Question

You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%.
The rate on T-bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund
and $40,000 in T-bills.
What is the expected return and standard deviation of your client's portfolio?

Answer 1

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Answer:

Risk premium is 10%, risk free rate is 6% and standard deviationof the portfolio is 14%.

Calculate expected rate of return on equity portfolio as shown below:

Hence, expected rate of return on portfolio is 16%.

The client invests $60,000 in your equity fund and $40,000 in the T-bill fund. Therefore, the proportion of her investment in your equity fund is:

Hence, weight of equity fund in portfolio is 60%

The proportion of her investment in T-bills is:

Hence, weight of T-bill fund is 40%

Calculate expected return on a portfolio as shown below.

Here, W(s) is the weights of asset portfolios and r(s) is the rate of return of respective assets in the portfolio.

Substitute values and calculate expected return as shown below.

Hence, expected rate of return is 12%

Calculate standard deviation of a portfolio as shown below.

Here, is the weight of asset portfolios and is the standard deviation of respective assets. Since, T-bills are a risk-free asset standard deviation will be 0.

Hence, standard deviation of the portfolio will be as shown below.

Therefore, standard deviation of the portfolio is .