1) An investor chooses a portfolio comprising a risk-free asset, yielding r₀ = 2%, and a single risky asset with expected rate of return _Z = 6%, and standard deviation of return _Z = 0.1, to maximize the objective function, _P 5_p², where P is the expected rate of return on the portfolio and _P² is the variance of the rate of return on the portfolio.

A. The proportion of the portfolio invested in the risk-free asset equals 0.60. B. The proportion of the portfolio invested in the risk-free asset equals 0.40. C. The proportion of the portfolio invested in the risky asset equals 0.06 (i.e., 6%).

D. The proportion of the portfolio invested in the risky asset equals 0.60,(i.e.,60%).

There is at least one correct answer.

2) An investor chooses a portfolio that maximizes a mean-variance objective function. [Notation: r₀: risk-free interest rate; _j: expected rate of return on asset j; _j: stan- dard deviation of return on asset j; _P : expected rate of return on the optimum port- folio P ; _P : standard deviation of the return on the optimum portfolio P ; _jP : co- variance between the rate of return on asset j and portfolio P .]

At the investors optimum, the following condition holds for every asset, j:

A. (_j r₀)/_j² =(_P r₀)/²_P. B. (i r₀)/_i = (_j r₀)/j, for every pair of assets i and j (i j).

C. (_j r₀)/^_jP = (_P r₀)/_²P .

D. (_P r₀)=(_j r₀)_jP, where _jP =_jP/²_P.

E. (_j r₀)/_j = (_P r₀)/_jP .

There are at least 1 correct answer.

3) The expected rate of return on an asset, _j, equals 10%. Its standard deviation of return, j , equals 0.20, the standard deviation of the market return, _M , equals 0.4, and the risk-free interest rate is 2%. The standard deviation of return for a benchmark portfolio, _B , equals 0.5, to be used in calculating the Risk Adjusted Performance.

A. Assuming the CAPM holds, the assets beta-coefficient equals 0.5.

B. Assuming the CAPM holds, the assets beta-coefficient equals 0.8.

C. The assets Risk Adjusted Performance equals 4%. D. The assets Risk Adjusted Performance equals 8%.

E. The assets Risk Adjusted Performance equals 12%.

F. The assets Risk Adjusted Performance equals 22%.

There are at least 1 correct answer.

4. Asset js standard deviation of return is _j = 0.4, while for the market portfolio _M=0.2. The expected rate of return on the market portfolio is _M =8% and risk- free interest rate is r₀ = 3%. Let _jM = the correlation between the rate of return on asset j and that of the market portfolio.

a) If _jM = 1, asset js beta-coefficient, _j = 1.

b) If _jM = 0.6, asset js beta-coefficient, _j = 1.2.

c) Asset js beta-coefficient _j = 2.0 irrespective of the value of _jM .

d) The information is necessarily incompatible with the Capital Asset Pricing Model, CAPM, if _jM <0.

e) If _jM = 0.6, the CAPM predicts that js expected rate of return equals 9%.

f) If _jM = 0, the CAPM predicts that asset js expected rate of return equals 5%.

There are at least one correct answer.

5. Asset js standard deviation of return is _j = 0.4, while for the market portfolio _M = 0.5. The covariance between the asset js return and the market return is: _jM = 0.2. The expected rate of return on the market portfolio is _M = 6% and risk-free interest rate is r₀ = 1%.

a) Asset js beta-coefficient is _j = _jM /_M = 0.4.

b) Asset j lies on the Capital Market Line, CML, (i.e., the Sharpe ratio for asset j equals that for the market portfolio) in the Capital Asset Pricing Model, CAPM.

c) The CAPM predicts that asset js expected return is _j = 6% because its beta- coefficient equals 1.

d) The CAPM predicts that asset js expected return is _j = 1% because its beta-coefficient is zero.

e)The CAPM predicts that asset js expected return is _j = 4% because its beta- coefficient is 0.6.