Chapter 2: Return and Risk ( I ). Basic return concepts Basic risk concepts Stand-alone risk Portfolio risk and market risk Risk and return: CAPM/SML . 1. What are investment returns?. Investment returns measure the financial results of an investment.
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Chapter 2: Return and Risk ( I ) • Basic return concepts • Basic risk concepts • Stand-alone risk • Portfolio risk and market risk • Risk and return: CAPM/SML 1
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.
Realized Return 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%.
Expected Return • Expected Return is the weighted average of all the possible returns, weighted by the probability that each return will occur. • Expected Return (%) = ΣPbi*ri • Where Pbi = probabilities of outcome i • ri = expected % return in outcome
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.
What is Investment Risk? Probability Distribution: Which stock is riskier? Why?
Standard Deviation (S.D.) • Standard deviation (S.D.) is one way to measure risk. It measures the volatility or riskiness of portfolio returns. • S.D. = square root of the weighted average squared deviation of each possible return from the expected return.
Risk Measure For Basic Foods, S.D.=? 10
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. • So which one of sale.com and basic foods is high risky? • But what if this case?
Measuring Stand–Alone Risk: The Coefficient of Variation How do we choose between two investments if one has a higher expected return and the other a lower standard deviation? To help answer this question, we often use another measure of risk, the coefficient of variation (CV) , which is the standard deviation divided by the expected return: CV = Standard deviation / expected return CVS-Stock = 32.6% / 16.7% = 1.9521 CVL-Stock = 20.4% / 11.9% = 1.7143 CVT-BILLS = 3.1% / 3.7% =0.8378 12
Portfolio Return and Risk • Portfolio return rpis the weighted average of the expected returns on the individual assets in the portfolio. Suppose there are n stocks. The expected return on Stock i isri . The fraction of the portfolio's dollar value invested in Stock i (that is, the value of the investment in Stock i divided by the total value of the portfolio) is wi, and all the wi must sum to 1.0. The expected return on the portfolio is 13
^ rp = (3.0%)*0.10 + (6.4%)*0.20 + (10.0%)*0.40 + (12.5%)*0.20 + (15.0%)*0.10 = 9.6% p = [(3.0 - 9.6)2*0.10 + (6.4 - 9.6)2*0.20 +(10.0 - 9.6)2*0.40 + (12.5 - 9.6)2*0.20 + (15.0 - 9.6)2*0.10]1/2 = 3.3% CVp = 3.3%/9.6% = .34 Portfolio Return and Risk
Portfolio vs. Its Components • Portfolio expected return (9.6%) is between stock A (17.4%) and stock B (1.7%) returns. • Portfolio standard deviation is much lower than: • either stock (20% and 13.4%). • average of stock A and stock B (16.7%). • The reason is due to negative correlation (r) between stock A and stock B returns.
Conclusion Stand-alone risk = Market risk + Diversifiable risk: • Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. • Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.
Beta and Systematic Risk CAPM suggests that Beta is a factor in determining the relation between returns and systematic risk. Market Risk Premium 19
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:
Portfolio Beta • An important aspect of the CAPM is that the beta of a portfolio is a weighted average of its individual securities' betas: Calculate beta for a portfolio with 50% Stock H and 50% Stock L: bp = Weighted average= 0.5(bStock H) + 0.5(bStock L) = 0.5*2 + 0.5*0.5 = 1.25 22