4. On a market with an average expected return of 11% the efficient frontier has the followin equation: E(Rpf) = 5%+3*Opf Compute the Treynor Ratio and the Jensen's alpha coefficient of an actively managed wel diversified portfolio of which return equals 13.5% and variance equals 0.0676%.
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- 5. There are three risky assets with rates of return r₁, 12, and r3, respectively. The covariance matrix and the expected rates of return are [0.4 0.2 0 = Σ 0.2 0.4 0.2 0 0.2 0.4 [0.04] 0.08 0.06 (a) Find the global minimum-variance portfolio. (b) For the required return z = 0.075, find (the weight of) the optimal portfolio with risky assets. For (c) and (d) only, assume there is an additional risk-free asset with return Tf 0.03. = (c) Find the tangent portfolio.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 ratio
- Use 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)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 : NumberThe 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?
- 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)
- 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%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.