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1、Chapter 5,Risk and Return,Glossary,Standard Deviation标准差或者标准离差 Expected return 期望回报率 Normal distribution 正态分布 Coefficient of variation 离差系数 variance方差 Continuous Distributions连续分布 discrete distribution离散分布 Certainty Equivalent (CE)资本回收保证量 Risk Preference风险偏好 Risk Indifference风险中立 Risk Aversion风险规避 T
2、he Capital Asset Pricing Model (CAPM)资本资产定价模型 Systematic Risk系统风险 Unsystematic Risk非系统风险,Defining Return,Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment.,Dt + (Pt - Pt-1 ),Pt-1,R =,Return Example,The sto
3、ck price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?,Return Example,The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9
4、.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?,$1.00 + ($9.50 - $10.00 ),$10.00,R =,= 5%,Defining Risk,Greater the variability, the riskier the security is said to be,The variability of returns from those that are expected.,Determining Expecte
5、d Return (Discrete Dist.),R = S ( Ri )( Pi ) R is the expected return for the asset, Ri is the return for the ith possibility, Pi is the probability of that return occurring, n is the total number of possibilities.,n,i=1,How to Determine the Expected Return and Standard Deviation,Stock BW Ri Pi (Ri)
6、(Pi) -.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090,The expected return, R, for Stock BW is .09 or 9%,Determining Standard Deviation标准差或者标准离差 (Risk Measure),n,i=1,s = S ( Ri - R )2( Pi ) Standard Deviation, s, is a statistical measure of the variability of a distr
7、ibution around its mean. It is the square root of variance(方差）. Note, this is for a discrete distribution（离散分布） .,How to Determine the Expected Return and Standard Deviation,Stock BW Ri Pi (Ri)(Pi) (Ri - R )2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33
8、 .10 .033 .00576 Sum 1.00 .090 .01728,Determining Standard Deviation (Risk Measure),s = S ( Ri - R )2( Pi ) s = .01728 s = .1315 or 13.15%,n,i=1,Coefficient of Variation,The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk. CV = s /
9、 R CV of BW = .1315 / .09 = 1.46,Discrete vs. Continuous Distributions连续分布,Discrete Continuous,Determining Expected Return (Continuous Dist.),R = S ( Ri ) / ( n ) R is the expected return for the asset, Ri is the return for the ith observation, n is the total number of observations.,n,i=1,Determinin
10、g Standard Deviation (Risk Measure),n,i=1,s = S ( Ri - R )2 ( n ) Note, this is for a continuous distribution where the distribution is for a population. R represents the population mean in this example.,Continuous Distribution Problem,Assume that the following list represents the continuous distrib
11、ution of population returns for a particular investment (even though there are only 10 returns). 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5% Calculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.,Lets Use the Calculator!,En
12、ter “Data” first. Press: 2nd Data 2nd CLR Work 9.6 ENTER -15.4 ENTER 26.7 ENTER Note, we are inputting data only for the “X” variable and ignoring entries for the “Y” variable in this case.,Lets Use the Calculator!,Enter “Data” first. Press: -0.2 ENTER 20.9 ENTER 28.3 ENTER -5.9 ENTER 3.3 ENTER 12.2
13、 ENTER 10.5 ENTER ,Lets Use the Calculator!,Examine Results! Press: 2nd Stat through the results. Expected return is 9% for the 10 observations. Population standard deviation is 13.32%. This can be much quicker than calculating by hand, but slower than using a spreadsheet.,Certainty Equivalent (CE)资
14、本回收保证量is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time.,Risk Attitudes,Certainty equivalent Expected value Risk Preference风险偏好 Certain
15、ty equivalent = Expected value Risk Indifference风险中立 Certainty equivalent Expected value Risk Aversion风险规避 Most individuals are Risk Averse.,Risk Attitudes,Risk Attitude Example,You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000. Mary requires a guaranteed $25,000, or more
