Risk & Return
 Expected Rate of Return n
k ^   pi ki
i 1
 Example:
State of Economy
Depression
Recession
Average
Boom
Prob(Occurrence)
.05
.10
.65
.20
K | This Economy
(100%)
(10%)
15%
30%
Risk & Return
 Expected Rate of Return n
k ^   pi ki
i 1
 Example:
State of Economy
Depression
Recession
Average
Boom
Prob(Occurrence)
.05
.10
.65
.20
K | This Economy
(100%)
(10%)
15%
30%
What is Risk?
 Risk/Return Trade-off
 Risk Defined







Measuring Risk: Variance
 Variance is
n
Variance   =  (k i  k̂) P i
2
2
i =1
 Example:
(k i  k̂) 2
(k i  k̂) 2 Pi
(k i  k̂) 2 Pi
Measuring Risk: Standard Deviation
 Standard Deviation is
Standard Deviation     2 =
n
2
(k

k̂
)
Pi
 i
i =1
 Example:
Coefficient of Variation
 Coefficient of Variation is
Coefficien t of Variation  CV  
 Example:
k^
Diversification
 Stand Alone Risk vs. Portfolio Risk
 Diversification
Portfolio Returns
 Expected Rate of Return on a Portfolio of Assets n
^
k portfolio
  wi ki^
i 1
 Example:
Stock
AT&T
Boston Celtics
IBM
Expected Return
11%
8%
12%
Portfolio Weight
20%
30%
50%
Portfolio Risk
 The standard deviation of a portfolio is
 Example #1: Perfect Negative Correlation

Portfolio Risk, cont.
 Example #2: Perfect Positive Correlation
•
 Example #3: Partially Correlated Assets
•
Standard Deviation of a Portfolio
 Generic Case:
p 
N
N 1 N
2 2
w
 i  i    wi w j  ij i j
i 1
i 1 j i 1
 2 Asset portfolio:
 p  wa2 a2  wb2 b2  2wa wb  a,b a b
Std. Dev. of a Portfolio, cont.
 Example #1: Consider an investor with a 2 asset portfolio. Thirty Percent of the
investor’s portfolio is invested in BP stock with an expected return of 16.5%,
while the remaining seventy percent of the portfolio in invested in Halliburton
stock which offers an expected return of 12.25%. The standard deviation of return
for the two individual investments are 25% and 20% respectively. If the
correlation coefficient between the two asset’s returns is 0.27, what is the
expected return, and standard deviation of expected return for this portfolio?
Std. Dev. of a Portfolio, cont.
 3 Asset Portfolios:
 p  wa2 a2  wb2 b2  wc2 c2  2wa wb  a ,b a b  2wb wc b,c b c  2wa wc  a ,c a c
 Variance/Covariance Matrix:
Std. Dev. of a Portfolio, cont.
 Example #2: Consider an investor with a 3 asset portfolio. Thirty Percent of the
investor’s portfolio is invested in Anadarko Petroleum stock with an expected return
of 15%, an additional thirty percent of the investor’s portfolio is invested in
Chesapeake Energy stock with an expected return of 12%, while the remaining forty
percent of the portfolio in invested in Exxon Mobil Inc. stock which offers an
expected return of 11%. The standard deviation of return for the three individual
investments are 18%, 16%, and 14% respectively. If the correlation coefficient
between the Anadarko and Chesapeake stock returns is 0.50, the correlation
coefficient between the Chesapeake and Exxon Mobil stock returns is 0.65, and the
correlation coefficient between the Anadarko and Exxon Mobil stock is 0.70, what is
the expected return, and standard deviation of expected return for this portfolio?