ProIndex’s Beta Assignment | Homework For You
1. Using the data in the “Thompson Asset Management”, prepare a short report evaluating the performance of the ProIndex fund during years 2009-2013. Your evaluation should be based on a comparison with the S&P 500 index. You should use some (but, most likely, not all) of the performance measures in Exhibit 4. Comment on which performance measure(s), in your opinion, is the most appropriate for different types of investors (for example, you could take two examples: a university endowment with a diversified portfolio managed by multiple firms; and an individual who is interested in entrusting their entire portfolio to TAM.)
Compute ProIndex’s beta. Given ProIndex’s investing style, do you think a single beta estimate does a good job of summarizing the fund’s risk profile?
| Exhibit 2: ProIndex and Market Return Data | ||
| Year | ProIndex | S&P 500 |
| 2009 | 56.48% | 23.45% |
| 2010 | 14.16% | 12.78% |
| 2011 | 11.43% | 0.00% |
| 2012 | 17.20% | 13.41% |
| 2013 | 72.78% | 29.60% |
| Cumulative, 2009-2013 | 303.0601% | 104.63% |
| Daily Standard Deviation | 1.91% | 1.23% |
| Annualized Standard Deviation | 30.32% | 19.47% |
| annualized HPR for S&P500 | 20.93% | |
| beta | 1.014 | |
| annualized HPR | 60.612% | |
| correlation | 0.000637734 | |
| sharpe ratio | 1.990987386 | |
| Treynor ratio | 0.595286163 | |
| Jensen’s Alpha | 0.393956655 | |
| Exhibit 4: Portfolio Performance Measures | ||
| Statistic | Explanation | |
| Holding Period Return (HPR) | Return to the portfolio over a specific period of time, calculated as (ending value – beginning value) / (beginning value). | |
| Annualized Return | Return expressed in annual terms. Daily HPR are converted to annual HPR by multiplying by 252 (trading days per year). | |
| Standard Deviation | Usual statistical calculation for standard deviation. | |
| Annualized Standard Deviation | Standard deviation expressed in annual terms. Daily standard deviations are converted to annual standard deviations by multiplying by the square root of 252. | |
| Correlation | Usual statistical calculation for Pearson correlation coefficient. | |
| Beta | A relative risk measure, calculated by regressing a portfolio’s returns against the market returns. Also calculated by dividing the covariance between the portfolio and the market by the variance of the market. | |
| Sharpe Ratio | Measure of a portfolio’s return per unit of risk. Calculated as the (Portfolio Return – Risk-free Rate) / (Standard Deviation of Returns). | |
| Treynor Ratio | Measure of a portfolio’s return per unit of risk. Calculated as the (Portfolio Return – Risk-free Rate) / (Portfolio Beta). | |
| Jensen’s Alpha | A measure of a portfolio’s return above its required return based on the Capital Asset Pricing Model. Calculated as (Portfolio Return – Risk-free Rate) – Portfolio Beta x (Market Return – Risk-free Rate). | |
| Daily Tracking Error | Excess return of the portfolio over a benchmark portfolio. Calculated as the standard deviation of the (Daily Portfolio Return – Daily Benchmark Return). | |
| Annualized Tracking Error | Tracking error expressed in annual terms. Daily tracking errors are converted to annual tracking errors by multiplying by the square root of 252. | |
| Information Ratio | Measure of a portfolio’s return per unit of risk. Calculated as the (Annual Portfolio Return – Annual Benchmark Return) / (Annual Tracking Error). | |
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