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You have $100 to invest in a portfolio. The portfolio is composed of a risky asset...

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Finance

You have $100 to invest in a portfolio. The portfolio iscomposed of a risky asset with an expected rate of return of 12percent and a standard deviation of 15 percent and a Treasury billwith a rate of return of 5 percent. What percentage of your moneyshould be invested in the risky asset to form a portfolio with anexpected rate of return of 9 percent?

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4.2 Ratings (894 Votes)

Risky Asset=Asset 1   Treasury Bill=Asset 2
Return of asset1=R1= 12%
Return of asset2=R2= 5%
Standard deviation of asset 1=S1 15%
Standard deviation of asset 2=S2 0
Covariance(1,2)= 0
w1=Investment in asset 1
w2=Investment in asset 2
Portfolio Return=Rp
w1*R1+w2*R2=w1*12+w2*5 ……..Equation (1)
Vp=Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
Portfolio Variance=(w1^2)*(15^2)+(w2^2)*0+2*w1*w2*0
Vp=Portfolio Variance=(w1^2)*225……………Equation (2)
Portfolio Standard Deviation=Square root of Variance
w1 w2 Rp=w1*12+w2*5 Vp=(w1^2)*225 Sp=Square root of Vp
Weight of Weight of Portfolio portfolio Portfolio
Risky Asset T-Bill Return(%) Variance Std. Deviation(%)
0 1 5 0 0
0.1 0.9 5.7 2.25 1.5
0.2 0.8 6.4 9 3
0.3 0.7 7.1 20.25 4.5
0.4 0.6 7.8 36 6
0.5 0.5 8.5 56.25 7.5
0.5714 0.4286 8.9998 73.462 8.571
0.6 0.4 9.2 81 9
0.7 0.3 9.9 110.25 10.5
0.8 0.2 10.6 144 12
0.9 0.1 11.3 182.25 13.5
1 0 12 225 15
Investment in RISKY ASSET $57.14 (0.5714*100)
Investment in TREASURY BILLS $42.86 (0.4286*100)
Standard Deviation of the Portfolio 8.571 %

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Transcribed Image Text

You have $100 to invest in a portfolio. The portfolio iscomposed of a risky asset with an expected rate of return of 12percent and a standard deviation of 15 percent and a Treasury billwith a rate of return of 5 percent. What percentage of your moneyshould be invested in the risky asset to form a portfolio with anexpected rate of return of 9 percent?

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