Question

In: Finance

Risky Asset 1 Risky Asset 2 Expected Return 0.11 .15 Standard Deviation 0.28 .88 coefficient of...

	Risky Asset 1	Risky Asset 2
Expected Return	0.11	.15
Standard Deviation	0.28	.88

coefficient of correlation ρ between these two assets is equal to .009, and the risk-free rate is 3.8%.

1. If you wished to construct the optimal risky portfolio using these two assets, what percentage this portfolio would consist of Asset 1?

2. What is the expected return of the portfolio from question 1?

3. What is the standard deviation of the portfolio from question 1?

4. If Rachel has a coefficient of risk aversion of 4.9, what percentage of her money should she invest in the riskless asset if the only risky assets she can invest in are the ones described above?

Expert Solution

A = Risk Asset 1

B = Risk Asset 2

Part A:

Optimal Portfolio: The portfolio with Minimal risk for the given securities

Particulars	Amount
SD of A	28%
SD of B	88%
r	0.0090

Weight in A = [ [ (SD of B)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]

= [ [ (0.88)^2 ] - [ 0.28 * 0.88 * 0.009 ] ] / [ [ (0.28)^2 ] + [ ( 0.88 )^2 ] - [ 2 * 0.28 * 0.88 * 0.009 ] ]

= [ [ 0.7744 ] - [ 0.0022176 ] ] / [ [ 0.0784 ] + [ 0.7744 ] - [ 2 * 0.0022176 ] ]

= [ 0.7721824 ] / [ 0.8483648 ]

= 0.9102

Weight in B = [ [ (SD of A)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]

= [ [ (0.28)^2 ] - [ 0.28 * 0.88 * 0.009 ] ] / [ [ (0.28)^2 ] + [ ( 0.88 )^2 ] - [ 2 * 0.28 * 0.88 * 0.009 ] ]

= [ [ 0.0784 ] - [ 0.0022176 ] ] / [ [ 0.0784 ] + [ 0.7744 ] - [ 2 * 0.0022176 ] ]

= [ 0.0761824 ] / [ 0.8483648 ]

= 0.0898

Part B:

Security	Weight	Ret	Wtd Ret
A	0.9102	11.00%	10.01%
B	0.0898	15.00%	1.35%
Portfolio Ret	11.36%

Part C:

Portfolio SD:

Particulars	Amount
Weight in A	0.9102
Weight in B	0.0898
SD of A	28.00%
SD of B	88.00%
r(1,2)	0.009

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(1,2)]

=SQRT[((0.9102*0.28)^2)+((0.0898*0.88)^2)+2*(0.9102*0.28)*(0.0898*0.88)*0.009]

=SQRT[((0.254856)^2)+((0.079024)^2)+2*(0.254856)*(0.079024)*0.009]

=SQRT[0.0716]

26.75%

Pls do rate, if the answer is correct and Comment, if any further assistance is required

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