What would be the capital allocation between the risk free asset and the optimal risky investment portfolio for an individual with risk aversion coefficient of 3? If the initial investment is $100,000, how much money should the investor allocate to each of the 5 assets (risk free asset and 4 risky assets)

-85.824% invested in risky asset and 185.824% in risk free asset

Explanation:

Optimal portfolio comprises of risky assets portfolio and risk free assets. Let assume w1 is the weight of risky asset portfolio, therefore the remaining weight will be (1-w1) which would be weight of risk free asset.

Thus; optimal portfolio return equals= w1 x risky asset + (1-w1) x risk free asset.

Optimal portfolio return= risk free asset - w(risky - risk free)

Optimal portfolio return is given as = 0.01218804

risk free return = 0.02

Now: 0.01218804 - 0.02 = -0.0078116.

To amplify utility

Capital allocation between risky and risk free asset is

Weight of risk asset= -0.0078116/3x(0.055088262)^2

= -0.0078116/0.00910

= -0.85824

= -85.824% invested in risky asset

And 1-(-85.824) =185.824% invested in the risk free asset.

Note the following values are taken from the Table attached therewith

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