You are going to invest in Asset J and Asset S. Asset J has an expected...

You are going to invest in Asset J and Asset S. Asset J has an expected return of 14.4 percent and a standard deviation of 55.4 percent. Asset S has an expected return of 11.4 percent and a standard deviation of 20.4 percent. The correlation between the two assets is .50. What are the standard deviation and expected return of the minimum variance portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Solutions

Expert Solution

Minimum Variance Portfolio :

A minimum variance portfolio is a collection of securities that combine to minimize the price volatility of the overall portfolio. with the given weights to securities/ Assets in portfolio, portfolio risk will be minimal.

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) ] ]
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) ] ]

A = Asset J

B = Asset S

Particulars	Amount
SD of A	55.40%
SD of B	20.40%
r(A,B)	0.5000

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) ] ]
= [ [ (0.204)^2 ] - [ 0.554 * 0.204 * 0.5 ] ] / [ [ (0.554)^2 ] + [ ( 0.204 )^2 ] - [ 2 * 0.554 * 0.204 * 0.5 ] ]
= [ [ 0.041616 ] - [ 0.056508 ] ] / [ [ 0.306916 ] + [ 0.041616 ] - [ 2 * 0.056508 ] ]
= [ -0.014892 ] / [ 0.235516 ]
= -0.0632

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) ] ]
= [ [ (0.554)^2 ] - [ 0.554 * 0.204 * 0.5 ] ] / [ [ (0.554)^2 ] + [ ( 0.204 )^2 ] - [ 2 * 0.554 * 0.204 * 0.5 ] ]
= [ [ 0.306916 ] - [ 0.056508 ] ] / [ [ 0.306916 ] + [ 0.041616 ] - [ 2 * 0.056508 ] ]
= [ 0.250408 ] / [ 0.235516 ]
= 1.0632
Expected Ret:

Portfolio Return is the weighted avg return of securities in that portfolio

Stock	Weight	Ret	WTd Ret
Stock J	(0.0632)	14.40%	-0.91%
Stock S	1.0632	11.40%	12.12%
Portfolio Ret Return			11.21%

Portfolio SD:

Particulars	Amount
Weight in A	-0.0632
Weight in B	1.0632
SD of A	55.40%
SD of B	20.40%
r(A,B)	0.5

Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)]
=SQRT[((-0.0632*0.554)^2)+((1.0632*0.204)^2)+2*(-0.0632*0.554)*(1.0632*0.204)*0.5]
=SQRT[((-0.0350128)^2)+((0.2168928)^2)+2*(-0.0350128)*(0.2168928)*0.5]
=SQRT[0.0407]
= 0.2017
= I.e 20.17 %

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

You are going to invest in Asset J and Asset S. Asset J has an expected...

You are going to invest in Asset J and Asset S. Asset J has an expected return of 11.2 percent and a standard deviation of 52.2 percent. Asset S has an expected return of 8.2 percent and a standard deviation of 17.2 percent. The correlation between the two assets is .50. What are the standard deviation and expected return of the minimum variance portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

You are going to invest in Asset J and Asset S. Asset J has an expected...

You are going to invest in Asset J and Asset S. Asset J has an expected return of 13.8 percent and a standard deviation of 54.8 percent. Asset S has an expected return of 10.8 percent and a standard deviation of 19.8 percent. The correlation between the two assets is .50. What are the standard deviation and expected return of the minimum variance portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Assume that you are going to invest $140,000 in a two asset portfolio. You will invest...

Assume that you are going to invest $140,000 in a two asset portfolio. You will invest $100,000 in the fully diversified market portfolio and the remainder of your funds will be invested in the riskless security. Assume the market risk premium is 8% and the riskless return is 4%. Compute the expected return on this portfolio. Respond in percentage form without the percent sign and round to the second decimal place.

You invest $98 in a risky asset and the T-bill. The risky asset has an expected...

You invest $98 in a risky asset and the T-bill. The risky asset has an expected rate of return of 18% and a standard deviation of 0.24, and a T-bill with a rate of return of 5%. A portfolio that has an expected outcome of $111 is formed by investing what dollar amount in the risky asset? Round your answer to the nearest cent (2 decimal places).

You invest $100 in a risky asset with an expected rate of return of 0.13 and...

You invest $100 in a risky asset with an expected rate of return of 0.13 and a standard deviation of 0.11 and a T-bill with a rate of return of 0.03. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

You invest $100 in a risky asset with an expected rate of return of 0.11 and...

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? Select one: a. 30% and 70% b. 50% and 50% c. 60% and 40% d. 40% and 60% e. Cannot be determined....

You invest $100 in a risky asset with an expected rate of return of 0.25 and...

You invest $100 in a risky asset with an expected rate of return of 0.25 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.05. If the portfolio standard deviation is 0.12, what is the expected return of this portfolio? A. 14.0% B. 12.0% C. 13.0% D. 17.0% E. Cannot be determined

You invest $100 in a risky asset with an expected rate of return of 9% and...

You invest $100 in a risky asset with an expected rate of return of 9% and a standard deviation of 0.15 and a T-bill with a rate of return of 5%. What percentages of your money must be invested in the risky asset to form a portfolio with an expected return of 9%?

You invest $100 in a risky asset with an expected rate of return of 0.14 and...

You invest $100 in a risky asset with an expected rate of return of 0.14 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.06. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? A. 30% and 70% B. 50% and 50% C. 60% and 40% D. cannot be determined E. 40% and 60%

You invest $100 in a risky asset with an expected rate of return of 15% and...

You invest $100 in a risky asset with an expected rate of return of 15% and a standard deviation of 15% and a T-bill with a rate of return of 5% and E (U)= E(r) - 0.5Aσ2. Suppose your risk aversion factor is 5. What weight would you assign to the risk-free asset? A) 0.8889. B) 0.1111. C) 0.2457. D) 0.2111.

Subjects