1. ) You estimate that a passive portfolio, that is, one invested in a risky por

Question

1. ) You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index (passive portfolio), yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%.

Your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. However, you want to explain to your client the disadvantage of the switch. Therefore, you want to show to your client that your portfolio can achieve the goal return at a lower risk.

To do so, you want to have a target expected rate of return of 11.5% for the complete portfolio that includes only your active portfolio and risk free asset. What is the proportion (y) should be invested in your fund?

2.)

You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index (passive portfolio), yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%.

Your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. However, you want to explain to your client the disadvantage of the switch. Therefore, you want to show to your client that your portfolio can achieve the goal return at a lower risk.

To do so, you want to have a target expected rate of return of 11.5% for the complete portfolio that includes only your active portfolio and risk free asset.

What is the standard deviation for the complete portfolio that includes only your active portfolio and risk free asset?

Please round your answer to the fourth decimal: 0.0000

Explanation / Answer

1) My active portfolio return is 18% and risk free rate is 8%

Now to get the target return of 11.5% which only has my active portfolio and risk free asset, Let X is the percentage of active portfolio and (1-x) is the risk free asset

then, 18%*X + 8%*(1-X) = 11.5%

10%X = 3.5%

X = 35%

So, 35% should be invested in the fund and rest 65% in risk free asset.

2) Standard deviation of active portfolio is 28%

Now for the 35% of active portfolio and 65% of risk free portfolio,

Standard deviation of complete portfolio = 35%*28% = 9.8%

[ Standard deviation of portfolio when 1 is risk free asset, is Weight of risky asset* standard deviation of risky asset.]

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