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What is the standard deviation of returns of the mutual fund

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Consider the following capital market: a risk-free asset yielding 3.00% per year and a mutual fund consisting of 75% stocks and 25% bonds. The expected return on stocks is 13.95% per year and the expected return on bonds is 4.50% per year. The standard deviation of stock returns is 42.00% and the standard deviation of bond returns 18.00%. The stock, bond and risk-free returns are all uncorrelated.

  1. What is the standard deviation of returns of the mutual fund?
  2. Using the data above; assume the correlation between stock and bond returns is 0.36 and the correlations between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero). What is the standard deviation of returns for the mutual fund with this new higher correlation?
  3. Using the data from problem 2, what is the standard deviation of the minimum variance portfolio formed from this stock and bond portfolio?
  4. Using the data from problem 2 where the risk-free rate is 3.00%, what is the stock weight of the tangency portfolio formed by creating the optimal risky portfolio from this stock and bond portfolio?
  5. Using the data from problem 4, what is the Sharpe Ratio of the tangency portfolio formed by creating the optimal risky portfolio from this stock and bond portfolio?

Reference no: EM132466113

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