Difficulties in adjusting average returns for risk present a host of issues, as the proper measure of risk may not be obvious, and risk levels may change along with portfolio composition.

1. You purchased a rental property for K50 000 and sold it one year later K55 000. At the time of the sale, of the sale, you paid K2 000 in commission and K600 in taxes. If you received K6 000 in rental income (all of it received at the end of the year), what annual rate of return did you earn? (10 marks)
2. A two year investment of K2 000 results in a return of K150 at the end of the first year and a return of K150 at the end of the second year, in addition to the return of the original investment. What is the internal rate of return on the investment? (05 marks)
3. Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11 % and 14 %, respectively. The beta of A is 0.8 % while that of B is 1.5. The T-bill is currently 6 %, while the expected rate of return of the S&P 500 index is 12 %. The standard deviation of portfolio A is 10 % annually, while that of B is 31 % , and that of the index is 20 %:
4. If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
5. If instead you could invest only in bills and one of these portfolios, which would you choose, and why? Investor Y, who put K1 in large stocks (the S & P 500 portfolio) on December 31, 1925, and re-invested all dividends in that portfolio, would have ended on December 31, 2003, with K1992.80.
6. The following data relates to the portfolios of a funds two equity managers

Total Return Beta

Manager A 24 % 1.0

Manager B 30.0 % 1.5

S&P 500 21.0

Lehman 31.0

1. day Treasury bills 12.0

Calculate and compare the risk-adjusted performance of the two managers relative to each other and to the S&P 500.

Explain the reasons why the conclusions drawn from this calculation may be misleading.

1. Given the following sample data, calculate the performance measures for portfolio P and the market (Sharpe, Jensen/Alpha and Treynor. The T-bill rate during the period was 6 %). By which measure did portfolio P outperform the market?

Portfolio P Market M

Average return 35 % 28 %

Beta 1.2 1.0

Standard deviation 42 % 30 %