Question

You are trying to allocate your assets into a risky portfolio and the purchase of a risk free asset with a return of 2%. You use the following data to estimate information about the risky portfolio:

Year	Return
2014	-15%
2015	-5%
2016	30%
2017	-10%
2018	35%

If you have a risk-aversion factor of 2.5, what percentage of your total portfolio should be in the risky portfolio?

Answer 1

First we will calculate expected return or average return and standard deviation of risky portfolio

Average return = Sum of returns/no. of periods

Standard deviation = √ (∑ (Return-Average return)^2)/(no. of periods - 1))

Year	R	R- AR (AR = 11)	(R-AR)^2
2014	-15%	-22%	4.8400%
2015	-5%	-12%	1.4400%
2016	30%	23%	5.2900%
2017	-10%	-17%	2.8900%
2018	35%	28%	7.8400%
Total	35%		22.3000%
Average Return = 35%/5 =	7.00%
Standard deviation = √(22.300%/(5-1))
0.2361143791 or 23.6114%

Risky portfolio expected return = 7%

standard deviation of Risky portfolio = 23.6114%

risk free rate =2%

Risk aversion factor = 2.5

Formula for investment in risky portfolio

Weight of ORP = ( Expected retun of Risky portfolio - Risk free rate)/(risk aversion coefficiennt * Std. dev. of ORP ^2)

(7%-2%)/(2.5*(23.6114%)^2)

=0.3587455465 or 35.87%

So 35.87% should be invested in risky portfolio