Question

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

Answer 1

	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	%