You are trying to allocate your assets into a risky portfolio and the purchase of a...

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?

Solutions

Expert Solution

Year   Return   Dev. =Return-E(r)   Squared Dev.
2014   -15.00%   -22.00%   4.8400%
2015   -5.00%   -12.00%   1.4400%
2016   30.00%   23.00%   5.2900%
2017   -10.00%   -17.00%   2.8900%
2018   35.00%   28.00%   7.8400%

Total 35.00% 22.3000%

Expected Return= Total/number of years
35%/5
=7.00%

Standard deviation =√( sum of squared deviation/(n-1))
√(22.3%/(5-1))
=23.61%

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)
(Er (P) - Rf)/ (A*Sd^2)

=(7%-2%)/(2.5*(23.61%)^2)
=0.3587880928   or 35.88%

So portfolio invested in Risky portfolio=   35.88%

jeff jeffy answered 2 weeks ago

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