Question

In: Finance

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 3 months ago
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