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Answer :
The beta of the other stock in the portfolio must be 1.63 if one of the stocks has a beta of 1.37 and the total portfolio is exactly as risky as the market value.
To solve this problem, we need to use the concept of beta, which measures the volatility or systematic risk of a stock relative to the overall market. A stock with a beta of 1 means that it has the same level of risk as the market, while a beta greater than 1 implies higher risk and a beta less than 1 indicates lower risk.
Given that the total portfolio is as risky as the market, we know that the portfolio's beta is equal to 1. Since the portfolio is equally invested in a risk-free asset and two stocks, each stock has a weight of 1/3 in the portfolio.
Let's call the beta of the other stock "x". Using the formula for the beta of a portfolio, we can write:
1 = (1/3)*0 + (1/3)*1.37 + (1/3)*x
Simplifying this equation, we get:
1 = 0.46 + x/3
Multiplying both sides by 3, we get:
3 = 1.37 + x
Subtracting 1.37 from both sides, we get:
x = 1.63
Therefore, the beta of the other stock in the portfolio must be 1.63. This means that this stock is more risky than the market and has higher potential returns, but also greater volatility. The risk-free asset serves to reduce the overall risk of the portfolio and provide a stable source of income.
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