Q1. Calculate the variability (standard deviation) of the stock returns of California REIT and Brown Group during the past 2 years. How variable are they compared with Vanguard Index 500 Trust? Which stock appears to be riskiest?

The stock returns for each month are given in Table 1. Based on the monthly returns, the standard deviation or variability of each stock has been calculated. The standard deviation for California REIT is 9.23% and the standard deviation for Brown Group is 8.17%. This standard deviation is the monthly standard deviation for each of the stocks. On the other hand the standard deviation of Vanguard Index 500 Trust is 4.61%. This shows that the standard deviation of both the individual stocks is double of the standard deviation of the market. Based on the standard deviation of both the stocks, it can be concluded that the California REIT stock is more risky as compared to Brown Group. This shows that the returns of the California REIT stock disperse or deviate more frequently as compared to its average means. This means that the returns are volatile for this stock and therefore, this stock is the riskiest.

Q 2. Suppose Beta’s position had been 99% of equity funds invested in the index fund, and 1% in the individual stock. Calculate the variability of this portfolio using each stock. How does each stock affect the variability of the equity investment, and which stock is riskiest? Explain how this makes sense in view of your answer to Question #1 above.

Ms. Wolfe is now planning to invest her $ 200,000 in either Brown Group stock or California REIT stock. In this way she would make her exposure of equity to $ 20 million of the total investment of $ 25 million. However, for the purpose of performing the calculations for the portfolio’s standard deviation we will work on the weight ages of the investments in the Vanguard trust and the respective stocks. If we assume that 99% of Ms. Wolfe’s total equity exposure will be invested in Vanguard Index 500 Trust and the remaining 1% would be invested in Brown Group or California RIET, than the respective variability of the portfolios will be 4.57% if 1% is invested in California RIET and it will be 4.61% if 1% is invested in Brown Group.

The results show that the variance of the Brown Group stock is more than California RIET, towards the portfolio. Therefore, the Brown Group stock is more risky. However, this contradicts with our findings of the previous question. The reason for this is that previously, only standard deviation was taken into account and that was also found on an individual basis. In order to determine the riskiness of the stocks in a portfolio, correlation and covariance among the stocks is necessary to be incorporated. We see that the correlation of Brown Group stock is more positively related with the market, therefore the overall risk of the portfolio is increased by it. This is because the correlation of Brown Group is 8 times higher than that of California RIET.

Q 3. Perform a regression of each stock’s monthly returns on the Index returns to compute the “beta” for each stock. How does this relate to the situation described in Question #2 above?

Regression has been performed on the monthly returns for each stock with respect to the index returns to calculate the beta value for each of the individual stocks. The beta for California RIET is around 0.14 and the beta for Brown Group stock is around 1.11. Beta shows the riskiness of a particular stock with respect to the market. The value of beta is lower, then the returns of the stock would be less sensitive to the movements of the market. As the value of beta for the stock of Brown Group is much higher than that of California RIET, therefore, it could be concluded that the Brown Group stock is more risky as compared to the California RIET stock. When we compare this analysis with the analysis performed in the second question, it shows that the results of the analysis are same. Therefore, the stock of Brown Group is more risky because its beta is higher than that of California RIET stock...................

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