Question

. There are two investment funds. One of them is a passive portfolio, meaning that it mimics the S&P 500. The passive portfolio generates has an expected return of 13% with a standard deviation of 25%. In contrast, you are the manager of an active portfolio, which generates an expected return of 18% and has a standard deviation of 28%. Note that the risk-free rate is 8%.

A) Your client is currently holding 70% of their total wealth in your active fund, with the other 30% invested in the risk-free asset. They are thinking about switching from your fund to invest instead in the passive fund. Write a paragraph to your client explaining why this is not a good idea.

B) How much would you have to be charging in investment fees (as percent of total investment plus return) for switching to be a good idea?

Answer 1

A)

We know that the portfolio return is the weighted average of the returns of the stock in the portfolio

Client has invested 70% in active portfolio and 30% in Risk free asset

return on the portfolio of the client = Weight of active portfolio * return of active portfolio + weight of risk free asset * risk free rate

= 70% * 18 + 30% * 8

= 12.6 + 2.4

= 15%

If the client shifts from active portfolio to passive portfolio then the return on the portfolio will be

= 70%* 13 + 30% * 8 = 9.1 + 2.4 = 11.5 %

If the client shifts from the active portfolio to passive portfolio the return will drop by 3.5% . Hence it is not a good idea to shift to passive portfolio.

B)

Investment fees has to ne minimum of the difference between the return of the two portfolios calculated earlier. Hence the fees has to be minimum 3.5% of the investment amount involved.