Chapter 2 RISK AND RETURN BASICS

Chapter 2 Questions What are the sources of investment returns? How can returns be measured? How can we compute returns on investments outside of their home country?

Chapter 2 Questions What is risk and how is it measured? How is expected return and risk estimated via scenario analysis? 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.

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.

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.

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).

Returns on Foreign Investments HCR Relative = FR Relative (Current Exchange Rate/Initial Exchange Rate) HCR=(1 + FR)Current Exchange Rate – 1 Initial Exchange Rate

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. 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.

Arithmetic Mean Example YearHolding Period Return 1 10% 2 30% 3 -20% 4 0% 5 20% R A = (  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. R G = [  (Return Relatives)] 1/n – 1

Geometric Mean Example YearHolding Period ReturnReturn Relative 1 10% % % % % 1.20 R G = [(1.10)(1.30)(.80)(1.00)(1.20)] 1/5 – 1 R G =.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? YearHolding Period Return Investment Value 1 10%$1, %$1, %$1, %$1, %$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.

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.

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

Expected Return Example Economic ConditionsProbabilityReturn Strong.20 40% Average.50 12% Weak % E(R) =.20(40%) +.50 (12%) +.30 (-20%) E(R) = 8%

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 = [  (R t -R A ) 2 ]/n-1

Standard Deviation of Historic Returns YearHolding Period Return 1 10% R A = 8% 2 30%  2 = %  = 19.2% 4 0% 5 20%  2 = [(10-8) 2 +(30-8) 2 +(-20-8) 2 +(0-8) 2 +(20-8) 2 ]/4 = [ ]/4 = [1480]/4

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

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, now just from a probability distribution.  2 =  P i (R i -E(R)) 2

Standard Deviation of Expected Returns Economic ConditionsProbabilityReturn Strong.20 40% Average.50 12% Weak % E(R) = 8%  2 =.20 (40-8) (12-8) (-20-8) 2  2 = 448  = 21.2% Note: CV = 21.2%/8% = 2.65

Components of Return Recall from Chapter 1 that the required rate of return on an investment is the sum of the risk-free rate (RFR) of return available in the market and a risk premium (RP) to compensate the investor for risk. Required Return = RFR + RP The Capital Market Line (CML) is a visual representation of how risk is rewarded in the market for investments.

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).