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Individual Securities
Characteristics of:
1) expected return – return an individual expects over the next period
2) variance and sd – measure of volatility of a security’s return and it’s
sqr root
covariance and correlation – cov and corr measures interraltionship btwn
2 securities
Exected return, variance, and covariance
Expected return and variance
Four equally likely states of co: depression, recession, normal, and boom
times
Suprtech rtrns (Rat)
Slowpoke (Rbt)
Deprsn
20
5
Recessn
10
20
Norm
30
12
Boom
50
9
1) expected return is mean of all Rat and Rbt
2) deviation RatRabar (mean of Ra)
3) squared deviations
4) ave sqrd deviation is variance
5) std dev is sqr root of variance
std dev(r) = sqrrt(var(r))
Covariance and correlation
Measurements of how two random varies are related
Find covariance:
1) Product of deviations: (RatRabar)*(RbtRbbar)
2) Average of 1 = Cov(Ra,Rb) = σab = expected val of (1)
~no relationship btwn vars, cov=0; positive relationship, cov<0
Correlation = cov(Ra,Rb)/(SDa*SDb)
Return and risk for portfolios
How to choose best combo or portfolio of securities given expected
returns and SDs?
The Example of Supertech and Slowpoke
~The expected return on a Portfolio
Expected rtn = weighted ave of expected return of invidl securities
~
Variance and SD of a portfolio
Var(portfolio) = Xa^2vara+2XaXbcov(A,B)+Xb^2varb, where Xa and
Xb are fraction of a and fraction of b that are in portfolio
Covar(a,b) = corr(a,b)*SDa*SDb
As long as p (corr) < 1, SD of portfolio of 2 securities is less than the
weighted ave of the SDs of of the indivdl securities (b/c weighted ave is
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 Spring '10
 jaffe
 Volatility

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