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Risk and Return. FIL 404 Prepared by Keldon Bauer. What are investment returns?. Investment returns measure the financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in: Dollar terms. Percentage terms.
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Risk and Return FIL 404 Prepared by Keldon Bauer
What are investment returns? • Investment returns measure the financial results of an investment. • Returns may be historical or prospective (anticipated). • Returns can be expressed in: • Dollar terms. • Percentage terms.
An investment costs $1,000 and is sold after 1 year for $1,100. Dollar return: $ Received - $ Invested $1,100 - $1,000 = $100. Percentage return: $ Return/$ Invested $100/$1,000 = 0.10 = 10%.
What is investment risk? • Typically, investment returns are not known with certainty. • Investment risk pertains to the probability of earning a return less than that expected. • The greater the chance of a return far below the expected return, the greater the risk.
Defining/Measuring Return • Expected Return as defined in statistics is as follows:
Alta has the highest rate of return. Does that make it best?
Defining/Measuring Risk • Risk in statistics (and financial economics) is measured by standard deviation, which measures the tightness of the results.
Standard Deviation of Alta Ind. s = [(-22 – 17.4)20.1 + (-2 – 17.4)20.2 (20 – 17.4)20.4 + (35 – 17.4)20.2 (50 – 17.4)20.1]1/2 = 20.0%
Stand-Alone Risk • Standard deviation measures the stand-alone risk of an investment. • The larger the standard deviation, the higher the probability that returns will be far below the expected return.
Measuring Stand-Alone Risk • If investors have invested everything in one investment, then standard deviation should be standardized by expected return.
Portfolio Returns • In the real world, investors can hold more than one investment. • But risk is still important in pricing assets given their expected return.
Portfolio Returns • Risk and return should not be evaluated in isolation. Each security should be evaluated in its risk/return trade-off to the portfolio. • Portfolio expected return:
Portfolio Risk • Unlike portfolio return, which is just a weighted average return of all returns in the portfolio, portfolio standard deviation is much more complicated.
Portfolio Risk • It depends on the weight (wi) of the new asset to the overall portfolio. • It depends on the standard deviation (si) of the new asset’s returns. • It depends on the correlation (rij) between the new asset and all other assets in the portfolio.
Correlation Coefficient • rij is a measure of the degree of relationship between two variables. • It ranges from -1 to +1. • For rij<1, overall portfolio risk decreases. • Which is why risk goes down as number of stocks in a portfolio goes up. • For rij=-1, portfolio risk could be eliminated.
Portfolio Risk Reduction • Risk can only be reduced so far. • Almost all stocks are positively correlated. • As the number of stocks increase, the risk approaches sm.
Conclusions • As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. • sp falls very slowly after about 40 stocks are included. The lower limit for sp is sM . • By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.
Can an investor holding one stock earn a return commensurate with its risk? • No. Rational investors will minimize risk by holding portfolios. • They bear only market risk, so prices and returns reflect this lower risk. • The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk.
How is market risk measured for individual securities? • Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. • It is measured by a stock’s beta coefficient. For stock i, its beta is: • bi = (ri,Msi) / sM
Capital Asset Pricing Model • CAPM shows return is a function of only the systematic risk. • Unsystematic risk can be reduced through diversification. • CAPM is used to determine the required rate of return. • Measured by degree of “correlation” with the market.
Capital Asset Pricing Model • bj is a measure of a stock’s sensitivity to market fluctuations. • When bj = 1, equal volatility with market. • Only measures systematic risk. ri = rRF + (Risk Premium) bi ri = rRF + (rMarket - rRF) bi
Capital Asset Pricing Model • Risk has two components • Market and firm-specific risks. • Firm specific risk can be eliminated through diversification. • Market risk cannot be eliminated. • Therefore, one must be compensated to hold market (systematic) risk.
Capital Asset Pricing Model • The greater the systematic risk, the higher return will be required by the market. • The beta (regression) coefficient measures systematic risk. • Because beta determines how the stock affects the riskiness of a diversified portfolio, beta is the most relevant measure of a stock’s risk!
Portfolio Beta Coefficients • Like expected return, the portfolio beta, bp, is a weighted average of individual stock b’s.
Use the SML to calculate eachalternative’s required return. • The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). • SML: ri = rRF + (RPM)bi . • Assume rRF = 8%; rM = rM = 15%. • RPM = (rM - rRF) = 15% - 8% = 7%.
Impact of Inflation on SML • In chapter 1, we said that inflationary expectation are embedded in interest rates (as inflation is expected to go up - interest goes up). • The risk premium is expected to stay constant over time.
Impact of Risk Aversion on SML • If there were no risk aversion, all assets would earn the same return. • As risk aversion increases, the risk premium (the slope of the line) increases.
Impact of Stock Risk on SML • If a stock becomes less risky (the systematic risk goes down), what will happen to the SML? • Nothing! The beta of the stock changes, and the required return merely moves down the SML!
Has the CAPM been completely confirmed or refuted? • No. The statistical tests have problems that make empirical verification or rejection virtually impossible. • Investors’ required returns are based on future risk, but betas are calculated with historical data. • Investors may be concerned about both stand-alone and market risk.
