MIT Sloan School of Management
J. Wang 15.415 C&D
E52-435 Spring 1999
Solutions to Assignment 6: Portfolio Theory
Beta Management Company
(a) The standard deviations can be calculated using Excel's STDEV() function.
Stock Cal. REIT Brown Group Vanguard 500
St.Dev (StD) 9:23% 8:17% 4:61%
The individual stocks have almost double the variability of the Vanguard Index 500.
So the individual stocks are riskier.
California REIT seems riskier than Brown based on Standard Deviation.
(b) The variability of a portfolio with w in asset 1 and 1 ?? w in asset 2 is
p = hw22
1 + 2w(1 ?? w)1;2 + (1??w)22
2i
1
2
where 1; 2 are StDs, and 1;2 is the covariance between asset 1 and 2. Using Excel
function COVAR(), we can calculate the covariance between Vanguard 500 Index and
the two stocks.
Stock Cal. REIT Brown Group
Cov(Vanguard, Stock) 0:0003 0:0024
Variability (StD) of the portfolio (99%Vanguard, 1% Cal. REIT)
=[(:992)(:04612) + 2(:99)(:01)(:0003) + (:012)(:09232)]
1
2 = 4:57%
Variability (StD) of the portfolio (99%Vanguard, 1% Brown Group)
=[(:992)(:04612) + 2(:99)(:01)(:0024) + (:012)(:08172)]
1
2 = 4:61%
Comparing these portfolios, we see that the Brown stock adds more variability to the
portfolio. Thus, Brown is riskier.
This answer di ers from that in part (a) because a large part of the portfolio's risk
is related to the covariance between the individual stock and Vanguard. Since the
covariance between Brown's stock and Vanguard is almost 8 times that between Cal.
REIT and Vanguard, the portfolio that includes Brown is riskier.
(c) The regression results are obtained using the Excel's LINEST() function. Beta can
also be cal ...