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%.

Expected return (Kj)

The 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 .

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.

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?

Suppose the CAPM is true. Consider two assets, X and Y, and the market M. Suppose cov(X,M) = .3, cov(Y,M) = .5. %3D (a) Is the expected return higher on X or Y? (b) Suppose var(M) = 1.5, what are the betas of X and Y? (c) Suppose the expected market return is 20% and the risk free rate is 5%, what is the expected returns of X and Y?. (d) Given your analysis in (a)-(c), what type of investor would prefer asset X to asset Y?

Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively.  a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20   b.  If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20%   c.  If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4

Suppose you are given the following inputs for the Fama-Frech-3-Factor model. Required Return for Stock i: bi=0.8, kRF=8%, the market risk premium is 6%, ci=-0.6, the expected value for the size factor is 5%, di=-0.4, and the expected value for the book-to-market factor is 4%. Task:  Estimate the required rate of return of this asset using the Capital asset pricing model and compare it with the Fama-French-3-factor model.

Asset X has an expected return of 10% and volatility of 10% . If its Sharpe Ratio is 0.60, what is the risk-free rate?