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Beta Management Group is a small investment management company based in Boston, which was founded by Ms. Sarah Wolfe (The founder and CEO of the Beta Management Group) in 1988. Ms. Wolfe follows a market timing investment strategy based on two portfolios; the Vanguard index and money market instruments. The goals of Beta Management were to enhance returns but reduce risks for clients via market timing. Ms. Wolfe would keep the vast majority of Beta’s funds in no-load, low-expense index funds; and, the rest of the money would go into money market instruments. Keeping the market exposure between 50% and 99%, she eventually established the limited use of Vanguard’s Index 500 Trust because it had a very low expense ratio and its success resembled the S&P 500 Index’s return. By January 4, 1991, Beta had 79.2% of its $25 million in assets ($19.8 million) invested in the Vanguard index fund. Wolfe had been quite successful in 1990. She had reduced Beta’s equity position to 50% in June, partially missing a large two-month market decline. The company’s success had brought in enough new money to double the size of Beta in under six months. But she had lost some potential new clients who had thought it unusual that Beta Management used only an index mutual fund and picked none of its own stocks. In order to solve the problem of losing potential client, it decided to add individual stocks to its equity portfolio for diversification and also for marketing purpose. She preferred to pick smaller companies because larger stocks are thoroughly analyzed which leads to the fact that the probability of making excess profits is lower.
Ms. Wolfe focused on acquiring share of one of the two stocks: California REIT and Brown Group, whose prices had eroded over the past two years to levels that seemed unreasonably low.
We can examine the risk of the two individual stocks by

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