Question: Problem 5: Diversification and the CAPM Consider portfolios made up of two possible assets, A and B, with expected returns and standard deviations summarized below.

Problem 5: Diversification and the CAPM Consider portfolios made up of two possible assets, A and B, with expected returns and standard deviations summarized below. Asset E(r) (r)

A 10% 25%

B 8% 25%

(a) For a portfolio with 1/2 weight in each of the two assets, what correlation between the assets would make the portfolio standard deviation 25%, the same as each asset individually? Correlation:

(b) For a portfolio with 1/2 weight in each of the two assets, what correlation between the assets would make the portfolio standard deviation 12.5%, half of the standard deviation for an individual asset? Correlation:

(c) For a portfolio with 1/2 weight in each of the two assets, what correlation would result in the lowest possible portfolio standard deviation? Given that correlation, what would be the standard deviation of the portfolios return?

Correlation: Resulting standard deviation:

(d) Assuming the two assets have a correlation of 0.7 and the risk-free rate is 2%, find the tangency portfolio (portfolio with highest Sharpe Ratio) among all possible portfolios of asset A and asset B. Provide this portfolios weight in asset A and its Sharpe Ratio (Hint: you can solve this by using Solver in Excel or mannually deriving the optimal weight).

Tangency portfolio weight in asset A: Tangency portfolio Sharpe Ratio:

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