurance policies, etc. Liabilities: student loans, auto loans, home mortgages, etc. Portfolio Selection  A study of how people should invest their wealth optimally  A process of trading off risk and expected return to find the best portfolio of assets and liabilities  How much to invest in stocks, bonds, and other securities  Whether to buy or rent one‘s house  What types and amounts of insurance to purchase 146

 How to manage one‘s liabilities  How much to invest in one‘s human capital  Although there are some general rules for portfolio selection that apply to virtually everyone, there is no single portfolio or portfolio strategy that is best for everyone. Hence Product selection depends on multiple factors like: 1. The Life Cycle In portfolio selection, the best strategy depends on an individual‘s personal circumstances (family status, occupation, income, wealth). 2. Time Horizon In formulating a plan for portfolio selection, you begin by determining your goals and time horizons.  Planning horizon: the total length of time for which one plans  Decision horizon: the length of time between decisions to revise the portfolio  Trading horizon: the minimum time interval over which investors can revise their portfolios / its determination and impacts  Investment strategy & trading horizon: portfolio insurance or dynamic portfolio strategy. 3. Risk Tolerance A major determinant of portfolio choices is influenced by such characteristics as age, family status, job status, wealth, and other attributes that affect a person‘s ability to maintain his standard of living in the face of adverse movements in the market value of his investment portfolio 4. Professional Asset Managers Investment advisors & ―finished products‖ from a financial intermediary Specialization, information and cost advantages 5. The Trade-off between Expected Return and Risk The objective is to find the portfolio which offers investors the highest expected rate of return for the degree of risk they are willing to tolerate. Two step process:  find the optimal combination of risky assets.  mix this optimal risk-asset with the riskless asset. Product Diversification: Diversification is a technique that reduces risk by allocating investments among various financial instruments, industries and other categories. It aims to maximize return by investing in different areas that would each react differently to the same event. Most investment professionals agree that, although it does not guarantee against loss, diversification is the most important component of reaching long-range financial goals while minimizing risk. Here, we look at why this is true, and how to accomplish diversification in your portfolio. 147

Different Types of Risk Investors confront two main types of risk when investing:  Undiversifiable - Also known as \"systematic\" or \"market risk,\" undiversifiable risk is associated with every company. Causes are things like inflation rates, exchange rates, political instability, war and interest rates. This type of risk is not specific to a particular company or industry, and it cannot be eliminated, or reduced, through diversification; it is just a risk that investors must accept.  Diversifiable - This risk is also known as \"unsystematic risk,\" and it is specific to a company, industry, market, economy or country; it can be reduced through diversification. The most common sources of unsystematic risk are business risk and financial risk. Thus, the aim is to invest in various assets so that they will not all be affected the same way by market events. Objective of Diversification: Let's say you have a portfolio of only airline stocks. If it is publicly announced that airline pilots are going on an indefinite strike, and that all flights are canceled, share prices of airline stocks will drop. Your portfolio will experience a noticeable drop in value. If, however, you counterbalanced the airline industry stocks with a couple of railway stocks, only part of your portfolio would be affected. In fact, there is a good chance that the railway stock prices would climb, as passengers turn to trains as an alternative form of transportation. But, you could diversify even further because there are many risks that affect both rail and air, because each is involved in transportation. An event that reduces any form of travel hurts both types of companies - statisticians would say that rail and air stocks have a strong correlation. Therefore, to achieve superior diversification, you would want to diversify across the board, not only different types of companies but also different types of industries. The more uncorrelated your stocks are, the better. It's also important that you diversify among different asset classes. Different assets - such as bonds and stocks - will not react in the same way to adverse events. A combination of asset classes will reduce your portfolio's sensitivity to market swings. Generally, the bond and equity markets move in opposite directions, so, if your portfolio is diversified across both areas, unpleasant movements in one will be offset by positive results in another. There are additional types of diversification, and many synthetic investment products have been created to accommodate investors' risk tolerance levels; however, these products can be very complicated and are not meant to be created by beginner or small investors. For those who have less investment experience, and do not have the financial backing to enter into hedging activities, bonds are the most popular way to diversify against the stock market. Unfortunately, even the best analysis of a company and its financial statements cannot guarantee that it won't be a losing investment. Diversification won't prevent a loss, but it can reduce the impact of fraud and bad information on your portfolio. 148

How Many Stocks You Should Have Obviously owning five stocks is better than owning one, but there comes a point when adding more stocks to your portfolio ceases to make a difference. There is a debate over how many stocks are needed to reduce risk while maintaining a high return. The most conventional view argues that an investor can achieve optimal diversification with only 15 to 20 stocks spread across various industries. Diversification can help an investor manage risk and reduce the volatility of an asset's price movements. Remember though, that no matter how diversified your portfolio is, risk can never be eliminated completely. You can reduce risk associated with individual stocks, but general market risks affect nearly every stock, so it is important to diversify also among different asset classes. The key is to find a medium between risk and return; this ensures that you achieve your financial goals while still getting a good night's rest.. 3.1.3. Additional Lump Sum Investments vs. Systematic Staggered Investments Money has no legs of its own and yet it keeps on moving around faster than all of us. This makes money all powerful. But time is a great leveler. What looks like a mountain of money today may become dust tomorrow if money does not keep on moving with time. If I have a mountain of money after 30 years, what is its actual worth today? Well, you just need to make smart use of your calculator to know that. If somebody promises to pay you ₹1 crore after 30 years, you may feel that after 30 years you would have a mountain of money. But don‘t entertain the notion that after 30 years you could lead the lavish life of a present-day millionaire! You should always compare the future value of your money with its present value to see its true worth. What is it worth now? For that you need to discount the future value of money to its present value by the expected rate of return on present investments. Discounting is just the opposite of compounding. Financial experts use different mathematical formulas for doing compounding or discounting. However, if you are not familiar with formulas then doing some reverse thinking may help. You can rephrase your question like this: If ₹1 lakh is worth ₹17.45 lakh after 30 years at a 10% rate of return compounded annually, then how much more should you invest now so that it is worth ₹1 crore at the same rate of return? You can use financial formulas for doing calculations but if you are allergic towards any kind of formula then a little bit of trial and error on your calculator will tell you that the present value of ₹5.70 lakh would be close to ₹1 crore after 30 years at the same rate of return. So what‘s the conclusion? The ₹1 crore that you would be getting after 30 years is as good as getting ₹5.70 lakh now. That may sound disappointing. But cheer up! The present value of your future money may not be good enough to let you buy a new house but you can definitely buy a decent car. 149

The mountain of money after 30 years really looks like a mountain of peanuts in terms of its present value! Don‘t be so disappointed. You should always keep in mind that the present value of your future money depends upon the length of time and the rate of return you use for discounting. A higher rate of return and longer period of time would lead to a lower present value of the future money. Conversely, a lower rate of return and shorter period of time would lead to a higher present value of the future money. The length of time you have to choose is obvious but what is the rate of return you should choose for discounting the future money? You have to choose a realistic rate of return that makes some sense. But the problem is that different investments may yield different rates of return. Some of these investments may be more risky than others. A 30-year bond may yield a rate of return different from a 30-year investment in stocks or real estate. When there is a possibility of earning different returns on different investments with different risk profiles, choosing the actual rate of return for discounting is a tough job. There is always scope for an error of judgement and the present value may be grossly undervalued or overvalued. Here we have to exercise our good sense. Choose the average rate of return on different investments or the rate of return on the safest investment for the purpose of discounting the future cash flow. Neither be a liberal nor a conservative when it comes to counting your money. How can knowing the present value of future money help us? Knowing the present value of future money can help us in many ways. You can make wiser investment decisions by comparing the amount of money required for investment with the present value of future cash inflows from your investment. If the present value of the future cash inflows is greater than the value of the present investment, then it means that making investment makes good sense. Otherwise, you may be sacrificing your glorious present for the sake of a darker tomorrow. That‘s true. Sometimes we may miss the present while chasing the dreams of tomorrow. Lump-sum vs. Systematic Investing The volatility of today‘s financial markets and the accompanying uncertainty of investment returns has resulted in a lot of lost sleep for many investors who heretofore thought the stock market could only move upwards over time. In fact, over the last 75 years, the stock market has moved in many different directions, influenced by many different socio- economic factors. However, all of these different markets can be ―boiled down‖ to essentially three types of markets: Up Markets, Down Markets & Flat Markets.  ―Up‖ Markets exist when stock prices are generally rising over time.  ―Down‖ Markets exist when stock prices are generally falling over time.  Flat Markets exist when stock prices cannot sustain any meaningful price movement —positive or negative— over time. ―Over time‖ refers to timeframes that are at least ten years in length in the examples on the back of this flyer. 150

―Up‖ Markets are the easiest for sophisticated and unsophisticated investors alike to prosper because stock prices are generally rising over time. It does not appear to matter which investment approach is utilized, as both grow over time. ―Down‖ Markets are the toughest for both approaches as stock prices are generally falling. The Lump-Sum approach fails because stock prices fall after the initial investment is made. The Systematic approach works better here because as stock prices fall, the Systematic investor is able to accumulate more shares at successively lower prices. Once the market begins to recover—even if it does not return to its original level—losses generated by the falling share prices can be recouped quickly with rising share prices. The key word being ―time‖ as investors will need to consider their ability to purchase shares continuously during periods of falling share prices. ―Flat‖ Markets may be the most ―enigmatic‖ markets in that it is difficult to understand what drives these markets as they gyrate up and down with no real sense of direction. A Lump-Sum investor in a Flat Market does not lose, but he does not really gain either, because stock prices have ended the period at the same level as they began. If the time value of money is factored in, the Lump-Sum investor has actually lost money in this scenario. Conversely, the Systematic investor has a better opportunity to prosper because he acquires fewer shares when prices are high and more shares when prices are low. Over time, the average cost per share for the Systematic investor to acquire stock will usually be less than the Lump-Sum investor and thus, be more profitable for the Systematic investor. The moral to the story: No one knows exactly what type of market is presenting itself at any given time. And no single approach can assure a profit or protect against a loss in a declining market. However, a Systematic investment approach appears to provide the best methodology in all kinds of markets because of its process. A process which is naturally ―unemotional‖ (as to which type of market currently exists) and which may help many investors recover some of their lost sleep and to sleep better at night on an ongoing basis. How Lump-sum Investments Fares Compared to SIPs 3-Year Returns (%) 5-Year Returns (%) Fund Lump SIP Lump SIP sum sum BNP Paribas Equity Fund Franklin India Bluechip 22.4 30.3 14.4 20.3 Fund HDFC Top 200 Fund 16.1 21.9 12.9 14.9 ICICI Prudential Focused Bluechip Equity Fund 19.3 27.7 13.8 17.6 ICICI Prudential Top 100 20.6 27.2 16.0 18.9 Fund JP Morgan India Equity 23.3 28.6 14.6 19.2 Fund 17.6 25.4 13.0 16.4 151

L&T Equity Fund 18.5 27.3 14.6 17.6 18.6 24.5 13.0 16.2 SBI Magnum Equity Fund 18.2 23.9 12.8 15.8 Tata Pure Equity Fund – 21.6 28.9 15.7 19.5 Plan A UTI Equity Fund Data as on 30 Sep 2014, Source: Value Research 3.1.4. Monitoring Progress in Investment Portfolio for Goal Achievement As a saver-investor, it is essential that you be aware of your short-, mid- and long-term objectives. You should also assess if you have the ability, interest and rationality required to manage your portfolio yourself. Whether you opt for self-management or entrust the management of your investments to a third party, the following tips should guide you in your course of action:  Stay true to yourself in terms of your objectives and the progress of your financial life;  Be disciplined in terms of investment (per security) and portfolio monitoring (overall direction);  Compare your results with those of other similar investments available on the market. Portfolio Monitoring When you entrust your portfolio management to a third party, you should be able to appropriately monitor this person‘s work. Portfolio monitoring involves analyzing several factors. 1. Management Style By taking the time to understand the various portfolio management styles offered on the market, you will be able to select a style that is adapted to your objectives and needs. 2. Compliance The terms and conditions of the contract with the portfolio manager are usually confirmed in writing and identify the investment policy and management framework. Compliance of the portfolio manager‘s work can mainly be assessed in terms of compliance with the following aspects:  The assignment terms and conditions. For example, the contract could stipulate that the entire bond portion must have an overall rating of A or higher, that no security may make up more than 10% of the portfolio, that no single industry may make up more than 30%, etc.;  The investment policy, which stipulates the desired distribution between income and growth as well as the minimum and maximum to be allocated to each asset category;  The management style for which the portfolio manager was selected. 152

3. Performance When assessing the portfolio manager‘s performance, take into account the performance history and the level of risk assumed. To evaluate the performance of your portfolio, find out what your return was last year, by account and on a consolidated basis, and then compare, based on your portfolio‘s asset allocation, if your results are better, the same or lower than the reference indices. 4. Service Quality To assess the quality of the service you are receiving from your portfolio manager, you should meet with this person at least twice a year and document in writing the issues discussed during these meetings so that you can monitor the outcome of decisions made. The portfolio manager should also submit a complete and detailed management report on a regular basis. 5. Administration You should assess the amount of the various fees paid, including: management, custodial or brokerage fees, as well as any interest charges, if applicable. You can then determine if the service you are receiving is appropriate and reasonably priced, according to your capital invested. There are significant variances between the management fees for various products and services offered on the market (private management, mutual funds, baskets, etc.). 6. Taxation Portfolio monitoring also involves taking various tax aspects into consideration such as the deductibility of the various fees incurred as well as the management of gains and losses at the end of the year. In addition, after-tax rates of returns on various types of investments must also be considered 3.1.5. Addressing Risk Aversion Risk aversion is the behavior of humans (especially consumers and investors), when exposed to uncertainty, to attempt to reduce that uncertainty. It is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. For example, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Fear of loss can cause investors to not only miss out on opportunities, but take emotional actions—such as liquidating their assets—that could run counter to their long-term investment goals. Fear plays a big part in market psychology, and it can be a powerful force! What many investors perceive as ―safety‖ can come at a cost: loss of potential return. You can imagine how the desire to try and avoid market losses often causes investors to move their money out of stocks and into cash or fixed income vehicles, but rather than avoiding losses, they often wind up trading potential market losses for potential negative real returns, especially once the impact of inflation is factored in. 153

So how do you overcome the emotional reaction of loss aversion? Having a defined asset allocation plan, and engaging in regular portfolio rebalancing can help. Working with an advisor to gain some rational perspective can help, too. 3.1.6. Avoiding Speculation Investing vs Speculating About now you may be sitting back thinking about your brother-in-law who ―made a killing‖ in options. Or maybe you‘re reminiscing about that Nevada vacation when one lucky quarter magically drew out 700 more with the pull of a slot machine lever. Why put your money in slow-and-steady investment vehicles that merely promise double-digit returns when you could have near-instant riches? With compounding, you have to wait patiently for years for your riches to accumulate. What if you want it all now? Granted, there is nothing exhilarating about predictability. Sure, tales of your fifth year beating the performance of the Standard and Poor‘s 500 Index won‘t make you the life of the party. However, neither will the far more common tales about how you lost your savings on some speculation, and your subsequent adventures in bankruptcy court. (Actually, that might make for some entertaining party chatter, especially given our penchant for reveling in the misery of others. But let‘s try for the moment to ignore sad musings about human nature.) What are the odds of winning the lottery jackpot? Well, it depends on the lottery - they may be 1 in 7 million, or 1 in 18 million, or somewhere in between. You have a far greater chance of dying from flesh-eating bacteria - 1 in a million - than you do of winning that jackpot! You don‘t need a card dealer, dour strangers, or Wayne Newton background muzak to gamble. There are plenty of stock market gamblers who do an admirable job of losing their money on seemingly legitimate pursuits. At the Motley Fool we think that commodities and options are just as risky as a Vegas craps game. In fact, we believe investors ―gamble‖ every time they commit money to something they don‘t understand. This, of course, may be true of stocks as well as of commodities and options. Say you overhear your best friend‘s dentist‘s nanny talking about a company called Huge Fruit at a cocktail party. ―This thing is gonna go through the roof in the next few months,‖ she says in a stage whisper. If you call your broker the first thing the next morning to place an order for 100 shares, you‘ve just gambled. Do you know what Huge Fruit does? Are you familiar with its competition (Heavy Melon)? What were its earnings last quarter? There are a lot of questions you should ask about a company before you throw your hard-earned cash at a ―hot‖ stock. There‘s nothing too hot about losing your money because you didn‘t take the time to understand what you were investing in. Remember: Every dollar that you speculate with and lose is a dollar that is not working for you over the long- term to create wealth. Speculation promises to give you everything you want right now but rarely delivers; patience almost guarantees those goals down the road. 154

3.1.7. Protecting Portfolio Erosion When markets are volatile, investors flock to the perceived security of short term investments. While short-term investments have a role to play as part of a diversified portfolio, using them incorrectly can undermine your long-term financial security. People often ―park‖ their capital in a safe, low-yielding investment until the markets settle down, and then move it to a more appropriate long-term vehicle. Too often, however, they wait too long. The potential costs are high. Keeping your investments in low-risk/low- return vehicles for too long can prevent you from achieving your long-term goals. Conservative ―no-risk‖ investments such as money market funds don‘t protect a portfolio from the erosion caused by inflation and income tax. Over the long term, inflation is a far more serious risk than market volatility. For example, ₹300,000 in savings now will be worth only about ₹200,000 in 10 years if inflation averages 3% annually. Over 20 years, the same rate of inflation cuts the nest egg to ₹163,138. Although inflation has been low for the past few years, over the past quarter century the average annual rate of inflation has been more than 5%. Inflation takes a bite over the short term as well. Suppose that your conservative investments pay 5% a year. If inflation averages 3%, your real return is just 2% per year. And if that income is subject to a marginal tax rate of 40%, your return drops to 0. The most effective way to produce stronger returns and protect against inflation erosion is through equity investments such as growth mutual funds. While equities can be volatile over the short term, in the long term they have historically outperformed fixed income and money market investments and outstripped inflation. Outside a registered plan, equities bring beneficial tax treatment. While interest income is fully taxed, capital gains are taxed on only 50% of their value and dividends from Canadian companies qualify for the federal dividend tax credit. Experience tells To protect your portfolio against short term market volatility, you need to diversify. For example, along with equity mutual funds your portfolio should include some bond and money market funds. In addition, your investments should be spread out across a number of geographical regions and encompass more than one investment style. 155

Sub-Section 3.2 Measuring Risk 3.2.1. Expected Returns from a Goal Portfolio Learning Outcome: The objectives of the topic 3.2 – Measuring Returns from a Goal Portfolio are as follows: 1. To learn the methodology of calculating the return of a security as well as that of a portfolio. 2. To understand the concept of Beta as well as Portfolio Beta and its use in portfolio management. 3. To learn the methodology of calculating the variance, semi-variance & covariance of securities and measuring their potential risks. 4. To learn the methodology of calculating the risk of a security as well as a portfolio to measure their range of deviation from mean return. 5. To understand the concept of Correlation & Correlation Coefficient and understand how two securities are related amongst themselves? Calculating Expected Returns on a Security To help us grasp the concept of risk, consider two possible investments. The first investment is in a government security that will certainly pay interest at 6 per cent. The second investment is in shares of a media company. We have made the following estimate of the probability of receiving various annual returns from the shares in a media company: Where E(R) is expected return pi = probability of return of security in state i Ri = return on security in state i Return Probability 0 per cent 0.1 4 per cent 0.2 12 per cent 0.4 20 per cent 0.2 24 per cent 0.1 Thus, investing in the media company‘s shares could provide returns as high as 24 per cent or as low as 0 per cent. On the average, we would expect a return of 12 per cent. This is the most probable return but there is also a 20 per cent probability of receiving a 4 per cent return; and a 20 per cent probability of receiving a 20 per cent return. The expected return is calculated by summing the products of each individual return multiplied by the probability of achieving that return. Another term for expected return is ‗the weighted average of possible returns‘). E(R) = ∑ (Pi * Ri) 156

Expected return E(R) = (0% X .10) + (4% X .20) + (12% X .40) + (20% X .20) + (24% X .10) = 12% If we compare the two investments, we see that the expected return of the government security is 6 per cent while the media company has an expected rate of return (or a weighted average of possible returns) of 12 per cent. However, the investment in the media company shares is more risky—there is a greater uncertainty about the final outcome, which can range from 0 per cent to 24 per cent. Figures 1.2 and 1.3 show these returns as a discrete probability distribution. Probability Distribution of returns for the government security The only possible return is 6 per cent, therefore the probability of receiving that return is 1, or 100 per cent. The most probable return is 12 per cent but other returns, ranging from 0 to 24 per cent, also have a significant probability of occurring. Example 1 You are thing of acquiring some shares of ABC Ltd. The rates of return expectations are as follows: Possible Rate of Return Probability 0.05 0.20 0.10 0.40 0.08 0.10 0.11 0.30 Compute the expected return E(R) on the investment. Expected Return = (0.20)(0.05)+ (0.40)(0.10)+(0.10) (0.08)+ (0.30)(0.11) = 0.091 = 9.1% 157

Example 2 Calculate the expected return from the given data :- POSSIBLE RETURNS (Xi ) PROBABILITY p (Xi) 30 0.10 40 0.30 50 0.40 60 0.10 70 0.10 Ans :-POSSIBLE RETURNS PROBABILITY p (Xi) Xi *p(Xi) POSSIBLE RETURNS (Xi ) 0.10 3 30 0.30 12 40 0.40 20 50 0.10 6 60 0.10 7 70 = ∑ Xi *p(Xi) = 48 Hence , Expected return is 48% Example 3 Based on the probability distributions of the rate of return from Security A and Security B, compute the expected rate of return from security A and security B State of the Probability of Rate of Return (%) Economy Occurrence Security A Security B Boom 0.30 16 40 Normal 0.50 11 10 Recession 0.20 6 -20 158

The expected rate of return on Security A is: E(R) = (0.30)(16) + (0.50)(11) + (0.20)(6) = 11.5% The expected rate of return on Security B is: E(R) = (0.30)(40) + (0.50)(10) + (0.20)(-20) = 13.0% Calculating Expected Returns of a Portfolio The portfolio return is the sum of weighted average of the expected return of individual securities in a portfolio. When the weights are assigned on the basis of the proportion of funds invested. The formula for the measurement of expected return on a portfolio is as follows. RP  Wi .Ri Where RP = Return of the portfolio wi= Weight of security i in portfolio Ri = Return of the security i The steps involved in the calculation are: Step 1: Calculate expected return on each security included in a portfolio by multiplying each return by its associated probability and summing up the results. Step 2: Now calculate weighted average of the expected returns for the individual investments in a portfolio. (Note that the weights are calculated by considering the beginning values of each investment in the portfolio). EXAMPLE 1 In our example, we consider two securities X and Y, and the expected rate of return on the securities and the probability are given in the table below: Probable Rate of Return Probability Security X Security Y 0.1 40% 40% 0.2 10% 20% 0.4 0% 10% 0.2 -5% 0% 0.1 -10% -20% First step is to calculate expected rate of return on the portfolio consisting of securities X and Y. Expected Return Security X =(0.1*40)+(0.2*10)+(0.4*0)+(0.2*-5)+(0.1*-10) = 4% Security Y=(0.1*40)+(0.2*20)+(0.4*10)+(0.2*0)+(0.1*-20)= 10% 159

Second step is to calculate weighted average return of security X and Y. Assuming that an equal investment is made, the portfolio return is Rxy = (0.5*4) + (0.5*10) Rp = 7% The return of the portfolio consisting of x and y with equal proportion is 7%. Example 2 Eklovya‘s portfolio has following expected returns: Portfolio Probability Expected Return (%) Company-A 0.40 15 Company-B 0.30 8 Company-C 0.30 12 Find the expected return of the portfolio. (2 marks) a) 15% b) 12% c) 35% d) 17% Sol. (b) .40*15+.30*8+.30*12 = 12% Example 3 Om prakash is planning to invest in two companies ABC and XYZ. The coefficient of correlation between the two stocks ABC and XYZ is 0.7. The standard deviation of returns for ABC is 18% and the standard deviation of returns for XYZ is 22%. The expected return for XYZ is 18% and the expected return for ABC is 15%. Calculate the expected returns of Om prakash‘s portfolio for which he plans to invest Rs. 4 lakh in XYZ Company and Rs. 2 lakh in ABC Company. (4 marks) Sol. (b) Weight in XYZ company = 4 Lakh/6 Lakh = 67% Weight in ABC company = 2 Lakh /6 Lakh = 33% E(R) of the portfolio = 67*.18+33*.15 = 17.01% 160

Example 4 Mr. Client portfolio consists of stock A and stock B. The weight of both is 50% each. Over a year it is expected that they will perform as per the given table: Probability X (Return) Y (Return) 0.1 40 40 0.2 10 20 0.4 0 0 0.2 -5 0 0.1 -10 -20 Calculate the: A) Expected Return of X, Y (Answer: X = 4%, Y = 6% ) B) Expected Return from Portfolio (Answer: 5% ) Solution: Steps Properties 1 Press ―Set Up‖ (Next to ―On‖ Button) 2 Go to ―STAT‖ function in set up & ―On‖ the same & then press ―Esc‖ 3 Press ―STAT‖ mode 4 A+BX: EXE X Y Frequency 1 40 40 0.10 2 10 20 0.20 5 3 0 0 0.40 4 -5 0 0.20 5 -10 -20 0.10 6 Press ―Shift Stat‖ 161

7 Press ―5.Var‖ 8 Pres ―2‖ 9 Press ―EXE‖, the answer ―4‖ will be displayed Note: In the similar way solve Return of Stock Y = 6% Portfolio Return = P1*R1 + P2* R2+ .................+ P1 & P2 = Proportion holding of two stock respectively. R1 & R2= Return from stock respectively. Portfolio Return = (0.5*4) + (0.5*6) = 5% Question 1.3: Calculate expected return on the following portfolio. There are 4 securities included in the portfolio having expected return of 10%, 11%, 12% and 13% respectively. Their weights in the portfolio are 0.20, 0.30, 0.30 and 0.20. 3.2.2. Beta and Portfolio Beta BETA (β) Beta is used in finance as a measure of investment portfolio risk. Beta in this context is calculated as the covariance of the portfolio's returns with its benchmark's returns, divided by the variance of the benchmark's returns. A beta of 1.5 means that for every 1% change in the value of the benchmark, the portfolio's value changes by 1.5%. Beta measures the sensitivity of stock responsiveness to market factors. Beta measures how much a stock would rise or fall if the market rises / falls. The index has a Beta of 1 (one). Beta of a portfolio, measures the portfolios responsiveness to market movements. It is nothing but the weighted average of the stock Betas. PORTFOLIO BETA (β) The beta of a portfolio is the weighted sum of the individual asset betas, According to the proportions of the investments in the portfolio. E.g., if 50% of the money is in stock A with a beta of 2.00, and 50% of the money is in stock B with a beta of 1.00, the portfolio beta is 1.50. ∑( ) Portfolio beta describes relative volatility of an individual securities portfolio, taken as a whole, as measured by the individual stock betas of the securities making it up. A beta of 1.05 relative to the NIFTY implies that if the NIFTY increases by 10% the portfolio is expected to increase by 10.5%. 162

Example 1 Mr. A‘s portfolio consists of two stocks A and B in which he has invested Rs. 75,000 and Rs. 67,000, respectively. Stock A has beta of 1.4 and stock B has beta of 0.80. What is the Beta of the portfolio? (Expected Rate of Return is 12.59%) (ANSWER: Beta of the portfolio is 1.11692) Solution: Step 1: Find allocation of stock A and B in relation to the portfolio value Stock A : 75,000 / (142,000) = 52.82% Stock B : 67,000 /(142,000) = 47.18% Step 2: Find Beta of the portfolio using weighted average formulae: (Weight of Stock A *Beta of Stock A) + (Weight of Stock B *Beta of Stock B) Therefore Beta of the portfolio = 1.11692 Example 2 Calculate the Beta of the portfolio? Security ABC XYZ Treasury Market Index Weight 30% 40% 5% 25% Beta of security 0.8 1.70 - - (ANSWER; Beta of Portfolio is 1.17) Solution: Beta of a portfolio : Weighted Average Beta of Individual Assets = (0.3*0.8)+ (.40*1.70)+ (0.05* 0) + (.25* 1) = 1.17 163

3.2.3. Variance, Semi-variance and Covariance & 3.2.4. Standard Deviation Including Standard Deviation of Portfolio We define risk as the deviation of results from expected return. Variance or Standard Deviation The usual method of measuring the risk of a single security is by calculating its variance or standard deviation, of returns. This measures variability in the expected returns from the security, which can be taken as a measure of risk. For example, for the government security, the expected return is 6 per cent and there are no other possible returns, so the standard deviation is 0 per cent or nil. With the media company shares, the expected return is 12 per cent, and actual returns may vary greatly either side of that amount. Without going into the calculation here, the standard deviation for the media company shares is approximately 10 per cent. The point is that different securities can vary greatly in the volatility or probability (riskiness) of their returns. This variance may vary from Industry to industry too. Semi-Variance: For most investors, risk considerations need to focus on downside risk, that is, the risk that the income earnings or the capital movements will be lower than expected. The downside risk is calculated by using only the negative deviations from the mean and is known as semi- variance. If the deviations on each side of the mean are symmetrical, the semi-variance would be half the variance. Measurement of Risk on a Security Let us now see how to measure the degree of variation around the expected return. The formula for the calculation of variance is: Variance = Pi Ri  E(Ri)2 where P i = Probability Ri = Return E(R) = Expected Return Standard deviation Variance Example Consider the same example of a media company. We have calculated the average or expected return is 12% and have seen that the return varies from 0% to 24%. 164

Figure 1.3: Probability Distribution of returns for shares in the media company (1) (2) (3) (4) (3)*(4) Return Expected Return minus Difference squared Probability 14.4 0 Return 144 0.1 12.8 4 -12 64 0.2 12 -8 0 0.4 0 20 0 64 0.2 12.8 24 8 144 0.1 14.4 12 54.4 Variance of the media company‘s share is 54.4 and the standard deviation is the square root of variance, SD = Variance = 7.375. This will make us conclude that the government security is for safer than Media Company because the risk of Media Company is 7.37% and that of govt. bond is zero. Example 2 Calculate standard deviation and variance by using the following data : Monthly return (in percent ) Are presented below for ITC stock and BSE National Index for a 12 month period month ITC BSE National Index 1 9.43 7.41 2 -5.33 3 0 -7.35 4 -4.31 -14.64 5 -18.92 1.58 6 -6.67 15.19 7 26.57 5.11 8 0.76 20 -0.97 9 2.93 165 5.25

10 21.45 10.44 11 23.13 17.47 12 32.83 20.15 total 111.69 49.82 Answer Month ITC BSE National Y2 X2 XY Index 1 9.43 7.41 88.9249 54.9081 69.8763 2 0 -5.33 0 28.4089 0 3 -7.35 54.0225 4 -4.31 -14.64 18.5761 214.3296 31.6785 5 -18.92 1.58 357.9664 2.4964 276.9888 6 -6.67 15.19 44.4889 230.7361 -10.5386 7 26.57 5.11 705.9649 26.1121 403.5983 8 0.76 0.5776 9 20 -0.97 400 0.9409 102.2 10 2.93 10.44 8.5849 108.9936 2.2268 11 5.25 17.47 27.5625 305.2009 -5.0925 12 21.45 20.15 460.1025 406.0225 223.938 Total 23.13 49.82 534.9969 1432.749 404.0811 32.83 1077.809 661.5245 111.69 3724.977 2160.481 Variance = Pi Ri  E(Ri)2 where P i = Probability Ri = Return E(R) = Expected Return Standard deviation Variance Standard deviation of ITC returns : From above table , Following arethe data available ∑ Y=111.69 n=12 ∑y2=3724.97 σ y= [(12*3724.97)-(111.69)2/12*12 ] 1/2 =( 4469.64-12474.66/144 )1/2 =(223.78)1/2 =14.96 166

VARIANCE AND STANDARD DEVIATION OF BSE INDEX RETURNS , From above table, the following data are available n=12 ∑X=49.82 ∑ X2=1432.749 σ2x=(12*1432.75)-(49.82)^2/12*12 = 17193-2482.03/144 = 14710.97 /144 =102.16 σ x= (102.16)1/2 = 10.11 Example 3 Based on following information: Year Total Returns (%) 1 14 2 12 3 -8 4 25 52 Calculate Standard Deviation Properties (Answer: 12.53%) Press ―STAT‖ mode Steps 1 – VAR : EXE 1 x 2 1 14 3 2 12 167

3 -8 4 25 52 4 Press ―Shift STAT‖ 5 Press ―5.Var‖ 6 Press ―Option 4‖ 7 Press ―EXE‖, the answer : 12.52996‖ will be displayed Measurement of Risk of a Portfolio Risk of a portfolio is calculated by considering the variance or standard deviation of individual securities included in the portfolio as well as the interactive risk between the securities, measured by covariance. Please note that while calculating portfolio return, the weighted average of returns is used. But for portfolio risk not only individuals risks but the covariance between securities are also included. What is Covariance? Due to interactive relationships securities move up or down together. If the rates of return on two securities move together, the covariance between the securities will be positive. If the rates of returns are independent, covariance will be zero. If the returns of the securities move in the reverse direction, the covariance of the two securities shall be negative. What is the advantage of considering the covariance term in portfolio risk assessment? An individual asset might have a high variance on its own returns but if its covariance with other asset is low or negative, and we construct a portfolio of these two securities it will reduce the risk of the portfolio and thus become very attractive as part of a portfolio. These low or negative covariance assets can be used to counter balance the fluctuation in other assets, therefore, reducing the overall portfolio risk. For ex, ONGC and HPCL may happen to move in reverse direction and have negative covariance. If we build the portfolio with these two securities we shall be able to reduce the total risk which might be simply because of the negative covariance. Example Let us take an example to illustrate the portfolio risk measurement. As you will see in our example, the formula for portfolio variance includes the variance for each security, weighted according to the proportion of the portfolio which is invested in each security, plus the covariance between returns for the two securities. The formula for the measurement of expected risk on a portfolio is where 168

     xy  Xx2 2  X2y 2  2XxXyCOVxy x y  xy = standard deviation of the portfolio X = proportion invested in security, Xx refers to proportion of total funds invested in security X.  x = variance in return of X COVxy= covariance between securities X and Y It can be expressed as = (Proportion of funds in X)2 . Variance of X + (Proportion of funds in Y)2. Variance of Y+2.Proportion of funds in X . Proportion of funds Y. Covariance between X and Y. EXAMPLE In our example, we consider two securities X and Y, and the expected rate of return on the securities and the probability are given in the table below: Probable Rate of Return Probability Security X Security Y 0.1 40% 40% 0.2 10% 20% 0.4 0% 10% 0.2 -5% 0% 0.1 -10% -20% Step 1 is to calculate expected rate of return on the portfolio consisting of securities X and Y. Expected Return Security X =(0.1*40)+(0.2*10)+(0.4*0)+(0.2*-5)+(0.1*-10) = 4% Security Y=(0.1*40)+(0.2*20)+(0.4*10)+(0.2*0)+(0.1*-20)= 10% Step 2: Calculate the standard deviation for securities X and Y by applying the following formula. Variance = Pi (Ri  E(Ri ))2 wi = Probabilty of returns used as weights Security X =(0.1*(40-4)^2)+(0.2*(10-4)^2)+(0.4*(0-4)^2)+(0.2*(-5-4)^2)+ (0.1*(-10-4)^2) = 13.38% Security Y=(0.1*(40-10)^2)+(0.2*(20-10)^2+(0.4*(10-10)^2+(0.2*(0-10)^2+ (0.1*(-20-10)^2)= 14.83% Therefore x =13.38 and Y = 14.83. Step 3: Calculate the covariance between securities X and Y. Let us assume that equal amount is invested in both the securities. We use the following formula to measure the covariance. 169

COVxy  Wi (Rix  ERx )(Riy  ERy ) Covariance of the portfolio of security X and security Y is (0.1*(40-4)(40-10)+(0.2*(10-4)(20-10)+(0.4*(0-4)(10-10)+(0.2*(-5-4)(0-10)+ (0.1*(-10-4) (-20-10) = 180 Securities X and Y have a positive covariance, meaning the returns of these securities move in the same direction either up or down. Step 4: Calculate the portfolio risk.  xy  (xx2 2 )  (x2y 2 )  (2 Xx XyCOVxy ) x y The standard deviation is xy  13.77 If we now consider a portfolio consisting of 60% in security x and 40% in security y with all other variables remaining same this portfolio would have an expected return of ERp = (0.6*4)+(0.4*10) = 6.4% and the risk of portfolio P i.e. standard deviation xy  (0.62 * 13.382 )  (0.42 * 14.832 )  (2 * 0.6 * 0.4 * 180) =13.64 Example 2: 3.2.5. Correlation and Correlation Coefficient Correlation Co-efficient In measuring the portfolio risk it is also possible to use correlation coefficient. This correlation coefficient between two securities will give information about their relative movements. A positive correlation coefficient indicates similar movement between securities whereas a negative correlation coefficient indicates inverse movement. A correlation coefficient of zero indicates that the two securities move randomly without correlation between them. The formula used for the calculation of Correlation coefficient (r) between returns on security x and security y is Ixy  COVxy  x y Applying the above formula, correlation coefficient between returns of security x and security y. The above example will be 170

rxy = 180 / (13.38 * 14.83) = 0.91 Correlation coefficient always lies between –1.0 and +1.0. The former value represents perfect negative correlation; the latter, perfect positive correlation. In most of the cases, the correlation lies in between these two values. Generally, it is very difficult to find securities which have perfectly negative correction i.e. -1 What is the advantage of calculating correlation coefficient? We can observe from the formula, correlation coefficient is the covariance in relative form actually, it simplifies the calculation of portfolio measurement. As we have seen earlier, portfolio risk takes into consideration not only standard deviations of individual securities but the interactive risk between pair of securities. Thus, when we use correlation coefficient the portfolio risk would be computed as follows: Where rxy is correlation between X and Y. Let us take an example to understand the calculation of portfolio variance and portfolio standard deviation. Two securities P and Q generate the following sets of expected returns, standard deviations and correlation coefficient: P Q r = 15% r = 20% rpq = -0.60 A portfolio is constructed with 40 per cent of funds invested in P and the remaining 60 per cent of funds in Q. The expected return of the portfolio is given by: = (0.40 x 15) + (0.60 x 20) = 18 percent The variance of the portfolio is given by: σ2 p = x1 2 σ1 2 + x2 2 σ2 2 + 2x1 x2 (r12σ1 σ2 ) = (0.40)2 (50)2 + (0.60)2 (30)2 + 2(0.40)(0.60)(- 0.60)(50)(30) = 400 + 324 - 432 = 292 Example 1 Mr. Client portfolio consists of stock A and stock B. The weight of both is 50% each. Over a year it is expected that they will perform as per the given table. 171

Probability X(Return) Y(Return) 0.1 40 40 0.2 10 20 0.4 0 10 0.2 -5 0 0.1 -10 -20 Let us calculate the: A) Expected Return of X, Y (Answer: X = 4%, Y= 10%) B) Expected Return from Portfolio (Answer: 7%) C) Correlation Co-efficient (Answer: Cor (x,y) .907) D) Standard Deviation of X, Y and Portfolio (Answer: SD of X= 13.379%, SD of Y=14.832%, SD of Portfolio 13.77%) E) Co-variance of Securities (Answer: Coy (x,y) =180) V Solution: Step Properties 1 Press ―Set Up‖(Next to ―On‖ button) 2 Go to‖ STAT‖ function in Set Up & ―On‖ the same & then press ―Esc‖ 3 Press ―STAT‖ mode 4 A+BX : EXE 5 X Y Frequency 1 40 40 0.10 172

2 10 20 0.20 3 0 10 0.40 4 -5 0 0.20 5 -10 -20 0.10 6 Press ―Shift Stat‖ 7 Press ―5.Var‖ 8 Press 9 You‘ll automatically be taken to the main screen with‖ xn‖ being displayed 10 Press ―EXE‖, the answer ―13.379‖ will be displayed Note: In the similar way solve SD of Stock Y = 14.832 To calculate Correlation of Coefficient between Stock (X,Y) Steps Properties Step Properties 1 Press ―Set Up‖(Next to ―On‖ button) 2 Go to‖ STAT‖ function in Set Up & ―On‖ the same & then press ―Esc‖ 3 Press ―STAT‖ mode 4 A+BX: EXE 5 X Y Frequency 1 40 40 0.10 2 10 20 0.20 3 0 10 0.40 4 -5 0 0.20 5 -10 -20 010 173

6 Press ―Shift Stat‖ 7 Press ―7.Req‖ 8 Press ―3.r (small r)‖ 10 Press ―EXE‖, the answer ―0.907‖ will be displayed Co-variance of Securities: Correlation (X,Y) * SD of Stock X * SD of Stock X = 180 Example 2 Consider the returns from a stock over a year period: R1 = 15%, R2 = 12%, R3= 20%, R4 = -10%, R5 = 14% and R6 = 9% Compute the variance and standard deviation of returns? Period Return (Ri) Deviation (Ri Square of Deviation (Ri-R Question 1.4 Compute the risk of the portfolio containing securities A and B by using the following information: 1) correlation coefficient of 0.92 2) standard deviation of A 14.83% and standard deviation of B 19.08% . Assume that equal amount of investment is made in each security. In the example used here we considered a portfolio of only two securities, but in practice, a portfolio may contain more than two securities. General formula for portfolio risk measurement is:  xy  (xx2 2 )  (x2y 2 )  (2 X xXy  x yrxy ) x y 174

where, n = number of assets i, j = specific assets ij σij = covariance between specific assets. Question Calculate Beta from the following data. The rate of stock –A and market portfolio is given for 15 periods. PERIOD RETURN ON STOCK A (%) RETURN ON PORTFOLIO 1 10 12 2 15 14 3 18 13 4 14 10 5 16 9 6 16 13 7 18 14 84 7 9 -9 1 10 14 12 11 15 -11 12 14 16 13 6 8 14 7 7 15 -8 10 175

Solution :- PERIOD RETURN RETURN DEVIATION DEVIATION PRODUCT SQUARE OF ON STOCK ON OF RETURN OF MARKET OF DEVIATION OF PORTFOLIO A (%) PORTFOLIO A FROM FROM ITS DEVIATIONS RETURN ON ITS MEAN MARKET MEAN PORTFOLIO FROM ITS MEAN 1 10 12 0 3 0 9 25 2 15 14 5 5 25 16 1 3 18 13 8 4 32 0 16 4 14 10 4 1 4 25 4 5 16 9 6 0 0 64 9 6 16 13 6 4 24 400 49 7 18 14 8 5 40 1 4 84 7 -6 -2 12 1 9 -9 1 -19 -8 152 624 10 14 12 4 3 12 11 15 -11 5 -20 -100 12 14 16 4 7 28 13 6 8 -4 -1 4 14 7 7 -3 -2 6 15 -8 10 -18 1 -18 ∑ RA = 150 ∑ RB = 135 221 RA=10 RB=9 BETA OF STOCK A = COV(RA,RM) 2 M COV=∑ (PRODUCT OF DEVIATIONS) = 221 = 15.79 n-1 14 2 = ∑(SQUARE OF DEVIATION OF RETURN ON MARKET PORTFOLIO FROM ITS MEAN) = 624 =44.57 n-1 14 176

HENCE BETA IS = COV(RA,RM) = 15.79 = 0.354 2 M 44.57 Question Equal amount of investment is made in portfolio consisting of securities X and Y. Standard deviation of X is 12.43%. ;Standard deviation of Y is 16.54%. ; Correlation coefficient is 0.82. ; The interactive risk of the portfolio, measured by covariance is _____________. (2 marks) a) 145.64 b) 156.22 c) 168.59 d) 172.56 Ans. (c) (c) Covariance = Correlation coefficient * Standard deviation of X * Standard deviation of Y = .82*12.43*16.54 = 168.59 Question With the following data shown in the table below compute the risk on the portfolio Security Std Deviation Proportion A 14.5 60% B 18.5 40% Corr. Co-eff (A,B) 0.91 (Answer: SD of Portfolio = 15.736%) 2 =Square root of { (W1)2* (1)2 + (W2)2* (2)2 +2*WI*W2* Cov 1,2} =Square root of { [(0.6)2*(14.5)2] + [(.40)2* (18.5)2] +[2*0.6*0.4* 0.91*14.5*18.5]} = SD of Portfolio = 15.736 177

Sub-Section 3.3 Diversification Strategies Learning Outcome The objectives of the topic 3.3 – Diversification Strategies are as follows: 1. To learn the different types of diversifications and their relative contributions towards risk reduction. 2. To distinguish between Diversifiable and Non-diversifiable Risks and understand how they could help in reducing the overall risk in an investment portfolio. 3. To know the range of investment products available to risk reduction. 4. To understand the concept of time diversification and the importance of long term investing. 5. To learn the effect of diversification on return & risk of a portfolio. 6. To understand how hedging and help in influencing the return of an investment portfolio and reducing the overall risk. 178

3.3.1. Types of Diversification - Horizontal, Vertical, Geographical, Cross Border Diversification means reducing non-systematic risk by investing in a variety of assets. If the asset values do not move up and down in perfect synchrony, a diversified portfolio will have less risk than the weighted average risk of its constituent assets, and often less risk than the least risky of its constituents. Diversification is one of two general techniques for reducing investment risk. The other is hedging. Diversification relies on the lack of a tight positive relationship among the assets' returns, and works even when correlations are near zero or somewhat positive. Hedging relies on negative correlation among assets, or shorting assets with positive correlation. The simplest example of diversification is provided by the proverb \"Don't put all your eggs in one basket\". Dropping the basket will break all the eggs. Placing each egg in a different basket is more diversified. There is more risk of losing one egg, but less risk of losing all of them. An example of an undiversified portfolio is to hold only one stock. This is risky; it is not unusual for a single stock to go down 50% in one year. It is much less common for a portfolio of 20 stocks to go down that much, especially if they are selected at random. If the stocks are selected from a variety of industries, company sizes and types (such as some growth stocks and some value stocks) it is still less likely. Types of Portfolio Diversification 1. Horizontal Diversification You might want to diversify your investments in different asset classes like equity (mutual funds, stocks), Real estate, Debt products, commodities like gold, silver and finally Cash. Its important to do this kind of diversification if you are not an expert in one asset class and cannot handle it fully. 2. Vertical Diversification When you invest your money in one asset class but in different kind of instrument or company, you are diversifying it across various instruments of same types. A very simple example is opening Fixed Deposits in various banks. If you had to open a 10 lacs FD, the chances are you will choose 4 banks and put 2.5 lacs in each rather than doing it for 10 lacs in just one bank. In the same way someone investing in 5 different equity mutual funds. While the underlying asset class is exactly same (equities), but still some kind of diversification is there (different fund managers handling it). 3. Geographical Diversification Then you can diversify location wise or geography wise. You can invest in real estate in India, US, UK. You can also invest in real estate across different cities within India. You can buy stocks in Indian stock market, US stock markets and other countries too. The idea is to take advantage of currencies fluctuations too, but this is only for experts who understand that. 4. Diversification across Market Capitalization When you invest in mutual funds, you can choose to invest in small cap funds, large cap funds, extra-large cap funds, small companies, big companies, etc. Note that the 179

risk and return potential will be different and anyways you will invest in different companies. 5. Time Diversification Your investments can be across time also, like long term investments, short term investments, medium term investments, You can have a 5 yrs deposit, 2 yrs deposit and 6 months deposit as well. Imagine if you have done 5 yrs deposits only – which can affect your liquidity. 3.3.2. Diversifiable/Unsystematic and Non-diversifiable/Systematic/Market Risk There are several factors which cause variations in return – price or dividend / interest. We have seen that some of these factors are internal to the firm and are controllable and some other factors are external to the firm which cannot be controlled. The total variability in return can thus be divided into two parts: 1) Un systematic Risk or controllable risk and 2) Systematic Risk or uncontrollable risk. Un systematic Risk is the risk that is unique to a firm or an industry. Factors like prudent management, labour unrest, economies of scale type of business etc., cause variability in returns of a company. Of the various sources of risk like financial performance risks. Business Risk, Financial Risk and Management Risk are the risks having an impact on a firm hence financial planner must examine these risks separately. The unsystematic risk inherent in a security or a portfolio can be reduced by spreading the investment of the portfolio over a larger number of securities or types of investments. Spreading risk in this way is referred to as diversification. At any given time, some of the investments may do well, some not so well, but they will probably not all do badly if they are spread over a diverse range of investment types. This is because different sectors, and industries within sectors, will be affected to different degrees by a range of factors including the vagaries of the economy, weather, politics, the industrial relations management style etc. The risk specific to individual securities is called diversifiable risk because it may be diversified away by picking and choosing securities which are negatively correlated. The level of risk of a portfolio can be reduced by diversification only up to a point; at that point further diversification will in fact cause very little additional risk reduction. Some research has indicated that the appropriate number of stocks to eliminate most diversifiable risk in a portfolio of shares is around 20. In fact, unsystematic or unique risk can be reduced to zero. In case of two securities, optimum weight of securities is equal to: Wx= y /( x  y ) where  x = Standard deviation of X Wy= 1 – Wx  y = Standard deviation of Y p = Correlation coefficient between X and Y Wx = Proportion of funds in X 180

Figure: Risk reduction by diversification Notice that risk reduces quite sharply in the early stages of diversification, but it will not fall below some base level, which is the risk associated with the share market in general commonly known as systematic risk or market risk. Have you ever wondered why the price of a share fluctuates widely when there is no change in its earnings? You may have also noticed the falling of share price despite an impressive growth reported by the company. Why does this happen? There may be several reasons for such a fluctuation, but mainly it is due to the movement in the overall market in general. Political uncertainty, war fears, monetary and fiscal policy changes inflationary conditions etc., are some of the reasons that could be attributed to the gloomy market outlook. Generally, most of the stocks move up or go down along the market, reflecting the market impact of these factors which have a common influence on all of the stocks. The variability in the returns caused by such movements are known as systematic risk and this risk cannot be diversified. The more obvious sources of risk that can be identified and researched include the following: Market Risk Market risk is the risk of capital loss caused by the market cycles such as those experienced quite dramatically in the stock market and to a lesser extent the property market. This definition could also be extended to cover systemic risk—the risk that losses may occur, due to the failure of the market system. Market risk is the risk faced by all of the entities in the market, It is uniform as well as inevitable. Business Risk It is a specific risk associated with the functioning of business of enterprises. Lot of factors effect functioning of business. Business risk is the risk that investment results may be disappointing or there could be loss of income or capital brought about by inefficient management, bad trading policies, lack of adequate long-range planning, changes affecting a particular industry, changing government legislation, business cycles, and so on. The uncertainty faced by an investor increases when there is an uncertainty about profit flows from business. For example, Computer software business may have more fluctuating fortunes and therefore riskier than cement or steel business when exchange rate of foreign currency is fluctuating. Financial Risk Two corporates from steel industry may have same business risk but a company with huge borrowings will have an additional risk of default as financial Risk. Financial risk is the risk of loss, including partial or complete loss of invested capital in the event of the failure of a company or any scheme resulting from an unsound financial structure. High amount of borrowed financing increases uncertainty of net returns available to equity shareholders because the Interest on loans have to be paid before any dividend is paid to equity investors. 181

Interest Rate Risk: Another type of risk, which does affect securities such as government bonds, arises from interest rate fluctuation and is commonly termed interest rate risk. If you purchase a bond with a yield of 12 per cent and interest rates rise to 14 per cent, you will in effect suffer a capital loss. To illustrate, a bond with a face value of ₹1000000 and an interest rate of 12 per cent will provide a return of ₹120 000. If interest rates were to rise to 14 per cent, an investor would only need to invest ₹857 143 to achieve the same amount of return. When Government bonds are earning 14 per cent; investors will purchase the 12 per cent bonds only if the price of the 12 per cent bonds is lower. In effect, the result will be a capital loss for those who bought bonds at 12 per cent. This will find expression in the value of that security in the secondary, where the price shall fall to adjust for the increase in the interest rate. Re-investment Risk Another risk that needs to be considered is ‗re-investment‘ risk. This risk occurs when financial instruments have a specific maturity date, which is earlier than that of the Investors‘ holding period. When they mature, the investor has to invest elsewhere and he may not be able to achieve as high a return as he received on the previous investment. For example: if a client purchased a debenture worth ₹10 000 that was paying 8 per cent on issue and held it to maturity, they would have received an 8 per cent return plus the repayment of the initial investment of ₹10 000. If, however, the interest rate had dropped after the purchase but before the investors‘ holding period, he may only be able to reinvest his ₹10 000 at 6 per cent. The same amount of money now is generating a lower income stream. The presence of such reinvestment risk in even Treasuring securities of shorter maturity than the Investors‘ holding period means that these securities do not qualify as risk free asset. Purchasing Power Risk (Inflation risk) Purchasing power risk refers to the impact of inflation on an investment. That is, investors expect a higher rate of return on the investments, should they expect the prices of goods and services go up. This is because of the simple reason that the purchasing power goes down in an inflationary period and unless the returns go up, the real rate of return earned on an investment would come down. For instance, if the required real rate of interest is 4% and the expected inflation in a year‘s time is 2%, the nominal rate of return should be at least 6% Liquidity Risk: The inability to acquire or dispose off an investment at a short notice without substantial loss of price is known as liquidity Risk. Liquidity risk, is, therefore the risk that the investments are not purchasable / saleable at a reasonable price within a reasonable time. Generally, Government securities can be bought and sold at a price almost equal to the quoted price and thus have no liquidity risk. But, investment in an antique, a painting etc., may require a long time to find a buyer. Some corporate bonds too may be illiquid and therefore may be sold at lower price than their worth. Generally, impact cost and turnover of security measure the liquidity. 182

Exchange Rate Risk: Exchange Risk refers to uncertainty about the rate at which foreign currency can be exchanged. Exchange rate risk arises when the investments are bought and sold around the world. An Indian investor who buys an American security denominated in dollars gets exposed to two types of risk: 1) the uncertainty of the return on dollar investment and 2) the uncertainty of return when the dollars are converted in to rupee. If the dollar weakens against the rupee, like now, the total return on the investment shall go down even if the dollar returns on the security remain same. Information Risk: Information risk is the risk that the information on a particular investment may not be accurate (this may be brought about by deliberate misstatements by those promoting the investment or just by plain bias). Political Risk Political risk arises due to some government restrictions. It refers to uncertainty about the ability of an investor to convert the foreign currency investment in to domestic currency. It arises for example; government might restrict, tax or completely prohibit the exchange of one currency into another from changes in governments and changes in government policies. Management Risk Management quality is an important attribute to be analysed while purchasing securities. Clients also need to understand that where a fixed interest rate security bonds agrees to pay-back face value, For ex, collective investment such as a unit trust, the manager may actively buy and sell securities. The skill of the manager will determine whether the total result of their activities achieves a capital gain or loss over any specific period for the mutual fund. There exists a risk of management of these funds entrusted to the stewardship of the fund manager of the mutual fund or collective investment scheme. Alpha (Investment Manager) Risk Alpha measures the performance of the portfolio manager or mutual fund manager. A change in effect of the portfolio manager causes a risk of higher returns. ‘Risk-free’ investments: While investment in better quality loan securities such as government or semi-government and bank-backed bonds may be considered reasonably safe, investment in other areas will tend to have an increased level of risk. It is worth pointing out, however, that the type of security being considered may not be relevant in assessing this risk. Investment in the ordinary shares of a large, well-managed public company may carry less risk than investment in the debentures of some finance companies. (Debentures are secured loans to companies for fixed terms.) Further, the level of business risk will vary in every individual case and each should be assessed separately from other investments in its class. Despite interest rate risk, government securities are often referred to as ‗risk-free‘, in that the security of the capital over the time of the investment is assured, that is, interest payments will be received on a regular basis without default and the face value of the security will be certainly received at maturity. However, these government risk free securities too are exposed to the price fluctuations owing to the interest rate changes in the economy. The 183

chance of a major government defaulting on repayment is minimal. These securities are therefore used as a basis for determining a ‘risk-free’ rate of return in an economy at a certain time. Generally short term T-bill rates are used as proxy for risk-free rates. Regulatory Risk The risk arising out of regulatory changes in the economy referred to as regulatory risk. Measurement of Systematic and Unsystematic Risks It is useful to distinguish between risk that relates to all securities in the market and risk which is specific to individual securities. Because it helps better understanding of the return - whether returns are due to systematic risk or due to diversifiable risk. Systematic and unsystematic risks are quantified by regressing returns on a security on returns on an index. Note that index is a representative of market movements (index computation and its usage is covered in Topic 3. Let us now analyse the riskiness of securities in terms of systematic and unsystematic components. Regression model shows that the return on any security is related to the return on the market index in a linear fashion. It is also for a single index model Ri = a + βi RM + e where Ri is the return on the security, a is the estimated return on the security when the market is stationary, β is the measure of systematic volatility, it is also knon as beta of the security e is the random error term embodying all of the factors that together make up unsystematic return. β (beta) measures how rapidly and consistently a security‘s return moves up and down with the market. The β (beta) coefficient of the market index is, by definition, 1. Securities having b values more than one are considered as aggressive or high risk securities while those with a b less than one are known as defensive or less risk securities. The total variance of the return on stock σ2 is equal to the sum of the variances associated with various factors in the return formula shown above. Since ‗a‘ is constant, its variance is zero. Thus σ2 (Ri) = β2σ2(Rm) + σ2(ei) β2σ2(Rm) is the measure of security‘s systematic risk and σ2(ei) is a measure of unsystematic risk. Example: Let us consider the following data of ABC Ltd. to calculate systematic and unsystematic risks. Month Index return (x) Variance XY X2 Y2 Stock return (Y) February 0.30 3.80 4.00 3.61 March 2.0 1.9 115.52 62.92 27.04 146.41 April 2.10 3.64 1.69 7.84 5.2 12.1 184 1.3 2.8

May 5.1 0.3 1.11 1.53 26.01 0.09 117.77 -12.35 1.69 90.25 June 1.3 -9.5 9.91 13.05 8.41 20.25 39.01 4.90 1.00 24.01 July 2.9 4.5 42.93 9.88 3.61 27.04 74.78 31.00 9.61 100.00 August -1.0 -4.9 20.68 -15.34 6.76 34.81 5.99 6.08 2.56 14.44 September -1.9 -5.2 2.08 1.69 2.56 4.20 17.64 October 3.1 10.0 13.02 1.0 17.64 1.29 9.61 18.49 November -2.6 5.9 0.14 0.09 0.01 42.84 1.96 46.24 December 1.6 3.8 15.20 39.69 90.25 10.98 2.56 37.21 January -1.3 -1.6 8.72 33.37 3.24 22.09 50.41 10.89 February -1 -4.2 30.83 1.65 0.25 46.24 0.68 0.01 4.00 March -3.1 -4.2 30.83 -0.20 0.01 782.01 234.36 202.90 April 0.3 4.3 8.69 May 1.4 0.1 1.57 June -6.3 -6.8 66.46 July 1.6 9.5 66.39 August 1.8 6.1 22.54 September 7.1 4.7 11.21 October -0.5 -3.3 21.64 November 0.1 6.8 29.68 December 0.1 -2.0 11.24 Total 17.2 31.1 739.9 Total number of observations = 23 Mean return on index = 0.748 Mean return on Stock = 1.352 Total variance = 32.17   nXY  X Y nX2  X2 =1.11 Y  X 0.52 e2   Y2   Y   XY  21.97 n 185

This is a high risk security or aggressive stock with a Beta value more than 1.0 the unsystematic risk of the security is also very high. Let us take another example to explain how total variance (or risk) can be divided into systematic and unsystematic risks: Year Security Return(%) Index return (%) 1 6 20 2 5 40 3 10 30 =7 30 Average 66.7 Variance from average =4.7 Correlation coefficient -.189 Coefficient of =0.0357 determination You can easily observe that when the index returns goes up (down), the security‘s return generally goes down (up) and results in negative correlation coefficient (r) between the security and the overall market. The coefficient of determination (r2) is the percentage of the variation of the security‘s return that is explained by the variation in the return of the index. Only about 3.5% of the variation of the security‘s return is explained by the index, remaining 96.5% is not. Variation explained by the index could be referred to as the systematic risk. The unexplained variance is called the residual variance, or unsystematic risk which is unique to the security. The systematic risk for an individual security can be given as Systematic risk = β2 (Variance of index) = 0.17 Unsystematic risk (e2) = (Total variance of security return) - (Systematic risk) =4.7 – 0.17 =4.53 Then Total risk = β2 = 0.17 +4.53 = 4.7 If an investor (or yourself as a financial planner) is in a position to estimate the expected return on an index, it is possible to, in turn, estimate any security‘s return. Note that the underlying assumption is that the values of alpha and beta for the security are stable. For example, assume that the return on the index is expected to be 25%. Calculated value of alpha is 8.5 and beta is –0.05 and the estimate of index is 25. The expected return on the stock is 8.5 – 0.05*25 =7.25 For portfolios, we need the weighted average of the estimated return for each security in the portfolio. The weights will be the proportions of the portfolio devoted to each security. For each security, we will require alpha and beta estimates. One estimate of the index (I) is needed. Thus 186

RPN  Xi i  iI where all terms are as explained earlier, except that Rp is the expected portfolio return, Xi is the proportion of the portfolio devoted to stock I and N is the total number of stocks. Example 2 Monthly return (in percent ) Are presented below for ITC stock and BSE National Index for a 12 month period month ITC BSE National Index 1 9.43 7.41 2 -5.33 3 0 -7.35 4 -4.31 -14.64 5 -18.92 1.58 6 -6.67 15.19 7 26.57 5.11 8 0.76 9 20 -0.97 10 2.93 10.44 11 5.25 17.47 12 21.45 20.15 23.13 49.82 total 32.83 111.69 Calculate Beta of ITC Stock Answer :- Correlation coefficient is calculated with following formula : R = formula Where :- X= One Data Series ( Rm) Y= Other Data Series ( Rj) N=Number of items 187

Calculations of correlations coefficient month ITC BSE National Index Y2 X2 XY 1 9.43 7.41 88.9249 54.9081 69.8763 2 -5.33 28.4089 3 0 -7.35 0 54.0225 0 4 -4.31 -14.64 18.5761 214.3296 31.6785 5 -18.92 1.58 357.9664 2.4964 276.9888 6 -6.67 15.19 44.4889 230.7361 -10.5386 7 26.57 5.11 705.9649 26.1121 403.5983 8 0.76 0.5776 9 20 -0.97 400 0.9409 102.2 10 2.93 10.44 8.5849 108.9936 2.2268 11 5.25 17.47 27.5625 305.2009 -5.0925 12 21.45 20.15 460.1025 406.0225 223.938 23.13 49.82 534.9969 1432.749 404.0811 total 32.83 1077.809 661.5245 111.69 3724.977 2160.481 ∑XY = 2160.481 ∑ Y=111.69 n=12 ∑X=49.82 X2=1432.749 Y=∑Y/n =111.69/12 =9.31 X= ∑ X/n = 49.82/12 =4.15 Formula   nXY  X Y nX2  X2 = (12*2160.49)-(49.82*111.69) / (12*1432.75)-(49.82)2 = 25925.88 -5564.40 / 17193- 2482.03 = 20361.48 / 14710.97 β=1.384 α= y- βx = 9.31- (1.384*4.15 ) = 9.31-5.74= 3.57 188

3.3.3. Nature of Products used for Diversification When it comes to investing, savvy money managers advise that you spread your money around -- that is, \"diversify\" your investments. Diversification protects you from losing all your assets in a market swoon. The sharp decline in stock prices in recent years are proof enough that putting all your eggs in one basket is a risky strategy. But in order to diversify correctly, you need to know what kinds of investments to buy, how much money to put into each one, and how to diversify within a particular investment category. Having a lot of investments does not make you diversified. To be diversified, you need to have lots of different kinds of investments. That means you should have some of all of the following: stocks, bonds, real estate funds, international securities, and cash. Investments in each of these different asset categories do different things for you.  Stocks help your portfolio grow.  Bonds bring in income.  Real estate provides both a hedge against inflation and low \"correlation\" to stocks -- in other words, it may rise when stocks fall.  International investments provide growth and help maintain buying power in an increasing globalized world.  Cash gives you and your portfolio security and stability. Though diversification protects you from devastating losses, it also costs you in average annual returns. That's because risk and reward go hand-in-hand in the financial markets. So anything that reduces your risk will also reduce your return. Give yourself permission to take a little risk, unless you're close enough to retirement that the additional security is particularly valuable. 3.3.4. Time Diversification When focusing on risk it is important to consider the time horizon of the investment. Table 1.1 looks at four different portfolios over a range of years. Each portfolio is at different risk levels, with A being the least risky and D is the most. risky portfolio. Portfolio A contains mainly low-risk investments such as government securities and shares of some major blue chip companies. Sometimes known as a capital stable investment. Portfolio B contains a diversified mixture of shares and fixed interest-paying investments such as term deposits. It is known as a balanced investment with low risk. Portfolio C contains a diversified mixture of shares, units in property trusts and high- interest yielding securities such as mortgage investments. This kind of portfolio is known as a balanced investment with higher returns. Portfolio D contains property investments and shares in mining and exploration companies. It is referred to as a growth investment and contains a high element of risk because the 189

ranges of returns are form - 13% to 39%. Risk Forecasts for Several Portfolios Overtime Ranges of Possible Returns % Per Annum Time horizon Portfolio A Portfolio B Portfolio C Portfolio D 1 Year .05 to 16.0 -6.7 to 23.3 -8.1 to 31.4 -13 to 39 3 Year 2.0 to 12.5 0.1 to 18.4 -1.8 to 22.4 5 Year 3.5 to 11.5 2.8 to 16.4 0.4 to 19.7 -3.1 to 26.4 -0.2 to 22.1 The above Table shows a range of possible percentage returns for each time horizon. As the portfolios become more risky, the range of possible returns increases. For example, the low risk Portfolio A has a range of possible returns from –0.5 to 16% within one year, whereas Portfolio D has a range from –13 to 39% for the same period. It is important to note that due to the increase in the risk for each portfolio, an investor would want a higher return as a compensation for high risk. Looking at the range of expected returns for each of the four portfolios, you can see the advantage of taking a long-term perspective. Portfolio B, for example, runs the risk of a 6.7% loss if held for only one year, while the maximum expected gain for the portfolio over the same period is 23.3%. Extending the time horizon eliminates the risk of a loss over the total time period while still offering high returns if all goes well. For example, if portfolio B is held for 5 years, an investor can expect a minimum return of 2.8% and also has a chance of making 16.4% per annum. The longer time horizon allows any negative returns from higher risk investments such as shares in any one year to be offset by positive returns in other years, It one holds on the investment for long period of time when while interest income and other more predictable returns provide a smoothing effect. This long-term perspective works for well chosen, diversified portfolios. It does not mean that any/all securities, if held for a long time, will always produce positive results. 190