Question

You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 10% with a standard deviation of 19%. Assume you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 24%. The T-bill rate is 5%. Your client would like to switch an 80% allocation in your portfolio to an 80% allocation in the stock market index. How much return would your client expect to make? Convert your answer to a percentage and round to two decimal places

Answer 1

Since I manage a risky portfolio with an expected rate of return of 12% and 24% standard deviation.

This means 100% of your capital is allocated to 12% return portfolio.

Now client want to switch 80% of allocation to a passive portfolio with 10% return and 19% standard deviation.

So, risky portfolio with 12% return remains with 20% capital allocation

Therefore, Expected return client would make = W_r * R_r + W_p * R_p = 20% * 12% + 80% * 10% = 2.4% + 8% = 10.40%