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Unformatted text preview: Chapter 2
RISK AND RETURN BASICS Chapter 2 Questions What are the sources of investment returns? How can returns be measured? What is risk and how can we measure risk? What are the components of an investment's required return to investors and why might they change over time? Sources of Investment Returns Investments provide two basic types of return: Income returns The owner of an investment has the right to any cash flows paid by the investment. Changes in price or value The owner of an investment receives the benefit of increases in value and bears the risk for any decreases in value. Income Returns Cash payments, usually received regularly over the life of the investment. Examples: Coupon interest payments from bonds, Common and preferred stock dividend payments. Returns From Changes in Value Investors also experience capital gains or losses as the value of their investment changes over time. For example, a stock may pay a $1 dividend while its value falls from $30 to $25 over the same time period. Measuring Returns Dollar Returns How much money was made on an investment over some period of time? Total Dollar Return = Income + Price Change Holding Period Return By dividing the Total Dollar Return by the Purchase Price (or Beginning Price), we can better gauge a return by incorporating the size of the investment made in order to get the dollar return. Annualized Returns If we have return or income/price change information over a time period in excess of one year, we usually want to annualize the rate of return in order to facilitate comparisons with other investment returns. Another useful measure:
Return Relative = Income + Ending Value Purchase Price Annualized Returns
Annualized HPR = (1 + HPR)1/n 1 Annualized HPR = (Return Relative)1/n 1 With returns computed on an annualized basis, they are now comparable with all other annualized returns. Measuring Historic Returns Starting with annualized Holding Period Returns, we often want to calculate some measure of the "average" return over time on an investment. Two commonly used measures of average: Arithmetic Mean Geometric Mean Arithmetic Mean Return The arithmetic mean is the "simple average" of a series of returns. Calculated by summing all of the returns in the series and dividing by the number of values. RA = ( HPR)/n Oddly enough, earning the arithmetic mean return for n years is not generally equivalent to the actual amount of money earned by the investment over all n time periods. Arithmetic Mean Example
Year Holding Period Return 1 10% 2 30% 3 -20% 4 0% 5 20% RA = ( HPR)/n = 40/5 = 8% Geometric Mean Return The geometric mean is the one return that, if earned in each of the n years of an investment's life, gives the same total dollar result as the actual investment. It is calculated as the nth root of the product of all of the n return relatives of the investment. RG = [(Return Relatives)]1/n 1 Geometric Mean Example
Year Holding Period Return Return Relative 1 10% 1.10 2 30% 1.30 3 -20% 0.80 4 0% 1.00 5 20% 1.20 RG = [(1.10)(1.30)(.80)(1.00)(1.20)]1/5 1 RG = .0654 or 6.54% Arithmetic vs. Geometric
To ponder which is the superior measure, consider the same example with a $1000 initial investment. How much would be accumulated? Year Holding Period Return Investment Value 1 10% $1,100 2 30% $1,430 3 -20% $1,144 4 0% $1,144 5 20% $1,373 Arithmetic vs. Geometric How much would be accumulated if you earned the arithmetic mean over the same time period? Value = $1,000 (1.08)5 = $1,469 How much would be accumulated if you earned the geometric mean over the same time period? Value = $1,000 (1.0654)5 = $1,373 Notice that only the geometric mean gives the same return as the underlying series of returns. What is risk? Risk is the uncertainty associated with the return on an investment. Risk can impact all components of return through: Fluctuations in income returns; Fluctuations in price changes of the investment; Fluctuations in reinvestment rates of return. Sources of Risk Systematic Risk Factors Affect many investment returns simultaneously; their impact is pervasive. Examples: changes in interest rates and the state of the macro-economy. Asset-specific Risk Factors Affect only one or a small number of investment returns; come from the characteristics of the specific investment. Examples: poor management, competitive pressures. How can we measure risk? Since risk is related to variability and uncertainty, we can use measures of variability to assess risk. The variance and its positive square root, the standard deviation, are such measures. Measure "total risk" of an investment, the combined effects of systematic and asset-specific risk factors. Variance of Historic Returns 2 = [ (Rt-RA)2]/n-1 Standard Deviation of Historic Returns
Year Holding Period Return 1 10% RA = 8% 2 30% 2 = 370 3 -20% = 19.2% 4 0% 5 20% 2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(20-8)2]/4 = [4+484+784+64+144]/4 = /4 Using the Standard Deviation If returns are normally distributed, the standard deviation can be used to determine the probability of observing a rate of return over some range of values. Coefficient of Variation The coefficient of variation is the ratio of the standard deviation divided by the return on the investment; it is a measure of risk per unit of return. CV = /RA The higher the coefficient of variation, the riskier the investment. From the previous example, the coefficient of variation would be: CV =19.2%/8% = 2.40 Components of Return The required rate of return on an investment is the sum of the nominal risk-free rate (Nominal RFR) and a risk premium (RP) to compensate the investor for risk. Required Return = Nominal RFR + RP Or to be more technically correct: RR = (1 + Nom RFR) x (1 + RP) - 1 The RiskReturn Relationship The Capital Market Line (CML) is a visual representation of how risk is rewarded in the market for investments. The greater the risk, the greater the required return, so the CML slopes upward. Components of Return Over Time What changes the required return on an investment over time? Anything that changes the risk-free rate or the investment's risk premium. Changes in the real risk-free rate of return and the expected rate of inflation (both impacting the nominal risk-free rate, factors that shift the CML). Changes in the investment's specific risk (a movement along the CML) and the premium required in the marketplace for bearing risk (changing the slope of the CML). ...
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This note was uploaded on 08/17/2008 for the course FRL 330 taught by Professor Muhtaseb during the Summer '08 term at Cal Poly Pomona.
- Summer '08