Question

In: Finance

Suppose there are three assets: A, B, and C. Asset A’s expected return and standard deviation...

Suppose there are three assets: A, B, and C. Asset A’s expected return and standard deviation are 1 percent and 1 percent. Asset B has the same expected return and standard deviation as Asset A. However, the correlation coefficient of Assets A and B is −0.25. Asset C’s return is independent of the other two assets. The expected return and standard deviation of Asset C are 0.5 percent and 1 percent.
(a) Find a portfolio of the three assets that has the smallest variance among all portfolios that yields the expected return of 0.9 percent.
(b) Find a portfolio of the three assets that has the smallest variance among all portfolios that yields the expected return of rp percent. Find the variance of the portfolio.
(c) Suppose the risk-free rate is zero. Find the tangency portfolio.
(d) Suppose an investor’s mean-variance utility function is E(r)−0.005·A·σ2, where A = 500. Find the investor’s optimal portfolio of the three risky assets and the risk-free asset.

Solutions

Expert Solution

Expected Return of assetA=R1 1%
Expected Return of assetB=R2 1%
S1=Standard Deviation of assetA 1%
S2=Standard Deviation of assetB 1%
Variance of asset A=V1                          1 %%
Variance of asset B=V2                          1 %%
Correlation between asset A and B=Corr(1,2) -0.25
Covariance(1,2)=Cov(1,2)=Corr(1,2)*S1*S2=0 -0.25 %%
w1=Investment in asset A
w2=Investment in asset B
Portfolio Return=Rp(Percentage)
w1*R1+w2*R2=w1*1+w2*1=w1+w2 ……..Equation (1)
Vp=Portfolio Variance=(w1^2)*V1+(w2^2)*1+2*w1*w2*(-0.25)
Vp=Portfolio Variance=(w1^2)*+(w2^2)-0.5*w1*w2….....Equation(2)
Sp=Portfolio Standard Deviation=Square root of Variance=SQRT(Vp)
ALL POSSIBLE PORTFOLIOS
w1 w2 Rp=w1+w2 Vp(Using Equation (2)
Weight of Weight of
AssetA AssetB Portfolio Return(%) Portfolio Variance(%%)
0 1 1 1.0000
0.2 0.8 1 0.6000
0.35 0.65 1 0.4313
0.4 0.6 1 0.4000
0.5 0.5 1 0.3750
0.51 0.49 1 0.3753
0.6 0.4 1 0.4000
0.8 0.2 1 0.6000
1 0 1 1.0000
BEST FEASIBLE CAL: Minimum Variance Portfolio
Variance 0.3750 %%
Weight of Asset 1(Stock Fund (S) 50%
Weight of Asset 2(Bond Fund (B) 50%
Portfolio Return 1%

jeff jeffy answered 3 months ago
Next > < Previous

Related Solutions

Consider the following two assets: Asset A’s expected return is 15% and return standard deviation is...
Consider the following two assets: Asset A’s expected return is 15% and return standard deviation is 20%. Asset B’s expected return is 10% and return standard deviation is 15%. The correlation between assets A and B is 0.5. (a) w1=0.75, w2=.50, find out expected returns and SD/VARIANCE (b) Instead of a correlation of 0.5 between assets A and B, consider a correlation of - 0.5 and re-compute the above.
Asset A has an expected return of 15% and standard deviation of 20%. Asset B has an expected return of 20% and standard deviation of 15%.
      1. Asset A has an expected return of 15% and standard deviation of 20%. Asset B has an expected return of 20% and standard deviation of 15%. The riskfree rate is 5%. A risk-averse investor would prefer a portfolio using the risk-free asset and _______.            A) asset A            B) asset B            C) no risky asset            D) cannot tell from data provided2. The Sharpe-ratio is useful for            A) borrowing capital for investing            B) investing available capital            C) correctly...
There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return...
There are 2 assets. Asset 1: Expected return 7.5%, standard deviation 9% Asset 2: Expected return 11%, standard deviation 12%, correlation with asset 1 is 0.4 You hold 30% of your portfolio in asset 1 and 70% in asset 2. a) (1 point) What is the expected return of your portfolio? b) (1 point) What is the covariance between assets 1 and 2? c) (1 point) What is the standard deviation of your portfolio?
suppose asset a has an expected return of 10% and a standard deviation of 20% asset...
suppose asset a has an expected return of 10% and a standard deviation of 20% asset b has an expected return of 16% and a standard deviation of 40%.if the correlation between a and b is 0.6,what are the expected return and standard deviation for a prtifolio comprised of 40% asset a
expected return and standard deviation. stateecon, probability, asset A, asset B, Asset C boom.              0.34.       0.02.     &nbs
expected return and standard deviation. stateecon, probability, asset A, asset B, Asset C boom.              0.34.       0.02.       0.22.       0.34 normal.            0.52.       0.02.       0.05.       0.18 recession.        0.14.      0.02.       -0.01.     -0.25 A) what is the expected return of each asset? B) what is the variance of each Asset? C) what is the standard deviation of each asset?
The (annual) expected return and standard deviation of returns for 2 assets are as follows: Asset...
The (annual) expected return and standard deviation of returns for 2 assets are as follows: Asset A : E[r] 10% , SD[r] 30% Asset B : E[r] 20% , SD[r] 50% The correlation between the returns is 0.15 a. Calculate the expected returns and standard deviations of the following portfolios: i) 80% in A, 20% in B : 12%/27.35% ii) 50% in A, 50% in B : 15% /30.02% iii) 20% in A, 80% in B : 18%/41.33% b. Find...
A. Suppose you have an asset with an expected return of 0.12 and a standard deviation...
A. Suppose you have an asset with an expected return of 0.12 and a standard deviation of 0.18. If the riskless rate is 0.04, what combination of the risky asset and a riskless asset would give you an expected return of 0.09? What would be the standard deviation of this combination? (5 pts.) B.Find the proportion of risky and riskless assets contained in a combined portfolio whose expected return is 0.12 per year, where the riskless rate is 0.05 and...
Consider a set of risky assets that has the following expected return and standard deviation: Asset...
Consider a set of risky assets that has the following expected return and standard deviation: Asset Expected Return E(r) Standard Deviation 1 0.12 0.3 2 0.15 0.5 3 0.21 0.16 4 0.24 0.21 If your utility function is as described in the book/lecture with a coefficient of risk aversion of 4.0  , then what is the second-lowest utility you can obtain from an investment in one (and only one) of these assets? Please calculate utility using returns expressed in decimal form...
You have the following assets available to you to invest in: Asset Expected Return Standard Deviation...
You have the following assets available to you to invest in: Asset Expected Return Standard Deviation Risky debt 6% 0.25 Equity 10% .60 Riskless debt 4.5% 0 The coefficient of correlation between the returns on the risky debt and equity is 0.72 2A. Using the Markowitz portfolio optimization method, what would the composition of the optimal risky portfolio of these assets be? 2B. What would the expected return be on this optimal portfolio? 2C. What would the standard deviation of...
You have the following assets available to you to invest in: Asset Expected Return Standard Deviation...
You have the following assets available to you to invest in: Asset Expected Return Standard Deviation Risky debt 6% 0.25 Equity 10% .60 Riskless debt 4.5% 0 given =The coefficient of correlation between the returns on the risky debt and equity is 0.72, previously solved = the composition of the optimal risky portfolio of these assets is -0.42, the expected return on this portfolio is 11.663796% and the standard deviation on this portfolio is 78.10% 2D. Hector has a coefficient...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT