Chapter 2

1. Chapter 2 RISK AND RETURN BASICS

2. 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?

3. 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.

4. 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.

5. 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.

6. 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.

7. 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

8. 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.

9. 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

10. 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 = (SHPR)/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.

11. Arithmetic Mean Example Year Holding Period Return 1 10% 2 30% 3 -20% 4 0% 5 20% RA = (SHPR)/n = 40/5 = 8%

12. 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 = [P(Return Relatives)]1/n – 1

13. 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%

14. 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

15. 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.

16. Investment Strategy • Generally, the income returns from an investment are “in your pocket” cash flows. • Over time, your portfolio will grow much faster if you reinvest these cash flows and put the full power of compound interest in your favor. • Dividend reinvestment plans (DRIPs) provide a tool for this to happen automatically; similarly, Mutual Funds allow for automatic reinvestment of income. • See Exhibit 2.5 for an illustration of the benefit of reinvesting income.

17. 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.

18. 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.

19. 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 s2 = [S(Rt-RA)2]/n-1

20. Standard Deviation of Historic Returns Year Holding Period Return 1 10% RA = 8% 2 30% s2 = 370 3 -20% s = 19.2% 4 0% 5 20% s2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(20-8)2]/4 = [4+484+784+64+144]/4 = [1480]/4

21. 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.

22. 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 = s/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

23. 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

24. The Risk-Return 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.

25. 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).