Beta Mgt Co.

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 diers 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 calculated using formula Cov(Stock,Vanguard)/Var(Vanguard).

Stock Beta Alpha

Cal. REIT 0:1474 􀀀0:0243

Brown Group 1.1633 -0.0195