2. On a market with an average expected return of 11% the efficient frontier has the following equation: E(Rpf) = 5%+3*Gpf Compute the Treynor Ratio and the Jensen's alpha coefficient of an actively managed well- diversified portfolio of which return equals 13.5% and variance equals 0.0676%.
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- a. Compute the expected rate of return on investment i given the following information: the market risk premium is 5%; Rf = 6%; βi = 1.2. b. Compute E(RM).a. Use the following information: E[rXOM] = 15.6%, standard deviationXOM = 15.9% E[rMS]=29.7%, standard deviationMS = 35.2% Correlation of returns: ρXOM,MS = 0.139, rf=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places) b. When choosing the best point of the POS (the curved line connecting two possible assets you can invest in) you need to find the point that: 1.Has the greatest difference between it’s return and the risk free rate, thus leading to the best return 2. You must solve for the optimal y allocation in order to find the best point on the POS 3. The point with the lowest standard deviation 4. The point with the greatest Sharpe ratioThe market has three risky assets. The variance-covariance matrix of the risky assets are as follows: r1 r2 r3 r1 0.25 0 -0.2 r2 0 4 0.1 r3 -0.2 0.1 1 Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08. (1) What is the variance of M?(2) What is the covariance of r2 and M?(3) What is β2?(4) If the rate of return of the risk-free asset is 0.02. Then what is the fair expected rate of return of security 2?(5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?
- Assume we beleive a 1 factor APT model describes securities returns. Consider 2 assets with the following data Security A B Suppose the relevant variances are: Component Systematic Factor Expected Return 5.65% 9.06% € A EB Variance 10.0365 0.0387 0.039 Beta 0.5 1.6 1. The beta of an equally weighted portfolio is: Number 2. The the variance of an equally weighted portfolio is (answer exactly): Number 3. Compute the risk free rate : NumberUse the following information: E[rXOM] = 15.6%, standard deviationyOM = 15.9% %3D E[IMSI=29.7%, standard deviationMS = 35.2% Correlation of returns: PXOM.MS = 0.139, r=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places)Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .
- III. 1. The average variance of financial assets on a market is 0.4% and the average covariance between assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100 assets. a. V(Rpf)=.. b. V(Rpf)=.. 2. On a market at equilibrium the effcient frontier has the following equation: E(Rp)=4%+1.2 opf The standard deviation of the market portfolio equals 5%. a. The expected return on a portfolio A with a beta of 1,2 equals .%. b. How much of the total risk of portfolio B is explained by the market if the correlation between A and B equals 0,5? Answer: R? =. %Compute the expected rate of return on investment i given the followinginformation: Rf = 8%; E(RM) = 14%; βi = 1.0.b. Recalculate the required rate of return assuming βi is 1.8.25. a. Compute the expected rate of return on investment i given the followinginformation: the market risk premium is 5%; Rf = 6%; βi = 1.2.b. Compute E(RM)Assume that the risk-free rate, RF, is currently 9% and that the market return, rm, is currently 16%. a. Calculate the market risk premium. b. Given the previous data, calculate the required return on asset A having a beta of 0.4 and asset B having a beta of 1.8.
- 4. Suppose portfolio P's expected return in 12%, its volatility (standard deviation) is 20%, and the risk-free rate is 5%. Suppose further that a particular mix of asset i and P yields a portfolio P’with an expected return of 18% and a volatility of 30%. a. Compute for the Sharpe ratio of P. b. Compute for the Sharpe ratio of P'. Is adding asset i beneficial? Explain.D4) Give the following true population SIM (not estimated SIM): Ri-Rf=0.1%+1.2(Rb-Rf)+ϵi When estimating this true SIM, what will be the estimated value of alpha (the intercept), when the variance of ϵi is small? Theriskless rate is 0% and the market risk premium is 0.5%. Your answer should be in percentage points. Select one: a.0 b. near 0.1% but not exactly 0.1% c. 0.5% d. 0.1% e. near 0.5% but not exactly 0.5%c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?