Question 1

You wish to assess the historical risk-adjusted performance of a managed portfolio. The       initial investment occurred at the end of May 2013 .  Data on subsequent portfolio values and cash injections or withdrawals appear in the table below:

(Assume the fund was valued on the dates given and the cash injections and withdrawals occurred immediately afterwards.)

a.         From the data, calculate the yearly time-weighted geometric average returns on the managed portfolio (using 2-digit decimal precision). Briefly compare the averages.

(20 marks)

b.      The returns on the market proxy (RM,t) and on the risk-free asset (Rf,t) over the same period are given in the table below.

c. Using these data and your results from part (a), answer the following:

i.      Calculate the beta of the managed portfolio, then assess the portfolio's                performance over the 5-year period using the Sharpe and the Treynor measures. Interpret your results and illustrate them graphically either in the exam book or    using graph paper.

(50 marks)

ii.      Using the results in part (i) above, infer the values of Jensen's  and M2 that the portfolio achieves using the fact that they can be algebraically related to the       Sharpe and Treynor measures, respectively. Interpret all results . For example,  are the measures consistent and would you expect them to be?

(30 marks) Total: 100 marks

Question 2

The success of active investment strategies is predicated on investor stock-picking or selectivity skills. In an essay, compare and contrast three ways to identify such skills:

•     Jensen’s Alpha (1968)

•     Fama’s (1972) “pure selectivity skills”

•     The Information Ratio

In your essay, discuss how the measures are related and whether they complement one another or may disagree . Discuss which of the measures could be easiest to estimate    empirically.

(Use mathematical expressions and graphical depiction as you see fit.)

Total 100 marks

Question 3

A fund manager summarizes the data received from security analysts and macro-forecasters in the following tables:

Using the data above:

a)  Construct the optimal portfolio according to the model of Black and Treynor (1973),   briefly explaining each of the key steps and interpreting each result. Critically discuss the features of the overall strategy that the model generates. (Be careful to only        perform calculations that are strictly required for the derivation of the optimal              portfolio.)

(60 marks)

b)  Assess the improvement in expected performance over the pure passive strategy      that results from implementing the strategy above. Use both the Sharpe ratio  and an M-squared statistic to justify and interpret your results.

(20 marks)

c)   Graphically show that investing in the optimal portfolio dominates investing in the  passive portfolio alone. (This will require a few more calculations. Ignore the active portfolio. Again, keep to what’s strictly necessary to answer the question.)

(15 marks)

d)  What final implementation step not addressed within the Black and Treynor model, should an investor conduct after they have identified the optimal portfolio?

(5 marks) Total 100 marks