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【文章內(nèi)容簡介】 nds and bills are much less mon. Investors in Treasury bonds and bills could be much more confident of the oute than mon stockholders 24 ? If we knew all the possible outes and associated probabilities, a continuous probability distribution could be developed. ? This type of distribution can be thought of as a bar chart (histogram), for a very large number of outes. Continuous probability distribution 25 Variance and standard deviation ? Investment risk depends on the dispersion 分散 or spread of possible outes ? The standard measures are variance and standard deviation ? Variance: average value of squared deviations離差 from mean (均值 ). A measure of volatility 分散性 ? Standard deviation: square root of variance. Another measure of volatility 26 27 ? rt=return for the ith oute prt= probability of occurrence of the ith oute n= number of outes considered inii prRR ?? ?? 1?????niii prRRSD1)(28 Self test 29 ? The larger the standard deviation, the more variable are an investment’s returns and riskier is the investment. ? A standard deviation of zero indicates no variability and thus no risk. 30 Measuring the variation in stock returns When estimating the spread of possible outes 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. Therefore, they calculate the standard deviation of past returns 31 32 ? You may find it interesting to pare the cointossing game and the stock market as alternative investments. The stock market generated an average annual return of percent with a standard deviation of percent. ? The game offers 10 and 21 percent, respectively—slightly lower return and about the same variability. 33 ? As expected, Treasury bills were the least variable security, and smallfirm stocks were the most variable. Government and corporate bonds hold the middle ground. 34 You have estimated the following probability distributions of expected future returns for stocks X and Y: ? A. what is the expected rate of return for Stock X? Y? ? B. What is the SD of expected returns for Stock X? Y? ? C. Which stock would you consider to be riskier? Why? Stock X Stock Y probability return probability return 10% 4% 18 18 26 40 35 ? expected rate of return for Stock X=18% ? expected rate of return for Stock Y=18% ? Stock X appears riskier than Stock Y because possible returns from X are more variab
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