1. Calculating Expected Return
Expected value
The single most likely outcome from a particular probability distribution
The weighted average of all possible return outcomes
Referred to as an ex ante or expected return

2. Calculating Risk
Variance and standard deviation used to quantify and measure risk
Measures the spread in the probability distribution
Variance of returns: 2 = (Ri - E(R))2pri
Standard deviation of returns:
 =(2)1/2
Ex ante rather than ex post  relevant

3. Risk and Return for a portfolio
Two-asset portfolio:
Asset A Asset B
Ri Ri Pi
E(Ri) 

4. Risk and Return for a portfolio
Wi = % of money invested in asset i.
WA = .5 WB = Pi
-.05 X X .5 =
.10 X X .5 =
.25 X X .5 =
E(Rp) = .10
p = 0

5. Covariance

6. Covariance COVAB =(-.05 - .10)(.25 - .10)(.30)+
( )( )(.40) +
( )( )(.30) =
Assets A and b are negatively covary.

7. Correlation Coefficient

8. Correlation Coefficient
Statistical measure of relative co-movements between security returns
AB = correlation coefficient between securities m and n
AB = +1.0 = perfect positive correlation
AB = -1.0 = perfect negative (inverse) correlation
AB = 0.0 = zero correlation

9. Portfolio Expected Return
Weighted average of the individual security expected returns
Each portfolio asset has a weight, w, which represents the percent of the total portfolio value
The expected return on any portfolio can be calculated as:

10. Portfolio Expected Return
WA = .5 and WB =.5
E(Rp) = (.5)(.1) + (.5)(.10) = .10

11. Portfolio Risk
Measured by the variance or standard deviation of the portfolio’s return
Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio

12. Risk Reduction in Portfolios
Assume all risk sources for a portfolio of securities are independent
The larger the number of securities, the smaller the exposure to any particular risk
“Insurance principle”
Only issue is how many securities to hold

13. Risk Reduction in Portfolios
Random diversification
Diversifying without looking at relevant investment characteristics
Marginal risk reduction gets smaller and smaller as more securities are added
A large number of securities is not required for significant risk reduction
International diversification is beneficial

14. Portfolio Risk and Diversification35 20
Total Portfolio Risk
Market Risk
Number of securities in portfolio

15. Random Diversification
Act of randomly diversifying without regard to relevant investment characteristics
15 or 20 stocks provide adequate diversification

16. Calculating Portfolio Risk
Two-Security Case:
N-Security Case:

17. Calculating Portfolio Risk
+2(.5)(.5)(-.0135)]1/2 = 0

18. The Single-Index Model
 measures the sensitivity of a stock to stock market movements
If securities are only related in their common response to the market
Securities covary together only because of their common relationship to the market index
Security covariances depend only on market risk and can be written as: 21