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CM ch22 to end notes

CM ch22 to end notes - Ch 22 Risk Return-risk premium in...

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Ch. 22 – Risk & Return -risk premium in discount rate -assume = shareholders value stocks for their financial returns, rather than intrinsic any satisfaction from being an owner of the firm -return on (group of) stocks = dividend yield + price change over some period of time -assume this period 1 year & investors: 1. look at number of securities w/ future returns (r1,r2,...,rn) 2. view returns as random variables & focus on mean (expected return) & standard deviation (risk) (Er1,Er2,...,Ern & o1,o2,...,on) 3. choose securities to maximize utility as a fxn of mean & standard deviation U = f (Er+,o-) - utility rises w/ return (investors prefer higher expected return, given risk) & falls w/ risk (investors risk averse, prefer security w/ lower risk, given return) -random variable (payoff r) = an association of a real number w/ each poss. outcome of an experiment -probability distribution = an assignment of probabilities, or non-negative numbers adding up to one, to the possible values of r -probabilities = 1 st assigned to outcomes of the experiment & then flow thru to the values of the random variable -possible outcomes = random variable r -mean = weighted probability value of r => find by multiplying each poss. Value of r by its prob. & take the sum -variance = weighted sum & standard deviation = square root of variance -for a normal curve about 68% of all observations lie w/i plus or minus 1 standard deviation from mean & nearly 95% lies w/i 2 standard deviations -return on a security = random variable => plotted by mean & standard dev. -utility fxn = utility rises w/ return but falls w/ an increase in risk -quadratic fxn = U = Er – (b/2)*o2 -b = parameter of risk aversion -utility = constant & rearranging => obtain an indiff. curve showing poss. combos of return & risk that yield equal utility or satisfaction -U = Er – (b/2)o2 = U0 | Er = U0 + (b/2)o2 -U0 = intercept of indiff. curve => its certainty equivalent -bo = slope => amount of additional return required to compensate investor for taking on a unit of additional risk -b = coefficient => higher b = more risk averse, lower b = less risk averse -risk-free security return = 6 -Er +- 3o Ch. 23 – Portfolios: Combos of 2 Securities -o =< w1o1+w2o2 -p = correlation coefficient = +1 => polar case w/ no gain from diversification -correlation < +1 => inequality holds & gain from divers. b/c variance reduced & standard dev. less than weighted avg. – can increase mean w/o proportionate increase in standard dev.
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-2 stocks w/ perf. neg. correlation => can be combined to form a riskless one – bad return on one always offset by good return on other – not likely to find -most stocks = pos. corr. since most rise/fall w/market – corr. Less than perfect so some gain from divers -diversifying = initially mean goes up & standard dev. goes down – w/ more than 10% in r2 standard dev. begins to rise w/ mean but it remains < weighted avg. of o1 & o2 -investor not risk averse => value of risk parameter = neg. or 0 – additional risk would not req. a premium & would see no diversification – would put all money in stock w/ highest expected return Ch. 24 – Extension to Multiple Securities -combination of 2 stocks will be on a
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