2Chapter ObjectivesAfter Studying this chapter, you would be able to answer:Why do individuals invest ?What is an investment ?How do we measure the rate of return on an investment ?How do investors measure risk related to alternative investments ?What factors contribute to the rate of return that an investor requires on an investment?What macroeconomic and microeconomic factors contribute to changes in the required rate of return for an investment?
3Why Do Individuals Invest ? By saving money (instead of spending it), individuals forego consumption today in return for a larger consumption tomorrow.
4How Do We Measure The Rate Of Return On An Investment ? The real rate of interest is the exchange rate between future consumption (future dollars) and present consumption (current dollars). Market forces determine this rate.TomorrowIf you are willing to exchange a certain payment of $100 today for a certain payment of $104 tomorrow, then the pure or real rate of interest is 4%$104$100Today
5How Do We Measure The Rate Of Return On An Investment ? If the purchasing power of the future payment will be diminished in value due to inflation, an investor will demand an inflation premium to compensate them for the expected loss of purchasing power.If the future payment from the investment is not certain, an investor will demand a risk premium to compensate for the investment risk.
6Defining an Investment Any investment involves a current commitment of funds for some period of time in order to derive future payments that will compensate for:the time the funds are committed (the real rate of return)the expected rate of inflation (inflation premium)uncertainty of future flow of funds (risk premium)
7Measures of Historical Rates of Return 1.1Holding Period ReturnWhere:HPR = Holding period returnP0 = Beginning valueP1 = Ending value
8Measures of Historical Rates of Return Annualizing the HPRWhere:EAR = Equivalent Annual ReturnHPR = Holding Period ReturnN = Number of yearsExample: You bought a stock for $10 and sold it for $18 six years later. What is your HPR & EAR?
10Measures of Historical Rates of Return Arithmetic MeanWhere:AM = Arithmetic MeanGM = Geometric MeanRi = Annual HPRsN = Number of yearsGeometric Mean
11ExampleYou are reviewing an investment with the following price history as of December 31st each year.Calculate:The HPR for the entire periodThe annual HPRsThe Arithmetic mean of the annual HPRsThe Geometric mean of the annual HPRs19992000200120022003200420052006$18.45$21.15$16.75$22.45$19.85$24.10$26.50
12A Portfolio of Investments The mean historical rate of return for a portfolio of investments is measured as the weighted average of the HPRs for the individual investments in the portfolio, or the overall change in the value of the original portfolio
13Computation of Holding Period Return for a Portfolio This table is in the book on page 11. It is also provided in the Investment Templates spreadsheet in an interactive spreadsheet form.
14Expected Rates of Return Risk is the uncertainty whether an investment will earn its expected rate of returnProbability is the likelihood of an outcome
15Risk AversionMuch of modern finance is based on the principle that investors are risk averseRisk aversion refers to the assumption that, all else being equal, most investors will choose the least risky alternative and that they will not accept additional risk unless they are compensated in the form of higher return
17Probability Distributions Risky Investment with 3 Possible Returns
18Probability Distributions Risky investment with ten possible rates of return
19Measuring Risk: Historical Returns Where:= Variance (of the pop)HPR = Holding Period Return iE(HPR)i = Expected HPR*N = Number of years* The E(HPR) is equal to the arithmetic mean of the series of returns.
20Measuring Risk: Expected Rates of Return Where:= VarianceRi = Return in period iE(R) = Expected ReturnPi = Probability of Ri occurringNote: Because we multiply by the probability of each return occurring, we do NOT divide by N. If each probability is the same for all returns, then the variance can be calculated by either multiplying by the probability or dividing by N.
21Measuring Risk: Standard Deviation Standard Deviation is the square root of the varianceStandard Deviation is a measure of dispersion around the mean. The higher the standard deviation, the greater the dispersion of returns around the mean and the greater the risk.
22Coefficient of Variation 1.9Coefficient of variation (CV) is a measure of relative variabilityCV indicates risk per unit of return, thus making comparisons easier among investments with large differences in mean returns
23Determinants of Required Rates of Return Three factors influence an investor’s required rate of returnReal rate of returnExpected rate of inflation during the periodRisk
24The Real Risk Free Rate Assumes no inflation. Assumes no uncertainty about future cash flows.Influenced by the time preference for consumption of income and investment opportunities in the economy
25Adjusting For Inflation: Fisher Equation The nominal risk free rate of return is dependent upon:Conditions in the Capital MarketsExpected Rate of Inflation
26Components of Fundamental Risk Five factors affect the standard deviation of returns over time.Business risk:Financial riskLiquidity riskExchange rate riskCountry risk
27Business Risk Business risk arises due to: Uncertainty of income flows caused by the nature of a firm’s businessSales volatility and operating leverage determine the level of business risk.
28Financial Risk Financial risk arises due to: Uncertainty caused by the use of debt financing.Borrowing requires fixed payments which must be paid ahead of payments to stockholders.The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.
29Liquidity RiskLiquidity risk arises due to the uncertainty introduced by the secondary market for an investment.How long will it take to convert an investment into cash?How certain is the price that will be received?
30Exchange Rate RiskExchange rate risk arises due to the uncertainty introduced by acquiring securities denominated in a currency different from that of the investor.Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.
31Country RiskCountry risk (also called political risk) refers to the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country.Individuals who invest in countries that have unstable political-economic systems must include a country risk-premium when determining their required rate of return
32Risk Premium and Portfolio Theory When an asset is held in isolation, the appropriate measure of risk is standard deviationWhen an asset is held as part of a well-diversified portfolio, the appropriate measure of risk is its co-movement with the market portfolio, as measured by BetaThis is also referred to asSystematic riskNondiversifiable riskSystematic risk refers to the portion of an individual asset’s total variance attributable to the variability of the total market portfolio
33Relationship Between Risk and Return (Expected)Rate ofReturnBetaRisk freeRateSecurityMarket Line(SML)LowRiskAverageHighSlope of the SML indicates therequired return per unit of risk
34Changes in the Required Rate of Return Due to Movements Along the SML ExpectedRateLower RiskHigher RiskSecurityMarket LineMovements along the SMLreflect changes in the market or systematicrisk of the assetRisk freeRateBeta
35Changes in the Slope of the SML The slope of the SML indicates the return per unit of risk required by all investorsThe market risk premium is the yield spread between the market portfolio and the risk free rate of returnThis changes over time, although the underlying reasons are not entirely clearHowever, a change in the market risk premium will affect the return required on all risky assets
36Change in Market Risk Premium Note that as the slope of the SML increases, so does the market risk premiumExpectedReturnNewSMLRm´OriginalSMLRmRisk Free RateBeta
37Capital Market Conditions, Expected Inflation, and the SML The SML will shift in a parallel fashion if inflation expectations, real growth expectations or capital market conditions change. This will affect the required return on all assets.Rate ofReturnNew SMLOriginal SMLRisk freeRateRisk