‘Portfolio theory and the capital asset pricing model (CAPM) are essential tools for portfolio managers and other stock market investors’ In order to be successful, an investor must understand and be comfortable with taking risks. Creating wealth is the object of making investments, and risk is the energy that in the long run drives investment returns. PORTFOLIO THEORY Modern portfolio theory has one, and really only one, central theme: “In constructing their portfolios investors need to look at the expected return of each investment in relation to the impact that it has on the risk of the overall portfolio”.

The practical message of portfolio theory is that sizing an investment is best understood as an exercise in balancing its expected return against its contribution to portfolio risk- In an optimal portfolio this ratio between expected return and the marginal contribution to portfolio risk of the next pound invested should be the same for all assets in the portfolio Unfortunately, many investors are not aware that such insights of modern portfolio theory have direct application to their decisions.

Too often modern portfolio theory is seen as a topic for academia, rather than for use in real-world decisions. For example, consider a common situation: When clients of a firm decide to sell or take public a business that they have built and in which they have a substantial equity stake, they receive very substantial sums of money. Almost always they will deposit the newly liquid wealth in a money market account while they try to decide how to start investing. In some cases, such deposits stay invested in cash for a substantial period of time.

Often investors do not understand and are not comfortable taking investment risks with which they are not familiar. Portfolio theory is very relevant in this situation and typically suggests that the investor should create a balanced portfolio with some exposure to public market securities (both domestic and global asset classes), especially the equity markets. MODERN PORTFOLIO THEORY EXAMPLE Imagine you are investing in a tiny country that has only two industries and two seasons. It has an alpine resort and a beach club.

When the weather is good, the beach club does well, and when the weather is bad, the alpine resort booms. The returns for the two resorts are: |Weather | |Alpine resort |Beach Club | |Good Weather | |-30% |60% | |Bad Weather | |60% |-30% |

If the probability of a particular season having good or bad weather is one in two, investing in the alpine resort would produce return of 60% half the time, and -30% half the time, giving an average, or expected return, of 15%; the same is true for investing in beach club. It would be risky, though, to invest in only one of the resorts because there might be many seasons one after other with the same weather, just as you might get a long row of head when flipping a coin. If you invested ? 100 in each of the resorts, your result over five seasons might be as followed Season |Alpine Resort |Beach club | | | | | | | |Good |-30 |60 | | |Bad |60 |-30 | | |Bad |60 |-30 | | |Bad |60 |-30 | | |Bad |60 |-30 | | |Total |210 |-60 |=150 | You have lost ? 60 on the beach club, but made ? 10 on the alpine resort, giving you an overall return on your ? 200 investment of ? 150. If you had invested all of you’re the whole ? 200 in the alpine resort, you would have made ? 420. if you had invested the whole ? 200 in the beach club, you would have lost ? 120 of your capital, leaving you with only ? 80 to re-invest-it would take time to get your money back to its original level, and if you attempted to do so by investing again in only one of the two resorts, you might well make a further substantial loss. Thus, the argument for spreading the risk is very strong. The two resorts have negative covariance. Here is the formula for calculating covariance:

Lets Ag and Ab be the actual return from alpine resort in good and bad weather respectively, and A be the expected return (average), Bg and Bb be the actual return from the beach club and B the expected return: The covariance between A and B = COVAB = Probability of good weather (Ag – A)(? g – ? ) + probability of bad weather (Ab- A)(Bb-? ) In my example, the probability of good or bad weather are both 0. 5, so: COVAB = [0. 5(-30-15)(60-15)] + [0. 5(60 – 15)(-30-15)] =0. 5(-45 * 45) + 0. 5(45 * -45) =-0. 10125 + – 0. 10125 = -0. 2025 In real life, however, stocks tend to move up and down together, so it is rare to find a perfect opportunity to eliminate risk. It is possible, though, to reduce risk by investing in shares with a low covariance or, better still, a negative covariance.

This is called diversification, and can be achieved by investing across a wide number of industries and countries. THE CAPITAL ASSET PRICING MODEL The Capital Asset Pricing Model is part of a larger body of economic theory known as capital market theory (CMT). CMT also includes security analysis and portfolio management theory, a normative theory that describes how investors should behave in selecting common stocks for their portfolios, under a given set of assumptions. In contrast, the CAPM is a positive theory, meaning it describes the market relationships that will result if investors behave in the manner prescribed by portfolio theory. The CAPM is a conceptual cornerstone of modern capital market theory.

Its relevance to business valuations and capital budgeting is that businesses, business interests, and business investments are a subset of the investment opportunities available in the total capital market; thus, the determination of the prices of businesses theoretically should be subject to the same economic forces and relationships that determine the prices of other investment assets. ASSUMPTIONS UNDERLYING THE CAPITAL ASSET PRICING MODEL Eight assumptions underlie the CAPM: 1. Investors are risk averse. 2. Rational investors seek to hold efficient portfolios, that is, portfolios that are fully diversified. 3. All investors have identical investment time horizons (i. e. , expected holding periods). 4.

All investors have identical expectations about such variables as expected rates of return and how capitalization rates are generated. 5. There are no transaction costs. 6. There are no investment-related taxes. (However, there may be corporate income taxes. ) 7. The rate received from lending money is the same as the cost of borrowing money. 8. The market has perfect divisibility and liquidity (i. e. , investors can readily buy or sell any desired fractional interest). The extent to which these assumptions are or are not met in the real world will have a bearing on the application of the CAPM for the valuation of closely held businesses, business interests, or investment projects.

For example, while the perfect divisibility and liquidity assumption approximates reality for publicly traded stocks, the same is not true for privately held companies. This is one reason why the company-specific, non-systematic risk factor may be rewarded in expected returns for closely held companies, even if it is not for public companies. The CAPM, like most economic models, offers a theoretical framework for how certain relationships would exist subject to certain assumptions. Although not all assumptions are met in the real world, the CAPM provides a reasonable economic model for estimation of the cost of capital. Other models are discussed in later chapters. THE CAPITAL-ASSET PRICING MODEL (CAPM) EXAMPLE You have ? 00,000 to invest and you decide to work out the expected return from four choices: 1. A risk-free investment in bank deposit 2. An investment of half your money in the stock market and the other half risk-free 3. Investing the whole sum in a portfolio with a beta in line with that of the market average 4. investing in high risk portfolio You find that you can get 5% interest from bank deposit, and that the market average return is 8%. Choice 1: Your expected return is the interest rate the bank gives you, i. e. 5%, or ? 5,000. Remembering that no investment is completely risk-free; in the UK, for example, only 75% of a deposit at a major bank is protected if the bank collapses.

Short of a major crisis, however, it is argued that it is reasonable to describe such an investment as risk-free, although inflation will eat into the capital and the interest. Choice 2: You decide to put ? 50,000 in a portfolio with a beta of 1, and the rest in a bank. Using the expected return formula, the expected rate of return = 5% + 0. 5(8% – 5%) = 6. 5%. note that although the portfolio has a beta of 1, you have only invested 50% of your money, so you must halve the beta value. Choice 3: You invest all the money in a portfolio with a beta of 1; your expected rate of return will therefore be in line with the market average, 8% Choice 4: You invest in a portfolio with a beta of 2. , which should generate higher returns; expected rate of return = 5% + 2. 5(8% – 5) = 12. 5% Beta is an officially approved way of measuring risk, and you can obtain estimates of the beta of a stock from broker and investment advisers. Beta measures the sensitivity of excess total returns (total returns over the risk-free rate returns) on any individual security or portfolio of securities to the total excess returns on some measure of the market, such as the New York Stock Exchange (NYSE) Composite Index. The table below shows, the beta for the market as a whole is 1. 0. Therefore, from a numerical standpoint, the beta has the following interpretations: |Beta > 1. |When market rates of return move up or down, the rates of return for the subject tend to move in the same| | |direction and with greater magnitude. For example, for a stock with no dividend, if the market is up 10%,| | |the price of a stock with a beta of 1. 2 would be expected to be up 12%. If the market is down 10%, the | | |price of the same stock would be expected to be down 12%. Many high-tech companies are good examples of | | |stocks with high betas. | |Beta = 1. 0 |Fluctuations in rates of return for the subject tend to equal fluctuations in rates of return for the | | |market. | |Beta < 1. |When market rates of return move up or down, rates of return for the subject tend to move up or down, but| | |to a lesser extent. For example, for a stock with no dividend, if the market is up 10%, the price of a | | |stock with a beta of . 8 would be expected to be up 8%. The classic example of a low-beta stock would be a| | |utility that has not diversified into riskier activities. | |Negative beta (rare)|Rates of return for the subject tend to move in the opposite direction from changes in rates of return | | |for the market. Stocks with negative betas are rare. A few gold-mining companies have had negative betas | | |in the past. |

To illustrate, using the preceding formula as part of the process of estimating a company’s cost of equity capital, consider stocks of average size, publicly traded companies i, j, and k, with betas of 0. 8, 1. 0, and 1. 2, respectively; a risk-free rate in the market of 7% (0. 07) at the valuation date; and a market equity risk premium of 8% (0. 08). For company i, which is less sensitive to market movements than the average company, we can substitute in the table above, as follows: [pic] Thus, the cost of equity capital for company i is estimated to be 13. 4% because it is less risky, in terms of systematic risk, than the average stock on the market. For company j, which has average sensitivity to market movements, we can substitute in the table above, as follows: [pic]

So the cost of equity capital for company j is estimated to be 15%, the estimated cost of capital for the average stock, because its systematic risk is equal to the average of the market as a whole. For company k, which has greater-than-average sensitivity to market movements, we can substitute in table above, as follows: [pic] Thus, the cost of equity capital for company k is estimated to be 16. 6% because it is riskier, in terms of systematic risk, than the average stock on the market. Note that in the preceding pure formulation of the CAPM, the required rate of return is composed of only two factors: 1. The risk-free rate 2. The market’s general equity risk premium, as modified by the beta for the subject security USING BETA TO ESTIMATE EXPECTED RATE OF RETURN

The CAPM leads to the conclusion that the equity risk premium (the required excess rate of return for a security over and above the risk-free rate) is a linear function of the security’s beta. This linear function is described in this univariate linear regression formula: [pic] The preceding linear relationship is shown schematically in graph below, which presents the security market line (SML). Graph: Security Market Line [pic] According to capital asset pricing theory, if the combination of an analyst’s expected rate of return on a given security and its risk, as measured by beta, places it below the security market line, such as security X in graph, the analyst would consider that security (e. g. , common stock) mispriced. It would be mispriced in the sense that the analyst’s expected eturn on that security is less than it would be if the security were correctly priced, assuming fully efficient capital markets. To put the security in equilibrium according to that analyst’s expectations, the price of the security must decline, allowing the rate of return to increase until it is just sufficient to compensate the investor for bearing the security’s risk. In theory, all common stocks in the market, in equilibrium, adjust in price until the consensus expected rate of return on each is sufficient to compensate investors for holding them. In that situation the systematic risk/expected rate of return characteristics of all those securities will place them on the security market line.

The Capital Asset Pricing Model expands on the build-up model by introducing the beta coefficient, an estimate of systematic risk, the sensitivity of returns for the subject to returns for the market CONCLUSION Many brokers will tell you that new technique for predicting the market may work for sometime, but as more and more people catch on to them they will become less effective. Most of the theories have probably been effective at one time or another in the history of stock market. The paradox is that the market seems to be protected against the monopoly of one method in the long term by its own nature – if its works, everyone including the managers will start doing it and it will stop working.

However, after completing the reports, I came to conclusion that CAPM and Portfolio theory are the essential tools for the managers and other investors if they study and are aware of the calculation because its all mathematics and many individuals do not understand at all. Also I mentioned above that these calculations in today’s world individuals do not follow it properly as they consider them to be part of the studies rather than implying on the real-life. Individuals or investor should seek the broker or advisors to be successful in investing. Reference: “How the stock market really works” Leo Gugh 1997 “How to win a volatile stock market” Alexander Davidson 2nd Edition 2002 “Investing In stocks & shares” Dr. John White 5th edition 2000 Graph reference already under the graph. Words: 2200

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