Question

State (Si)	P r(Si)	Return Growth Fund (S)	Return of Large Cap Fund (B)
Boom	.25	30%	5.00%
Moderate Growth	.20	12.50%	-4.50%
Low Growth	.30	6.00%	7.00%
Recession	.25	-20.00%	11.50%

If the risk free rate is 3%. Compute the weights of the Optimal Risky Portfolio

Answer 1

		GROWTH FUND
			A	B	C=A*B	D=B-6.8	E=D^2	F=E*A
		State	Probability	Return (%)	Prob.*Return	Deviation from expected	Deviation squared	Deviation squared *Probability
		Boom	0.25	30	7.5	23.2	538.24	134.56
		Moderate growth	0.2	12.5	2.5	5.7	32.49	6.498
		low growth	0.3	6	1.8	-0.8	0.64	0.192
		Recession	0.25	-20	-5	-26.8	718.24	179.56
				Total	6.8		TOTAL	320.81
		Expected return	6.80%
		Variance	320.81
		Sg=Standard Deviation	17.91	(Square root of variance
		LARGE CAP FUND
			A	B	C=A*B	D=B-5.325	E=D^2	F=E*A
		State	Probability	Return (%)	Prob.*Return	Deviation from expected	Deviation squared	Deviation squared *Probability
		Boom	0.25	5	1.25	-0.325	0.105625	0.02640625
		Moderate growth	0.2	-4.5	-0.9	-9.825	96.530625	19.306125
		low growth	0.3	7	2.1	1.675	2.805625	0.8416875
		Recession	0.25	11.5	2.875	6.175	38.130625	9.53265625
				Total	5.325		TOTAL	29.706875
		Expected return	5.325%
		Variance	29.706875
		Sl=Standard Deviation	5.450	(Square root of variance
		w1=Weight ofGrowth Fund
		w2=Weight of Large cap fund
		w1+w2=1
		Data on correlation coefficient or Covariance of return between these two folios are no given
		Assume that there is no correlation
	Rp=	Portfolio expected return=w1*(expected return of growth fund)+w2*(Expected return of large capfund)=w1*6.8+w2*5.325
	Vp=	Portfolio Variance=	(w1^2)*(Sg^2)+(w2^2)*(Sl^2)=			(w1^2)*320.81+(w2^2)*29.706875
		Sharp Ratio of the portfolio=(Rp-Riskfree return)/Sp=(Rp-3)/Sp
		Sp=Square Root of Vp
		w1	w2	Rp=w1*6.8+w2*5.325	Vp=(w1^2)*(sg^2)+(w2^2)*(Sl^2)	Sp=Square root of Vp	SR=(Rp-3)/Sp
		Weight of Growth fund	Weight of Large cap fund	Portfolio Return	Portfolio Variance	Portfolio Standard deviation	Sharp Ratio
		0.0	1.0	5.325	29.71	5.450688	0.4265517
		0.1	0.9	5.4725	27.2732	5.222375	0.4734436
		0.13	0.87	5.51675	27.909188	5.282915	0.4763942
		0.2	0.8	5.62	31.8468	5.643297	0.4642676
		0.3	0.7	5.7675	43.4308	6.590205	0.4199414
		0.4	0.6	5.915	62.0252	7.875608	0.3701302
		0.5	0.5	6.0625	87.63	9.36109	0.3271521
		0.6	0.4	6.21	120.2452	10.96564	0.2927326
		0.7	0.3	6.3575	159.8708	12.644	0.2655409
		0.8	0.2	6.505	206.5068	14.37034	0.2439051
		0.9	0.1	6.6525	260.1532	16.12927	0.2264517
		1.0	0.0	6.8	320.81	17.91117	0.2121581
		OPTIMAL RISKY PORTFOLIO is the portfolio where Sharp Ratio (SR) is MAXIMUM
		OPTIMAL RISKY PORTFOLIO WILL HAVE w1=Weight of Groeth Fund=0.13=13%
		And w2=Weight of Large Cap Fund=0.87=87%