Dr. Gutierrez Portfolio Theory 1
Why do people invest? What is the role of financial securities?
T E (CFt )
Recall: P0 = ∑ t
t =1 (1 + k )
Each individual’s goal is to:
maximize expected return for a given risk level
or minimize risk for a given expected return
Dr. Gutierrez Portfolio Theory 2
Standard Deviation (or Variance) is our first measure of risk.
Suppose we form a portfolio p of assets a through N. Then we can
define the return on the portfolio as a weighted average of the returns of
the individual assets.
rp = w a ra + w b rb + w c rc + ... + w N rN
How do we calculate the expected return of a portfolio?
E(rP ) = E( ∑ w i ri ) = ∑ w i E(ri )
i =1 i =1
How do we calculate the risk of a portfolio?
Var (rp ) = σ 2 = Var ∑ w w ri = ∑ ∑ w i w j cov ij
N N N
i =1 i =1 j=1
Bottomline: When we combine several assets together into a
portfolio of securities, the risk of the portfolio depends on the
interaction between the returns of the component assets.
Dr. Gutierrez Portfolio Theory 3
Each investor’s goal is to maximize return and minimize risk.
Different risk-return combinations can be had for the portfolio by
changing the weights in the assets comprising the portfolio.
frontier when correlation = 1.0
frontier when correlation = - 1.0
frontier when –1.0 < correlation < 1.0
Dr. Gutierrez Portfolio Theory 4
Assuming all stocks are not perfectly positively correlated, there are
benefits to holding a portfolio of stocks versus holding any one stock.
σp Diversifiable Risk
Number of stocks
Total Risk = Diversifiable Risk + Nondiversifiable Risk
Should investors expect to be compensated for the total risk of a
Dr. Gutierrez Portfolio Theory 5
Total return = E(r) + unexpected return
Applications of portfolio theory:
Asset pricing (CAPM)
1970 - 1995
12% 16% of returns