Beta Management Company

Calculate the variability (standard deviation) of the stock returns of California REIT and Brown Group during the 2 years. How variable are they compared with Vanguard Index 500 Trust? Which stock appears to be the riskiest?

Vanguard Index 500 TrustCalifornia REITBrown Group
STDEV4.61%9.23%8.17%

Based on the above, the riskiest stock would appear to be California REIT.

Suppose Beta’s position has been 99% of equity funds invested in the index fund, and 1% in the individual stock. Calculated the variability of this portfolio using each stock. How does each stock affect the variability of the overall equity investment, and which stock is riskiest in this context? Explain how this makes sense in view of your answer to Question (1) above.

σ^2= w_1^2 σ_1^2+w_2^2 σ_2^2+2w_1 w_2 Cov(r_1 r_2)

Vanguard, REITVanguard, Brown
Covariance0.00030.0024

Index Fund %Ind Stock %
99%1%
California REITBrown Group
Variability(STDEV)4.5676%4.6119%

Based on this context, Brown Group is a bit riskier. In looking at the covariance calculation, the covariance of Vanguard/Brown is a fair bit larger that the covariance of Vanguard/California REIT. As a result, it increases the risk of Vanguard/Brown

Perform a regression of each stock’s monthly returns (as the y variable) on the index fund returns (as the x variable) to compute the  for each stock (the slope of the regression). How does this relate to the situation described in Question #2 above?

REITBrown
Intercept-0.024278716-0.01953843
Vanguard Index 500 Trust0.1473514331.163349646

The Beta for Brown is higher, so it makes sense that it is a riskier security.

How might the expected returns for each stock relate to their respective levels of riskiness?

Brown should have a higher expected return as it is more riskier. An investor would demand additional return for the additional risk being taken. Using the equation RE = RF + RM – RF), the expected returns are proportional with the respective levels of riskiness