Question

stocks are 50/50.using Risk free rate (6.75%)and risk aversion of(3.75%) determine expected return and standard deviation of ur portfolio..

Standard Deviation for stock ABC =23.87% and XYZ = 14.61% and mean is 6.57% and 18.63%
Correlation is Abc=1.00 and XYZ = 0.3230

Answer 1

Formula

A	B	C	D	E	F	G	H	I
2
3
4
5		Risk free rate	0.0675
6
7		Fund	Return	Standard Return
8		ABC (S)	0.0657	0.2387
9		XYZ (H)	0.1863	0.1461
10
11		Correlation	0.323
12
13		Cov (S,H)	=?*?S*?B
14			=D11*E8*E9	=D11*E8*E9
15
16		Calculation of weight of optimal portfolio:
17		The minimum variance portfolio of two Risky asset can be calculated as follows:
18
19
20
21
22
23		Optimal asset allocation in stock ABC, wmin(S)	=(E9^2-D14)/(E9^2+E8^2-2*D14)
24		Optimal asset allocation in stock XYZ, wmin(H)	=1-D23
25
26		Calculation of expected return of minimum variance portfolio:
27		Portfolio expected return can be calculated as follows:
28
29
30
31
32		Where wi and ri are the weights and return of assets Ai
33
34		Expected return of minimum variance portfolio	=Sum Product of portfolio weight and return
35			=SUMPRODUCT(D23:D24,D8:D9)	=SUMPRODUCT(D23:D24,D8:D9)
36
37		Expected return of minimum variance portfolio	=D35
38
39
40		Given the risk aversion (A) of the investor, the weight of risky assets in the portfolio is given by following equation:
41
42
43
44		Where E(rp) is the expected return of the risky portfolio, rf is the risk free rate,
45		A is risk aversion of investor and ?p2 is the variance of risky portfolio.
46
47
48		Portfolio variance is given by following formula:
49		Portfolio variance = w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cov(A, B)
50		Where wA and wB are weights of assets A and B, ?A and ?B are standard deviation of assets A and B.
51		Given the following data:
52			ABC (S)	XYZ (H)
53		Expected Return	=D8	=D9
54		Standard Deviation	=E8	=E9
55		Weight	=D23	=D24
56		Covariance	=D14
57
58		Variance of Risky portfolio	=w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cov(A, B)
59			=(D55*D54)^2+(E55*E54)^2+2*D55*E55*D56	=(D55*D54)^2+(E55*E54)^2+2*D55*E55*D56
60
61		Hence Variance of risky portfolio is	=D59
62
63		Calculation of weight of risky asset in the portfolio:
64		Given the risk aversion (A) of the investor, the weight of risky assets in the portfolio is given by following equation:
65
66
67
68		Where E(rp) is the expected return of the risky portfolio, rf is the risk free rate,
69		A is risk aversion of investor and ?p2 is the variance of risky portfolio.
70		Using the following data:
71		Expected return of risky portfolio	=D37
72		risk free rate	=D5
73		Risk Aversion	3.75
74		Variance of risky portfolio	=D61
75
76		Weight of risky assets in the portfolio can be calculated as follows:
77		Weight of risky assets in the portfolio	=(E(rp)-rf)/(A*?p2)
78			=(D71-D72)/(D73*D74)	=(D71-D72)/(D73*D74)
79
80		Hence Weight of risky assets in the portfolio	=D78
81		Weight of risk free asset in the portfolio	=1-Weight of risky asset in the portfolio
82			=1-D80
83
84		Using the weight of risky asset in the portfolio and the weight of individual fund in the risky asset,
85		weight of fund in the portfolio can be calculated as follows:
86		Using the following data:
87		Weight of risky assets in the portfolio	=D80
88		Weight of ABC in risky asset	=D23
89		Weight of XYZ in risky asset	=D24
90
91		Weight of ABC in the portfolio	=Weight of risky asset in the portfolio*weight of S&P 500 in risky asset
92			=D87*D88	=D87*D88
93
94		Weight of XYZ in the portfolio	=Weight of risky asset in the portfolio*weight of Hedge fund in risky asset
95			=D87*D89	=D87*D89
96
97		Hence Capital allocation is as follows:
98		Weight of risk free asset	=D82
99		Weight if S&P 500	=D92
100		Weight of Hedge fund	=D95
101
102		Expected return of the overall portfolio can be calculated as follows:
103			Weight	Return
104		Risk Free Asset	=D98	=D5
105		ABC	=D99	=D8
106		XYZ	=D100	=D9
107
108		Expected Return	=SUMPRODUCT(D104:D106,E104:E106)	=SUMPRODUCT(D104:D106,E104:E106)
109
110		Hence expected return of the overall portfolio	=D108
111
112		Standard deviation of overall portfolio	=SQRT(Weight of risky portfolio)* Standard Deviation of Risky Portfolio
113			=SQRT(D80)*SQRT(D61)	=SQRT(D80)*SQRT(D61)
114
115		Hence Standard Deviation of overall portfolio	=D113
116