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1、Chapter 10Introduction to risk, return, and the opportunity cost of capital1Objectives1.Estimate the opportunity cost of capital for an “average-risk” project2.Calculate the standard deviation of return for individual common stocks or for a stock portfolio3.Understand why diversification reduces ris
2、k4.Distinguish between unique risk, which can be diversified away, and market risk which cannot2ContentnRates of return: a reviewnA century of capital market historynMeasuring risknRisk and diversificationnThinking about risk3Percentage return: 收益率Dividend yield: 股利收益率Capital gain: 资本利得Capital loss:
3、 资本损失Real rate of return: 实际收益率Nominal rate of return: 名义收益率Inflation rate: 通胀率4 When investors buy a stock or a bond, their return comes in two forms: (1) A dividend or interest payment and (2) A capital gain or a capital loss5Where: rt =actual, expected, or required rate of return during period t;
4、 Dt: cash received from the asset investment in the time period t-1 to t; Pt: price (value ) of asset at time t; Pt-1: price ( value ) of asset at time t-1, initial pricePercentage capital gain Rt=Dividend yield6problemnSuppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25. Over
5、the last year, you received $20 in dividends (20 cents per share 100 shares). At the end of the year, the stock sells for $30. How did you do?7nQuite well. You invested $25 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Your dollar gain was $520 = $20 +
6、($3,000 $2,500).nYour percentage gain for the year is:20.8% = $2,500$5208ContentnRates of return: a reviewnA century of capital market historynMeasuring risknRisk and diversificationnThinking about risk9Market index: 市场指数Dow Jones Industrial Average: 道琼斯工业股票平均价格指数Standard & Poors composite index: 标准
7、普尔综合指数Maturity premium: 期限溢价Risk premium: 风险溢价market portfolio: 市场组合10When you invest in a stock, you dont know what return you will earn. But by looking at the history of security returns, you can get some idea11Risk definednIn the most basic sense, risk is the chance of financial loss. Assets havi
8、ng greater chances of loss are viewed as more risky than those with lesser chances of loss.nMore formally, the term risk is used interchangeably with uncertainty to refer to the variability of returns associated with a given asset.12Market indexesnFinancial analysts cant trace every stock, so they r
9、ely on market indexes to summarize the return on different classes of securitiesnMarket index: measure of the investment performance of the overall market nDow Jones Industrial Average: index of the investment performance of a portfolio of 30 “blue-chip” stocksnStandard & Poors composite index: inde
10、x of the investment performance of a portfolio of 500 large stocks. Also called the S&P 50013The historical record14nThe safest investment, Treasury bills, had the lowest rates of return. Long-term government bonds gave slightly higher returns than Treasury billsnMaturity premium: extra average retu
11、rn from investing in long- versus short-term Treasury securitiesMaturity premium15Risk premiumnCommon stocks were in a class by themselves. Investors who accepted the risk of common stocks received on average an extra return of 7.6% a year over the return on Treasury bills. This is the risk premiumn
12、Risk premium: expected return in excess of risk-free return as compensation for risk16 The historical record shows that investors have received a risk premium for holding risky assets. Average returns on high-risk assets are higher than those on low-risk assets17nThe opportunity cost of capital for
13、safe projects is the rate of return offered by safe Treasury billsnThe opportunity cost of capital for “average-risk” projects is the expected return on the market portfolioUsing historical evidence to estimate todays cost of capital18The expected return on an investment provides compensation to inv
14、estors both for waiting (the time value of money) and for worrying (the risk of the particular asset)The calculations assume that there is a normal, stable risk premium on the market portfolio19ContentnRates of return: a reviewnA century of capital market historynMeasuring risknRisk and diversificat
15、ionnThinking about risk20Variance: 方差Standard deviation: 标准差Average return: 平均收益率21Probability distribution概率分布概率分布 nA probability distribution is a model that relates probabilities to the associated outcomes.nThe simplest type of probability distribution is the bar chart (histogram) 柱状图柱状图, which s
16、hows only a limited number of outcome-probability coordinates坐标 .22Common stocks risk shows up in the wide spread of outcomes; high or low returns for Treasury bonds and bills are much less common. Investors in Treasury bonds and bills could be much more confident of the outcome than common stockhol
17、ders23nIf we knew all the possible outcomes and associated probabilities, a continuous probability distribution could be developed.nThis type of distribution can be thought of as a bar chart (histogram), for a very large number of outcomes.Continuous probability distribution24Variance and standard d
18、eviationnInvestment risk depends on the dispersion 分分散散 or spread of possible outcomesnThe standard measures are variance and standard deviation nVariance: average value of squared deviations离差 from mean (均值). A measure of volatility 分散性nStandard deviation: square root of variance. Another measure o
19、f volatility2526nrt=return for the ith outcomeprt= probability of occurrence of the ith outcome n= number of outcomes considered27Self test 10.428nThe larger the standard deviation, the more variable are an investments returns and riskier is the investment.nA standard deviation of zero indicates no
20、variability and thus no risk.29Measuring the variation in stock returnsWhen estimating the spread of possible outcomes from investing in the stock market, most financial analysts start by assuming that the spread of returns in the past is a reasonable indication of what could happen in the future. T
21、herefore, they calculate the standard deviation of past returns3031nYou may find it interesting to compare the coin-tossing game and the stock market as alternative investments. The stock market generated an average annual return of 4.18 percent with a standard deviation of 19.54 percent. nThe game
22、offers 10 and 21 percent, respectivelyslightly lower return and about the same variability.32nAs expected, Treasury bills were the least variable security, and small-firm stocks were the most variable. Government and corporate bonds hold the middle ground.33You have estimated the following probabili
23、ty distributions of expected future returns for stocks X and Y:nA. what is the expected rate of return for Stock X? Y?nB. What is the SD of expected returns for Stock X? Y?nC. Which stock would you consider to be riskier? Why? Stock XStock Yprobabilityreturnprobabilityreturn0.210%0.2-4%0.6180.6180.2
24、260.24034nexpected rate of return for Stock X=18%nexpected rate of return for Stock Y=18%nStock X appears riskier than Stock Y because possible returns from X are more variable, measured by its standard deviation of 13.91 percent, than those from Stock Y, which have a standard deviation of only 5.06
25、 percent 35ContentnRates of return: a reviewnA century of capital market historynMeasuring risknRisk and diversificationnThinking about risk36Diversification: 分散投资Portfolio: 投资组合Unique risk or diversifiable risk: 特有风险或可分散风险Market risk or systematic risk: 市场风险或系统风险37nRisk is best judged in a portfoli
26、o context 环境 . Most investors do not put all their eggs into one basket: They diversify. Thus the effective risk of any security cannot be judged by an examination of that security alone. Part of the uncertainty about the securitys return is diversified away when the security is grouped with others
27、in a portfolio.38Do these standard deviations look high to you?Amazon. com68.2%Dell Computer45.5Ford42.7Boeing33.8McDonalds28.1General Electric24.3Wal-Mart23.1H.J. Heinz21.8Pfizer20.4Exxon Mobil15.739DiversificationThe market portfolio is made up of individual stocks, why isnt its variability equal
28、to the average variability of its components?Diversification reduces variabilityDiversification: strategy designed to reduce risk by spreading the portfolio across many investments40Notice that diversification reduces risk rapidly atfirst, then more slowly.Even a little diversification can provide a
29、 substantial reduction in variability.41nSuppose you calculate and compare the standard deviations of randomly chosen one-stock portfolios, two-stock portfolios, five-stock portfolios, etc. nA high proportion of the investments would be in the stocks of small companies and individually very risky. n
30、However, you can see from Figure that diversification can cut the variability of returns about in half. Notice also that you can get most of this benefit with relatively few stocks: The improvement is slight when the number of securities is increased beyond, say, 20 or 30.42Portfolio diversification
31、 works because prices of different stocks do not move exactly together. Diversification works best when the returns are negatively correlated.43Asset versus portfolio riskThe expected return on each stock is simply the average of the three possible outcomes.The variance is the average of the squared
32、 deviations from the expected return, and the standard deviation is the square root of the variance444546n1. Investors care about the expected return and risk of their portfolio of assets. The risk of the overall portfolio can be measured by the volatility of returns, that is, the variance or standa
33、rd deviationSummary47Summaryn2. The standard deviation of the returns of an individual security measures how risky that security would be if held in isolation. But an investor who holds a portfolio of securities is interested only in how each security affects the risk of the entire portfolio. The co
34、ntribution of a security to the risk of the portfolio depends on how the securitys returns vary with the investors other holdings. Thus a security that is risky if held in isolation may nevertheless serve to reduce the variability of the portfolio if its returns do not move in lockstep(步伐一致)with the
35、 rest of the portfolio48Diversification reduces the spread of returns49Market risk versus unique riskDiversification reduces risk rapidly at first and then more slowly50Diversification eliminates unique risk. But there is some risk that diversification cannot eliminate. This is called market risk51U
36、nique risknUnique risk : risk factors affecting only that firm. Also called diversifiable risk. Unique risk arises because many of the perils that surround an individual company are peculiar to that company and perhaps its direct competitors52nMarket risk: economywide (macroeconomic) sources of risk
37、 that affect the overall stock market. Also called systematic risk. Market risk stems from economywide perils that threaten all business. Market risk explains why stocks have a tendency to move together, so even well-diversified portfolios are exposed to market movementsFor a reasonably well-diversi
38、fied portfolio, only market risk mattersMarket risk53ContentnRates of return: a reviewnA century of capital market historynMeasuring risknRisk and diversificationnThinking about risk54Risk definednIn the most basic sense, risk is the chance of financial loss.nAssets having greater chances of loss ar
39、e viewed as more risky than those with lesser chances of loss. nMore formally, the risk is used interchangeably with uncertainty to refer to the variability of returns associated with a given asset.551.Some risks look big and dangerous but really are diversifiable2.Market risks are macro risksnInvestors holding diversified portfolios are mostly concerned with macroeconomic risks. They do not worry about microeconomic risks peculiar to a particular company or investment project. Micro risks wash out in diversified portfolios3.Risk can be measured56
