Question

1. There are 2 assets you can invest in: a risky portfolio with an expected return of 6% and volatility of 15%, and a government t-bill (always used as the 'risk-free' asset) with a guaranteed return of 1%. Your risk-aversion coefficient A = 4, and the utility you get from your investment portfolio can be described in the standard way as U = E(r) - 1/2 * A * variance. Assume that you can borrow money at the risk-free rate.

If the weight in the risky portfolio is 130%, how much weight (in %) is in the risk-free asset?


If the weight in the risky portfolio  is 130%, what is the expected return of the portfolio?    (in %, rounded to 1 decimal place)

If the weight in the risky portfolio is 130%, what is the volatility of the portfolio?    (in %, rounded to 1 decimal place)

If you were investing $1000 of equity, how much money (in $) do you borrow to get this leveraged portfolio with 130% weight in the risky asset?   

For your personal risk aversion, what is the weight in the risky asset for your optimal complete portfolio?    (in %, rounded to 1 decimal place)

Answer 1

1.
If the weight in the risky portfolio is 130%, how much weight (in %) is in the risk-free asset?
=-30.00%

2.
If the weight in the risky portfolio is 130%, what is the expected return of the portfolio?
=130%*6%+(1-130%)*1%
=7.5000%

3.
If the weight in the risky portfolio is 130%, what is the volatility of the portfolio?
=130%*15%
=19.5000%

4.
If you were investing $1000 of equity, how much money (in $) do you borrow to get this leveraged portfolio with 130% weight in the risky asset?
=300

5.
For your personal risk aversion, what is the weight in the risky asset for your optimal complete portfolio?
=(6%-1%)/(4*15%*15%)
=55.5556%