Question

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
 
 What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08?

Answer 1

Solution! of The values provided in the question are as follows: Invest in Risky Asset5 = $100 SERR) Expected Ratz Retum A Risky Asset = 0.11 OR11% >(OR) Standard deviation of Risky Assels = 0.21 OR 217. >(5p) Standard deviation of portfolio = 0.08 OR 8 % >(Erge) Expected Rate of Retum & Risk free Artes OR T-Bill with a Rate = 0.045 OR Retam 4.5%. Demand of (B), - ? Question (43 percentage of your money invested in Risky Aseting Percentage of your money invested in Risk free Assets (1), we know that standard deviation of Riskfree Assets (ORF) es o. Let the weight of Risky Assets be a po, weight of Risk free Assets be 1-se OR WRF = 1-3 → Calculation of weight of Risky Assets (WR) weight of Risk free Assets (WRF) (2) and

op= (orway? it (OREXWRs) + 2 x SRXOREX WRXWREX covariance 8 = (21x2]+[0x61-2)]{+ 2x21xo xxx (1-x) x covariance 8?- (212)?+ (0)2+ 8 ? =(213)? 2le x = = 0. 38095238095 21 e=0.38 OR 38 % (A) weight of Risky Assets (WR) = 30% Percentage of your money invested in Risky Apsels = 38 Y. B) weight of Risk free Assets (WRF) = -x So, WRF = 1-0.38 => 0.62 OR 62 % weight of Risk free Assets (WRF) 262% Percentage of your money invested in Rrok free Asset=62%