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Chapter 10: Risk and return: lessons from market history Corporate Finance Ross, Westerfield, and Jaffe Outline 1. Returns 2. Capital market returns 3. Portfolio risk statistics Dollar return Suppose that you bought a bond for $1050 a year ago. You have received two semiannual coupons of $50 each. The market price of the bond today is $1100. What is your total dollar return? Income = 50 + 50 = $100. Capital gain = 1100 – 1050 = $50. Total dollar return = 100 + 50 = $150. Total dollar return = income + capital gain (loss). Percentage return It is more intuitive to think of returns in terms of percentages. Return = (ending value – beginning value) / beginning value. Return = ((1100 + 100) – 1050) / 1050 = 14.29%. Return = income yield (return) + capital gain yield (return) = 100 / 1050 + 50 / 1050 = 9.52% + 4.76% = 14.29%. Holding period return Holding period return: the cumulative return that an investor would obtain when holding an investment over a period of N years. Holding period return example Suppose that an investment yielded 4%, 7%, 8%, 0%, and 10% for the past 5 years. What is the holding period return for the 5 years? Holding period return = (1 + 4%) × (1 + 7%) × (1 + 8%) × (1 + 0%) × (1 + 10%) – 1 = 32.2%. Why capital market returns? Examining capital market returns helps us determine the appropriate returns on nonfinancial assets (e.g., firm projects). Lessons from capital market return history: – – – There is a reward for bearing risk. Return is positively related to risk. This is called the “risk-return tradeoff.” Average return, I The simple average of a series of returns is called arithmetic average return. Geometric average return: average compound return per period over multiple periods. Average return example Year Ret Arithmetic R 1 + Ret Power of 1/N Geometric R 1 0.08 0.076 1.08 1.074811381 0.07481138 2 -0.01 0.99 3 0.12 1.12 GR < AR 4 0.13 1.13 5 0.06 1.06 Multiplication term 1.4344 Average return, II The geometric average will be less than the arithmetic average unless all the returns are equal. The arithmetic average is overly optimistic for multiple horizons. If the investment horizon is only 1 period, the arithmetic average is a better measure of likely return. Arithmetic average return based on historical returns are often used as an estimate of expected return in real life. Portfolio risk statistics An investor cares about the return variability of her/his portfolio. This variability at the portfolio level is usually measured by variance and/or standard deviation (std.). Portfolio risk statistics, example Year 1 2 3 4 5 Ret Arithmetic R Diff 0.08 0.076 0.004 -0 -0.086 0.12 0.044 0.13 0.054 0.06 -0.016 Sum Diff^2 0.000016 0.007396 0.001936 0.002916 0.000256 0.01252 Var Std 0.00313 0.055946 Historical performance, 1926-2008 Large stocks Small Stocks L-T Corporate Bonds L-T Government Bonds U.S. Treasury Bills Inflation Average Return 11.7% 16.4% 6.2% 6.1% 3.8% 3.1% Std 20.6% 33.0% 8.4% 9.4% 3.1% 4.2% If normally distributed? If we are willing to assume that asset returns are normally distributed, can you draw a return distribution based on the previous slide? Hint: about 95% within +/– 2 std. End-of-Chapter Concept questions: 1-10. Questions and problems: 1-16 and 19-23.