M.Sc. Finance
M.Sc. International Banking and Finance
and
M.Sc. International Accounting and Finance
2009/010
Portfolio Theory: Tutorial Four
Q1. A portfolio manager buys 30,000 shares in a company today at £9.00 per share. At
the end of each the next three years he sells 10,000 shares. The share price
increases to £10.00 per share at the end of year one, to £13.00 by the end of year
two and falls back to £12.50 by the end of year three. The shares do not pay any
dividends over the three year period.
a) Calculate the time weighted geometric and arithmetic average returns on the
portfolio.
b) Calculate the dollar weighted average return on the portfolio
Q2. You are given the following information on the average returns produced by three
investment funds over the last four years. The risk free rate is 6 per cent, the
average return on the market portfolio is 15 per cent and the standard deviation of
this return was 20 per cent.
Fund Average Annual Return Standard Deviation Beta
A 19% 25% 0.80
B 21% 24% 1.40
C 25% 32% 1.80
a) Calculate the Sharpe, Treynor and Jensen indices and comment on the
rankings produced.
b) Explain why the Treynor and Jensen measures, both based on the capital asset
pricing model, can provide different rankings of portfolios (illustrate this on a
diagrammatic basis).
Q3. Determine the M2 measure for a portfolio if the return on a portfolio with a
standard deviation of 16 per cent was 14 per cent if the risk free rate was 6 per
cent and the return on the market portfolio was 20 per cent with a standard
deviation of 21 per cent. Explain briefly the nature of the information provided by
the measure. Contrast this with Sharpe’s measure. Demonstrate that the Sharpe
and M2 measures provide an identical evaluation of portfolio performance.
Q4.
A fund manager has been given a target beta risk of 1.2. For the periods under
consideration the risk free rate is 6 per cent and the average return on the market
portfolio is 18 per cent with a standard deviation of 20 per cent. The average
return on the fund is 32 per cent, with a standard deviation of 38 per cent, while
the beta of the portfolio is 1.5. Use Fama’s decomposition of risk to assess the
portfolio’s performance, undertaking the relevant calculations and drawing an
appropriate diagram to demonstrate the outcome.