Beta Management Company Case Study

I. Case Interpretation

Beta Management company, managed by Sarah Wolfe, was founded in 1988. They have 25 Million Dollars under management. The following facts are extracted from the case:

1. Asset under management 25,000,000 USD
2. During the period 1989-1990 (2 years) the fund was invested partly in an index and partly in money market (risk free). Sarah’s management was to time the market and reduce/increase the percentage invested in the index (from 50% to 99%) according to market performance.
3. The performance was good in 1990 since Sarah reduce the exposure of the market during the downturn of August-September.
4. As of Jan 4, 1991, Beta Management had 79.2% (19,800,000$) invested in the index and the rest invested at the risk free rate.
5. As of beginning of 1991, Sarah was looking to add 1 stock to her equity portfolio by using 200,000$ from the money invested at risk free to increase exposure to equity to 80%.
6. Sarah was considering two stocks: Brown Group and California REIT.
7. Sarah was worried about the variability of the stocks being considered since she promised her clients reasonable returns with control over risk exposure.
8. Our interpretation of the question to be answered in this case is to check whether Sarah should remaining invested only in the index or introduce one of these two individual stocks. If it is better to introduce one stock, we need to check which one is better.

II. Data & Calculation

The data provided for the index and the two stocks under consideration is shown in table 1 below. The data is plotted on 1 graph so that the stock variation can be observed visually.  As shown in figure 1.

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Table 1. Data on monthly return of the index and the 2 stocks under consideration

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Figure 1. Percentage Monthly return of the index and the 2 stocks under consideration

From the data provided, we calculated for the index and the two stock the average return, the standard variation (total risk), the covariance of each stock with the index, the Beta of each stock (risk associated with the market) and Alfa. The results of these calculation are shown in Table 2 as well as the regression figures 2 and 3.

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Table 2. Data calculated for each stock

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Figure 2. Regression figure for REIT

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Figure 3. Regression figure for Brown

III. Portfolio Creation        

As suggested by the case, we need to study a portfolio made up of 99% investment in the index and 1% investment in one of the two stocks. Table 3 below show the characteristics of the two different portfolios created. The betat of the portfolio is calculated as the weighted average betas. We also calculated the variance of the portfolio that is very close to the index since 99% of the money is invested in the index We also calculated the expected return based on CAPM and taking the risf free rate as 0.5% (Logically, it has to be lower than the market return, otherwise no one would invest in the market).