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 nonnegative 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
riskfree 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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