Question
In: Finance
You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 10% with a standard deviation of 19%.
You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 10% with a standard deviation of 19%. Assume you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 24%. The T-bill rate is 5%. Your client would like to switch an 80% allocation in your portfolio to an 80% allocation in the stock market index. What would the standard deviation of the 80% allocation to the market portfolio be? Convert your answer to a percentage and round to one decimal places
Solutions
Expert Solution
The expected Return of Portfolio =12%
Risk free rate =5%
Beta of Portfolio =(The expected Return of Portfolio-Risk free
rate)/(Market return-Risk free rate)
=(12%-5%)/(10%-5%) =1.40
Covariance =Beta*Standard Deviation of Market =1.4*19%^2
Standard Deviation of Portfolio =((Weight of Stock *Standard
Deviation of Stock )^2+((Weight of Market*Standard Deviation of
Market)^2+2*Weight of Stock*Weight of Market*Covariance)^0.5
=((20%*24%)^2+(80%*20%)^2+2*0.2*0.8*1.4*19%^2))^0.5 =20.99%
jeff jeffy answered 2 years agoRelated Solutions
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