Question

You are constructing a portfolio for an investor with a risk aversion of A=4. You can invest their money in a riskless asset with a return of 0.022, or a risky asset with an expected return of 0.124 and a standard deviation of 0.39. What proportion of their assets should you put in the risky asset? An answer of 0 means none of their assets, an answer of 1 means all of their assets.

Answer 1

The proportion you would devote to investment in risky asset = (E (rp) – rf)/ (A *SDp^2)

Where,

Expected return of risky asset, E (rp) = 0.124

Return of riskless asset, rf = 0.022

Standard deviation of risky asset, SDp =0.39

Risk aversion coefficient is A = 4

Therefore,

The proportion you would devote in risky asset = (0.124 – 0.022)/ (4 * 0.39^2)

=0.102 / (0.6084)

= 0.1677 or 16.77%

Therefore 0.1677 proportions of the assets, you will put in the risky asset.