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Consider a market model with three scenarios and two risky assets with rates of return rı...
please help and show your work! Consider a market model with three assets: two risky assets...
please help and show your work!
Consider a market model with three assets: two risky assets (#1 and #2) and one risk-free asset (#3). The risk-free rate of interest is r = 3%. The parameters of the risky returns are as follows: 02 = 15%, Mi = 6%, H2 = 9%, 01 = 10%, P12 = -10%. 1. Let u(x) and g(x) with xe (-0,00) denote, respectively, the expected return and volatility of my portfolio if I allocate 100x% of...
Consider a portfolio consisting of the following two risky assets. Asset i Hi, Return on Asset...
Consider a portfolio consisting of the following two risky assets. Asset i Hi, Return on Asset i 7% 7% 0, Risk in Asset i 18% 14% The coefficient of correlation between the returns is p = -100%. (a) State the expected return and associated risk (as measured by the standard deviation) in terms of w if w is the weight allocation of Asset 1 in the portfolio. Hry (w) = 0.07 Or, (w) = sqrt(0.0632w^2-0.C (b) Suppose that the portfolio...
2. Suppose there are three assets with returns r1, r2, and r3 with the covariance matrix given by...
2. Suppose there are three assets with returns r1, r2, and r3 with the covariance matrix given by: 0.01 r" E(R)0.03 r3 0.09 and Var() Cov(ri, r2) Cov(ri,T3) V(R) Cov(ri,r2) Var(r2) Cov(r2,3) 0.01 0.02-0.02 0.06 0.03 (4) Cov(ri, r3) Cov(r2, Var(ra) -0.02 0.03 0.08 (a) Discuss in detail the different properties of the three assets. (b) Calculate the return and variance of a portfolio in which an investor puts 50% in asset 1 and 50% in asset 2, Hint: In...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
2. Consider a financial market composed of only two risky assets (which are imperfectly correlated). Risky asset 1...
2. Consider a financial market composed of only two risky assets (which are imperfectly correlated). Risky asset 1 has beta equal to B.-1.7 and expected return equal to E(n)-10%. Risky asset 2 has beta equal to B2-0.7 and expected return equal to E(T2)-7%. Find expected return on the market portfolio
Exercise 2. Suppose that there is one risk free asset with return rf and one risky...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance...
An efficient mini-market consists of only three risky assets A, B and C with the composition:...
An efficient mini-market consists of only three risky assets A, B and C with the composition: WF-40%, wg=20 %, and the remaining in Asset C. Using Table Q2 below: Variance / Covariance Expected Rate of Return Asset B Asset C Asset A Asset B Asset C Asset A 0.04 0.018 0.03 0.0225 0.036 12% 22% 0.09 Table 02 (a) Identify the variance of the market portfolio. (5 marks) (b) Identify the beta value of each of the risky assets. (9...
3. Two risky assets with returns ri, r2 and standard deviations 01, 02, and correlation p....
3. Two risky assets with returns ri, r2 and standard deviations 01, 02, and correlation p. Calculate the weights for the following two optimal portfolios. a. Minimum volatility (variance) portfolio minimizes the overall risk min o s.t. Wi+w2 = 1 b. Maximum Sharpe Ratio portfolio delivers the highest expected return of unit of risk may'p - ry ma Op s.t. Wi+w2 = 1
2. Let Ri and R2 be the i.i.d. random rates of return on two assets (with...
2. Let Ri and R2 be the i.i.d. random rates of return on two assets (with positive expected values). Assume the agent has only two options: put all his wealth in one asset, or divide it among the two. (a) Show that a risk-averse agent (with u"< 0) will always divide her wealth between the 2 assets. (b) Show that a risk-loving agent (with u" > 0) will always invest only in one asset.
Assume you are considering investing your personal portfolio in only two possible risky assets: 60% invested...
Assume you are considering investing your personal portfolio in only two possible risky assets: 60% invested in Asset Y and the rest in Asset Z. The characteristics of these two risky assets are as follows: Asset Y has an Expected Return of 12% and a standard deviation of 15% Asset Z has an Expected Return of 9% and a standard deviation of 12% Correlation between the returns of Asset Y and Asset Z is 0.20 Find the Expected Return of...
please help and show your work!
Consider a market model with three assets: two risky assets (#1 and #2) and one risk-free asset (#3). The risk-free rate of interest is r = 3%. The parameters of the risky returns are as follows: 02 = 15%, Mi = 6%, H2 = 9%, 01 = 10%, P12 = -10%. 1. Let u(x) and g(x) with xe (-0,00) denote, respectively, the expected return and volatility of my portfolio if I allocate 100x% of...
Consider a portfolio consisting of the following two risky assets. Asset i Hi, Return on Asset i 7% 7% 0, Risk in Asset i 18% 14% The coefficient of correlation between the returns is p = -100%. (a) State the expected return and associated risk (as measured by the standard deviation) in terms of w if w is the weight allocation of Asset 1 in the portfolio. Hry (w) = 0.07 Or, (w) = sqrt(0.0632w^2-0.C (b) Suppose that the portfolio...
2. Suppose there are three assets with returns r1, r2, and r3 with the covariance matrix given by: 0.01 r" E(R)0.03 r3 0.09 and Var() Cov(ri, r2) Cov(ri,T3) V(R) Cov(ri,r2) Var(r2) Cov(r2,3) 0.01 0.02-0.02 0.06 0.03 (4) Cov(ri, r3) Cov(r2, Var(ra) -0.02 0.03 0.08 (a) Discuss in detail the different properties of the three assets. (b) Calculate the return and variance of a portfolio in which an investor puts 50% in asset 1 and 50% in asset 2, Hint: In...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
2. Consider a financial market composed of only two risky assets (which are imperfectly correlated). Risky asset 1 has beta equal to B.-1.7 and expected return equal to E(n)-10%. Risky asset 2 has beta equal to B2-0.7 and expected return equal to E(T2)-7%. Find expected return on the market portfolio
Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance...
An efficient mini-market consists of only three risky assets A, B and C with the composition: WF-40%, wg=20 %, and the remaining in Asset C. Using Table Q2 below: Variance / Covariance Expected Rate of Return Asset B Asset C Asset A Asset B Asset C Asset A 0.04 0.018 0.03 0.0225 0.036 12% 22% 0.09 Table 02 (a) Identify the variance of the market portfolio. (5 marks) (b) Identify the beta value of each of the risky assets. (9...
3. Two risky assets with returns ri, r2 and standard deviations 01, 02, and correlation p. Calculate the weights for the following two optimal portfolios. a. Minimum volatility (variance) portfolio minimizes the overall risk min o s.t. Wi+w2 = 1 b. Maximum Sharpe Ratio portfolio delivers the highest expected return of unit of risk may'p - ry ma Op s.t. Wi+w2 = 1
2. Let Ri and R2 be the i.i.d. random rates of return on two assets (with positive expected values). Assume the agent has only two options: put all his wealth in one asset, or divide it among the two. (a) Show that a risk-averse agent (with u"< 0) will always divide her wealth between the 2 assets. (b) Show that a risk-loving agent (with u" > 0) will always invest only in one asset.
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