Chapter 1 Investment Analysis andPortfolio Management

1、Investment Analysis and Portfolio Management by Frank K. Reilly & Keith C. BrownThe Investment Setting What Is An Investment Return and Risk Measures Determinants of Required Returns Relationship between Risk and Return1-2What Is An Investment? Defining Investment: A current commitment of $ for a pe

2、riod of time in order to derive future payments that will compensate for: The time the funds are committed The expected rate of inflation Uncertainty of future flow of funds Reason for Investing: By investing (saving money now instead of spending it), individuals can tradeoff present consumption for

3、 a larger future consumption.1-3What Is An Investment? Pure Rate of Interest It is the exchange rate between future consumption (future dollars) and present consumption (current dollars). Market forces determine this rate. Example: If you can exchange $100 today for $104 next year, this rate is 4% (

4、104/100-1). Pure Time Value of Money The fact that people are willing to pay more for the money borrowed and lenders desire to receive a surplus on their savings (money invested) gives rise to the value of time referred to as the pure time value of money.1-4What Is An Investment? Other Factors Affec

5、ting Investment Value Inflation: If the future payment will be diminished in value because of inflation, then the investor will demand an interest rate higher than the pure time value of money to also cover the expected inflation expense. Uncertainty: If the future payment from the investment is not

6、 certain, the investor will demand an interest rate that exceeds the pure time value of money plus the inflation rate to provide a risk premium to cover the investment risk Pure Time Value of Money.1-5What Is An Investment? The Notion of Required Rate of Return The minimum rate of return an investor

7、 require on an investment, including the pure rate of interest and all other risk premiums to compensate the investor for taking the investment risk. Investors may expect to receive a rate of return different from the required rate of return, which is called expected rate of return. What would occur

8、 if these two rates of returns are not the same?1-6Historical Rates of Return Return over A Holding Period Holding Period Return (HPR) Holding Period Yield (HPY)HPY=HPR-1 Annual HPR and HPYAnnual HPR=HPR1/nAnnual HPY= Annual HPR -1=HPR1/n 1where n=number of years of the investmentInvestment of Value

9、 BeginningInvestment of Value EndingHPR =1-7Historical Rates of ReturnExample: Assume that you invest $200 at the beginning of the year and get back $220 at the end of the year. What are the HPR and the HPY for your investment? HPR=Ending value / Beginning value=$220/200=1.1 HPY=HPR-1=1.1-1=0.1=10%1

10、-8Historical Rates of ReturnExample: Your investment of $250 in Stock A is worth $350 in two years while the investment of $100 in Stock B is worth $120 in six months. What are the annual HPRs and the HPYs on these two stocks? Stock A Annual HPR=HPR1/n = ($350/$250)1/2 =1.1832 Annual HPY=Annual HPR-

11、1=1.1832-1=18.32% Stock B Annual HPR=HPR1/n = ($120/$100)1/0.5 =1.2544 Annual HPY=Annual HPR-1=1.2544-1=25.44%1-9Historical Rates of Return Computing Mean Historical ReturnsSuppose you have a set of annual rates of return (HPYs or HPRs) for an investment. How do you measure the mean annual return? A

12、rithmetic Mean Return (AM)AM= HPY / nwhere HPY=the sum of all the annual HPYs n=number of years Geometric Mean Return (GM)GM= HPY 1/n -1where HPR=the product of all the annual HPRs n=number of years1-10Historical Rates of ReturnSuppose you invested $100 three years ago and it is worth $110.40 today.

13、 The information below shows the annual ending values and HPR and HPY. This example illustrates the computation of the AM and the GM over a three-year period for an investment. YearBeginning EndingHPR HPY Value Value 1 100 115.0 1.15 0.152 115 138.0 1.20 0.203 138 110.4 0.80 -0.201-11Historical Rate

14、s of ReturnAM=(0.15)+(0.20)+(-0.20) / 3 = 0.15/3=5%GM=(1.15) x (1.20) x (0.80)1/3 1 =(1.104)1/3 -1=1.03353 -1 =3.353% Comparison of AM and GM When rates of return are the same for all years, the AM and the GM will be equal. When rates of return are not the same for all years, the AM will always be h

15、igher than the GM. While the AM is best used as an “expected value” for an individual year, while the GM is the best measure of an assets long-term performance.1-12Historical Rates of Return A Portfolio of Investments Portfolio HPY: The mean historical rate of return for a portfolio of investments i

16、s measured as the weighted average of the HPYs for the individual investments in the portfolio, or the overall change in the value of the original portfolio. The weights used in the computation are the relative beginning market values for each investment, which is often referred to as dollar-weighte

17、d or value-weighted mean rate of return.1-13Historical Rates of ReturnThe following exhibit demonstrates how to compute the rate of return for a portfolio of 3 stocks.1-14Expected Rates of Return In previous examples, we discussed realized historical rates of return. In contrast, an investor would b

18、e more interested in the expected return on a future risky investment. Risk refers to the uncertainty of the future outcomes of an investment There are many possible returns/outcomes from an investment due to the uncertainty Probability is the likelihood of an outcome The sum of the probabilities of

19、 all the possible outcomes is equal to 1.0.1-15Expected Rates of Return Computing Expected Rate of Returnwhere P i = Probability for possible return iR i = Possible return i=ni 1iReturn) (Possible Return) ofy Probabilit( )E(R )R(P.)(R(P)(R(Pnn2211=niiiRP1)(1-16 Probability DistributionsExhibit 1.2Ri

20、sk-free Investment1-17 Probability DistributionsExhibit 1.3Risky Investment with 3 Possible Returns1-18 Probability DistributionsExhibit 1.4 Risky investment with ten possible returns1-19Risk of Expected Return Risk refers to the uncertainty of an investment; therefore the measure of risk should ref

21、lect the degree of the uncertainty. The risk of expected return reflect the degree of uncertainty that actual return will be different from the expect return. The common measures of risk are based on the variance of rates of return distribution of an investment1-20Risk of Expected Return=-=-=niiiini

22、RERPturnExpectedturnPossiblexobabilityVariance1221)()ReRe()(Pr)(s Measuring the Risk of Expected Return The Variance Measure1-21Risk of Expected Return Standard Deviation (): It is the square root of the variance and measures the total risk =-=niiiiRERP12)(s Coefficient of Variation (CV): It measure

23、s the risk per unit of expected return and is a relative measure of risk.)(REReturnofRateExpectedReturnofDeviationStandardCVs=1-22Risk of Historical Rates of Returnwhere, 2 = the variance of the series HPY i = the holding period yield during period iE(HPY) = the expected value of the HPY equal to th

24、e arithmetic mean of the series (AM) n = the number of observationsn/HPY)(EHPY2n1ii2-=s Given a series of historical returns measured by HPY, the risk of returns is measured as: 1-23Determinants of Required Returns Three Components of Required Return: The time value of money during the time period T

25、he expected rate of inflation during the period The risk involved See Exhibit 1.5 Complications of Estimating Required Return A wide range of rates is available for alternative investments at any time. The rates of return on specific assets change dramatically over time. The difference between the r

26、ates available on different assets change over time.1-24Determinants of Required Returns The Real Risk Free Rate (RRFR) Assumes no inflation. Assumes no uncertainty about future cash flows. Influenced by time preference for consumption of income and investment opportunities in the economy Nominal Ri

27、sk-Free Rate (NRFR) Conditions in the capital market Expected rate of inflationNRFR=(1+RRFR) x (1+ Rate of Inflation) - 1RRFR=(1+NRFR) / (1+ Rate of Inflation) - 11-25Determinants of Required Returns Business Risk Uncertainty of income flows caused by the nature of a firms business Sales volatility

28、and operating leverage determine the level of business risk. Financial Risk 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 t

29、he stocks risk premium.1-26Determinants of Required Returns Liquidity Risk How long will it take to convert an investment into cash? How certain is the price that will be received? Exchange Rate Risk Uncertainty of return is introduced by acquiring securities denominated in a currency different from

30、 that of the investor. Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.1-27Determinants of Required Returns Country Risk Political risk is the uncertainty of returns caused by the possibility of a major change in the political or econ

31、omic 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.1-28Determinants of Required Returns Risk Premium and Portfolio Theory From a portfolio theory perspecti

32、ve, the relevant risk measure for an individual asset is its co-movement with the market portfolio. Systematic risk relates the variance of the investment to the variance of the market. Beta measures this systematic risk of an asset. According to the portfolio theory, the risk premium depends on the

33、 systematic risk.1-29Determinants of Required Returns Fundamental Risk versus Systematic Risk Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk. Risk Premium= ( Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country Ris

34、k) Systematic risk refers to the portion of an individual assets total variance attributable to the variability of the total market portfolio. Risk Premium= (Systematic Market Risk)1-30Relationship Between Risk and Return The Security Market Line (SML) It shows the relationship between risk and retu

35、rn for all risky assets in the capital market at a given time. Investors select investments that are consistent with their risk preferences. ExpectedReturnRisk(business risk, etc., or systematic risk-beta)NRFRSecurityMarket LineLowRiskAverageRiskHighRiskThe slope indicates therequired return per unit of risk1-31Relationship Between Risk and Return Movement al