1. Investments Vicentiu Covrig 1 Return and risk (chapter 2)

2. Investments Vicentiu Covrig 2 Sources of Investment Returns Investments provide two basic types of return: Income returns (yield) - The owner of an investment has the right to any cash flows paid by the investment. Changes in price or value (capital appreciation) - The owner of an investment receives the benefit of increases in value and bears the risk for any decreases in value.

3. Investments Vicentiu Covrig 3 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.

4. Investments Vicentiu Covrig 4 Annualized Returns Another useful measure: Return Relative = Income + Ending Value Purchase Price 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.

5. Investments Vicentiu Covrig 5 Returns on Overseas Investments A holding period return on a foreign investment generally needs to be translated back into the home country return. If the exchange rate has changed over the life of the investment, the home country return (HCR) can be very different than the foreign return (FR). HCR Relative = FR Relative (Current Exchange Rate/Initial Exchange Rate) HCR=(1 + FR)Current Exchange Rate – 1 Initial Exchange Rate

6. Investments Vicentiu Covrig 6 Measuring Historic Returns: 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. R A = (  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. YearHolding Period Return 1 10% 2 30% 3 -20% 4 0% 5 20% R A = (  HPR)/n = 40/5 = 8%

7. Investments Vicentiu Covrig 7 Measuring Historic Returns: 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. R G = [  (Return Relatives)] 1/n – 1 YearHolding Period ReturnReturn Relative 1 10% 1.10 2 30% 1.30 3 -20% 0.80 4 0% 1.00 5 20% 1.20 R G = [(1.10)(1.30)(.80)(1.00)(1.20)] 1/5 – 1 R G =.0654 or 6.54%

8. Investments Vicentiu Covrig 8 Scenario Analysis While historic returns, or past realized returns, are important, investment decisions are inherently forward- looking. We often employ scenario or “what if?” analysis in order to make better decisions, given the uncertain future. Scenario analysis involves looking at different outcomes for returns along with their associated probabilities of occurrence.

9. Investments Vicentiu Covrig 9 Expected Rates of Return Expected rates of return are calculated by determining the possible returns (R i ) for some investment in the future, and weighting each possible return by its own probability (P i ). E(R) =  P i R i Economic ConditionsProbabilityReturn Strong.20 40% Average.50 12% Weak.30 -20% E(R) =.20(40%) +.50 (12%) +.30 (-20%) E(R) = 8%

10. Investments Vicentiu Covrig 10 What is risk? Risk is the uncertainty associated with the return on an investment. Systematic or market risk factor - Affect many investment returns simultaneously; their impact is pervasive. - Examples: changes in interest rates and the state of the macro- economy. Firm-specific risk factors - Examples: poor management, competitive pressures.

11. Investments Vicentiu Covrig 11 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 = [  (R t -R A ) 2 ]/n-1 Standard deviation of returns:

12. Investments Vicentiu Covrig 12 Standard Deviation of Historic Returns YearHolding Period Return 1 10% 2 30% 3 -20% 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 = [1480]/4

13. Investments Vicentiu Covrig 13 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 =  /R A 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

14. Investments Vicentiu Covrig 14 Measuring Risk Through Scenario Analysis If we are considering various scenarios of return in the future, we can still calculate the variance and standard deviation of returns:  2 =  P i (R i -E(R)) 2 Economic ConditionsProbabilityReturn Strong.20 40% Average.50 12% Weak.30 -20% E(R) = 8%  2 =  = CV =

15. Investments Vicentiu Covrig 15 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 - Changes in the investment’s specific risk and the premium required in the marketplace for bearing risk

16. Investments Vicentiu Covrig 16 Selected Realized Returns, 1926 – 2001 Average Standard Return Deviation Small-company stocks17.3%33.2% Large-company stocks12.720.2 L-T corporate bonds 6.1 8.6 L-T government bonds 5.7 9.4 U.S. Treasury bills 3.9 3.2 You notice the positive relation between risk and return

17. Investments Vicentiu Covrig 17 Learning objectives What are the sources of investment returns? How can returns be measured? Dollar returns, Holding period returns, Annualized returns Returns on overseas investments Arithmetic vs geometric mean? Calculations and differences in terms of applications Expected returns based on scenario analysis What is risk and how it is measured? Variance, Standard deviation Sources of risk: market and firm specific risk Coefficient of variation Measuring risk through scenario analysis Components of returns; what are the major factors that affect the firm specific risk Don’t need to know about CML (p.45-47) Recommended problems: end-of-chapter problems 1-11