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Unformatted text preview: TBS 907 Financial Strategy AUTUMN 2005 MODULE 2 RISK AND RETURN MARKET EFFICIENCY 1 Return There is uncertainty associated with returns from shares. Return is defined as total loss or gain experienced by an investor over a given period of time. Return is calculated by dividing the assets change in value plus any cash distributions ( dividends) during the period by its beginningofperiod investment value. Assume we can assign probabilities to the returns expected, given an assumed set of circumstances. E( R) = R P
i =1 n i i 2 Expected Return Calculation Distribution of returns for security Return Probability 0.09 0.1 0.10 0.2 0.11 0.4 0.12 0.2 0.13 0.1 Expected return = (0.09 0.1) + (0.10 0.2) + (0.11 0.4) + (0.12 0.2) + (0.13 0.1) = 0.11 or 11.0 per cent
Risk is present whenever investors are not certain about the outcome an investment will produce. Risk is defined as the chance of financial loss or more formally the variability of returns associated with a given asset. Risk is measured in terms of how much a particular return deviates from an expected return (variance or standard deviation): = ( Ri - E ( Ri ) ) Pi
2 2 i =1 n Standard deviation is the square root of the variance and is the most common indicator's of an asset's risk. It measures the dispersion around the expected value. 4 Risk Calculation Calculation of the risk associated with security S: = (.0 9 - .1 1 ) 2 (.1 ) + (.1 0 - .1 1 ) 2 (.2 ) + (.1 1 - .1 1 ) 2 (.4 ) + (.1 2 - . 1 1 ) 2 (.2 ) + (.1 3 - .1 1 ) 2 (.1 ) = .0 0 0 1 2 5 = 1 .0 9 5 % (standard deviation) Risk Attitudes The marketplace is made up of investors with different expectations as to the income and risks they are prepared to take to get those returns. Riskneutral investor: Riskaverse investor: one who neither likes nor dislikes risk one who dislikes risk one who prefers risk Riskseeking investor: 6 Risk Attitudes (cont.) The standard assumption in finance theory is riskaversion. This does not mean an investor will refuse to bear any risk at all. Rather an investor regards risk as something undesirable, but which may be worth tolerating if compensated with sufficient return.
7 Risk of Assets and Portfolios Investors usually invest in a number of assets (a portfolio) and will be concerned about the risk of their overall portfolio. 8 Portfolio Theory Assumptions Investors perceive investment opportunities in terms of a probability distribution defined by expected return and risk. Investors' expected utility is an increasing function of return and a decreasing function of risk (risk aversion). Investors are rational.
9 Measuring Return for a Portfolio
Portfolio rate of return = fraction of portfolio rate of return + x in second asset on second asset ( ( fraction of portfolio in first asset )( )(
x rate of return on first asset ) )
10 Portfolio Risk
Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is:
Expected Return = (.60 10) + (.40 15) =12% 11 Measuring Risk
Variance Average value of squared deviations from mean. A measure of volatility. Standard Deviation Average value of squared deviations from mean. A measure of volatility. Measuring Risk
Diversification Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk Risk factors affecting only that firm. Also called "diversifiable risk." Market Risk Economywide sources of risk that affect the overall stock market. Also called "systematic risk."
13 Measuring Risk
Portfolio standard deviation 0 5 10 15 Number of Securities 14 Measuring Risk
Portfolio standard deviation Unique risk Market risk 0 5 10 15 Number of Securities 15 Relationship Measures Covariance Statistic describing the relationship between two variables. If positive, when one of the variables takes on a value above its expected value, the other has a propensity to do the same. If the covariance is negative, the deviations tend to be of an opposite sign. 16 Relationship Measures (cont.) Correlation coefficient describes the goodness of fit about a linear relationship between two variables. The correlation is equal to the covariance divided by the product of the asset's standard deviations. xy
cov( x, y ) = x y It is simply a standardisation of the Cov and for this reason is bounded by the range +1 to 1. 17 Portfolio Risk
The variance of a two stock portfolio is the sum of these four boxes Stock 1 Stock 1 Stock 2
2 2 x 1 1 Stock 2 x 1x 2 12 = x 1x 2 12 1 2 x 2 2 2 2 x 1x 2 12 = x 1x 2 12 1 2 18 Portfolio Risk
Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. Exxon - Mobil
2 2 Exxon - Mobil x1 1 = (.60) 2 (18.2) 2 Coca - Cola x1x 2121 2 = .40 .60 1 18.2 27.3 x 2 2 = (.40) 2 ( 27.3) 2 2 2 Coca - Cola x1x 2121 2 = .40 .60 1 18.2 27.3 19 Portfolio Risk
Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. Portfolio Variance = [(.60) 2 x(18.2) 2 ] + [(.40) 2 x(27.3) 2 ] + 2(.40x.60x18.2x27.3) = 333.9 Standard Deviation = 333.9 = 18.3 %
20 Portfolio Risk
Expected Portfolio Return = (x 1 r1 ) + ( x 2 r2 ) 2 2 Portfolio Variance = x 1 1 + x 2 2 + 2( x 1x 2 12 1 2 ) 2 2 21 Gains from Diversification The gain from diversifying is closely related to the value of the correlation coefficient. The degree of risk reduction increases as the correlation between the rates of return on 2 securities decreases. Combining two securities whose returns are perfectly positively correlated results only in risk averaging, and does not provide any risk reduction. 22 Gains from Diversification (cont.) Risk reduction occurs by combining securities whose returns are less than perfectly positively correlated. When the correlation coefficient is less than one, the third term in the portfolio variance equation is reduced, reducing portfolio risk. If the correlation coefficient is negative, risk is reduced even more. 23 Diversification with Multiple Assets (cont.) For a diversified portfolio, the variance of the individual assets contributes little to the risk of the portfolio. The risk depends largely on the covariances between the returns on the assets. 24 Total risk = systematic + Systematic and Unsystematic Risk
unsystematic risk Systematic risk (marketrelated risk or nondiversifiable risk): that component of total risk that is due to economywide factors Unsystematic risk (diversifiable risk): 25 that component of total risk that is unique Systematic and Unsystematic Risk (cont.) Unsystematic risk is removed by holding a welldiversified portfolio. The returns on a welldiversified portfolio will vary due to the effects of marketwide or economywide factors. Systematic risk of a security or portfolio will depend on its sensitivity to the effects of these marketwide factors.
26 Risk of an asset is largely determined by the Risk of an Individual Asset in a Diversified Portfolio
covariance between the return on that asset and the return on the holder's existing portfolio : Cov Ri , R p = i , p i p ( ) Welldiversified portfolios will be representative of the market as a whole, thus the relevant measure of risk is the covariance between the return on the asset and the return on the market: Cov( Ri , RM ) 27 Beta A measure of a security's systematic risk, describing the amount of risk contributed by the security to the market portfolio. 28 Beta and Unique Risk
Market Portfolio Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta Sensitivity of a stock's return to the return on the market portfolio.
29 Beta and Unique Risk im Bi = 2 m 30 Beta and Unique Risk im Bi = 2 m
Covariance with the market Variance of the market 31 Construction of a Portfolio Construction of a Portfolio The opportunity set: the set of all feasible portfolios that can be constructed from a given set of risky assets Expected Return Risk 32 Construction of a Portfolio (cont.) The efficient frontier Given riskaversion, each investor will try to secure a portfolio on the efficient frontier. The efficient frontier is determined on the basis of dominance. A portfolio is efficient if: No other portfolio has a higher return for the same risk, or No other portfolio has a lower risk for the same return. 33 Construction of a Portfolio (cont.) Investors are a diverse group and, therefore, each investor may prefer a different point along the efficient frontier. Investor risk preferences will indicate the preferred portfolio on the efficient frontier. 34 The Pricing of Risky Assets What determines the expected rate of return on an individual asset? Risky assets will be priced such that there is a relationship between returns and systematic risk. Investors need to be sufficiently compensated for taking on the risks associated with the investment.
35 Security Market Line
Return Market Return = rm Risk Free Return = rf Risk .
Efficient Portfolio Security Market Line
Efficient Portfolio Risk Free Market Return = r Return = rf 1.0 BETA Security Market Line
Risk Free Return = rf Security Market Line (SML) BETA Security Market Line Return
1.0 BETA SML Equation = rf + B ( rm rf ) Capital Asset Pricing Model
R = rf + B ( rm - rf ) CAPM Portfolio Beta Calculated as a weighted average of the betas of the individual assets in the portfolio: p = wi i
i =1 n where n = number of assets in the portfolio wi = proportion of the current market value of portfolio p constituted by the i th asset
41 Efficient Market Hypothesis (EMH) EMH: that the price of a security (such as a share) accurately reflects the information available. If the market processes new information efficiently, the reaction of market prices to new information will be instantaneous and unbiased.
42 A NonInstantaneous Price Reaction An instantaneous price reaction would, in practice, mean that after new information becomes available it should be fully reflected in the next price established in the market. If the market often fails to react instantaneously, share traders can develop simple rules to generate excess profits. Simply purchase shares immediately a company makes an unanticipated announcement of good news. 43 A Biased Price Reaction Overreaction A biased response of a price to information in which the initial price movement can be expected to be reversed. A biased response of a price to information in which the initial price movement can be expected to continue.
44 Underreaction Categories of Capital Market Efficiency The EMH implies that investors cannot earn abnormal returns by using information that is already available. The market may be efficient with respect to some sources of information, but not with respect to others. 45 Categories of Capital Market Efficiency (cont.) Fama (1970) provided a useful classification of market efficiency: Weakform efficiency: the information contained in the past sequence of prices of a security is fully reflected in the current market price of that security. Semistrongform efficiency: all publicly available information is fully reflected in a security's current market price. Strongform efficiency: all information, whether public or private, is fully reflected in 46 a security's current market price. Categories of Capital Market Efficiency (cont.) The information content of each successive classification is cumulative. The implication of strongform efficiency is that an investor cannot earn abnormal returns from having inside information. If this were true, investors would have no incentive to seek information. Paradox: the capital market can be efficient only if at least some investors believe it to be inefficient. However, if the market is less than strongform efficient, there are incentives for investors to seek information. 47 Implications of the EMH Suppose that, notwithstanding the evidence on anomalies, the stock market is semistrongform efficient. investors in securities and for financial managers. Then there are clear implications for 48 Implications of the EMH for Investors in Securities Charting, or Technical Analysis Plotting a share's historical price record on a chart and then using this as the basis for predictions as to the likely future shortterm course of prices. However, the alleged benefits of this type of analysis are dubious.
49 Implications of the EMH for Investors in Securities (cont.) Fundamental Analysis Based on the belief that the market either ignores some publicly available information, or systematically misinterprets that information. Therefore, careful analysis of available information may reveal mispriced securities, and therefore excess returns can be made by the skilled fundamental 50 analyst. Implications of the EMH for Investors in Securities (cont.) Random Selection of Securities Whilst the EMH asserts that all securities are `correctly' priced, given the information available, this does not imply that investors should select their investments randomly. A randomlychosen portfolio is likely to have a similar risk to the market portfolio, however, this may not suit the risk preferences of the investor. Investors should also consider their tax position when selecting investments, which is unlikely to be suitable if investments are selected randomly. 51 Implications of the EMH for Investors in Securities (cont.) Buyandhold policies A strategy in which shares are bought and then retained in the investor's portfolio for a long period. An inflexible buyandhold policy is not optimal. Portfolio will need to be rebalanced at times because, as share prices change over time, so will the risk of the portfolio, possibly diverging from the investor's desired risk level. Some investors may also come upon private information about a company, which if acted upon, will yield excess returns. 52 Beating the Market Implications of the EMH for Investors in Securities (cont.) In a market which is semistrongform efficient, it is not sensible for the average investor to try to beat the market. Only if an investor has private information does beating the market become a possibility. Most investors should adopt a longterm view, hold a diversified portfolio and trade infrequently.
53 Implications of the EMH for Financial Managers Project Selection: If investing in a project really does increase the company's `true value', the company's share price should reflect this fact when the information becomes available to the market. Communicating with the stock market: Managers must expect that announcements will elicit a price response that represents the market's collective view of the true situation and is not a mechanical response. 54 Implications of the EMH for Financial Managers (cont.) Using share price as a measure of company performance In an efficient market, the current share price is the best available estimate of a company's `true value'. 55 Implications of the EMH for Financial Managers (cont.) Issuing new securities Pricing the security: If the market is efficient and new shareholders are charged the market price, the wealth of existing shareholders is not affected. The timing of new issues: If the market is efficient, shares will be priced correctly, given the current publicly available information. Timing will only matter if a company's financial manager has some private information suggesting that the company's shares are mispriced.
56 Implications of the EMH for Financial Managers (cont.) The financial manger and evidence on the EMH: Until further research has clarified the issues, the implications of the EMH provide a useful guide to financial managers. However, whether this is correct will ultimately require a personal value judgement.
57 Summary Portfolio theory tells us that diversification reduces risk. Diversification works best with negative or low Risk can be divided into two positive correlations between assets and asset classes. categories: Systematic risk of an asset is Systematic riskcannot be diversified away. Unsystematic riskcan be diversified away. measured by the asset's Beta. Risk of asset is relative to market.
58 Summary (cont.) CAPM provides the relationship between risk and expected return for risky assets. CAPM uses asset's beta and assumes linear relationship between expected return and risk relative to market, measured by beta. 59 Summary (contd) Efficient market -- security prices reflect all available information. Prices should react to new information instantaneously, precluding consistent excess returns. Market efficiency can be classified by: Return predictability -- are there ways of predicting future returns? Event studies -- look for excess returns around an event and quick price adjustment. Tests for private information -- look for excess returns to parties that may have private info. 60 Examples of evidence suggesting market inefficiency Summary (cont.) include: calendarbased anomalies, firm size effects, returns and dividend yield, returns -- book to market ratio. Fundamental analysis and charting will not earn excess returns in an efficient market. Does not suggest random stock selection. Should not seek to beat market. While anomalies to EMH exist, it is a useful way to approach asset price formation and behaviour. 61 ...
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This note was uploaded on 07/10/2009 for the course FIN FIN taught by Professor Dr. during the Spring '09 term at Baptist College of Health Sciences.
- Spring '09