STAT Question

 Jennifer invests her money in a portfolio that consists of 60% Fidelity Spartan 500 Index Fund and 40% Fidelity Diversified International Fund. Suppose that, in the long run, the annual real return X on the 500 Index Fund has mean 15% and standard deviation 25%, the annual real return Y on the Diversified International Fund has mean 5% and standard deviation 15%, and the correlation between X and Y is 0.5.

The return on Jennifer’s portfolio is R = 0.6X + 0.4Y. What is the standard deviation of R?

Note: Provide your answer as in decimal form to 3 decimal places. Do not provide your answer as a percentage)

 Jennifer invests her money in a portfolio that consists of 60% Fidelity Spartan 500 Index Fund and 40% Fidelity Diversified International Fund. Suppose that, in the long run, the annual real return X on the 500 Index Fund has mean 15% and standard deviation 25%, the annual real return Y on the Diversified International Fund has mean 5% and standard deviation 15%, and the correlation between X and Y is 0.5.

The distribution of returns is typically roughly symmetric but with more extreme high and low observations than a Normal distribution. The average return over a number of years, however, is close to Normal. If Jennifer holds her portfolio for 20 years, what is the approximate probability that her average return is less than 8%?

Note: Provide your answer as in decimal form to 3 decimal places. Do not provide your answer as a percentage)