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## Treynor index.

**Question description**

You are given the following information concerning several money market funds:

Money Market Fund | Return in Excess of the Treasury Bill Rate | Beta |

A | 12.4% | 1.14 |

B | 13.2% | 1.22 |

C | 11.4% | 0.90 |

D | 9.8% | 0.76 |

E | 12.6% | .095 |

During the time period the Standard & Poor’s stock index exceeded the Treasury bill rate by 10.5 % (i.e., rm – rf = 10.5%)

Rank the performance of each fund without adjusting for risk and adjusting for risk using the Treynor index. Which, if any, outperformed the market? (Remember, the beta of the market is 1.0).

The analysis is part (a) assume each fund is sufficiently diversified so that the appropriate measure of risk is the beta coefficient. Suppose, however, this assumption does not hold and the standard deviation of each fund’s return was as follows:

Money Market Fund | Standard Deviation of Return |

A | 0.045 (= 4.5%) |

B | 0.031 |

C | 0.010 |

D | 0.014 |

E | 0.035 |

Thus, Fund A earned a return of 12.4%, but approximately 68% of the time this return has ranged from 7.9% to 16.9%. The standard deviation of the market return is 0.01 (i.e., 1 %), so 68 % of the time, the return on the market has ranged from 9.5 to 11.5%. Rank the funds using this alternative measure of risk. Which, if any outperformed the market on a risk-adjusted basis?

*Note: The Treynor Performance Index is an alternative measure for portfolio evaluation.

Ti = Rp (realized return on the portfolio) – Rf (the risk-free rate) / b (Portfolio beta, the measure of systematic risk)

Thus, if the portfolio manager X achieved a return of 15 percent when the risk-free rate was 7 percent the the portfolio’s beta was 1.1, the Treynor Index is

Ti = 0.15-0.07/1.1 = 0.0727

If portfolio manager Y achieved a return of 13.5 percent with a beta of 0.8, the Treynor Index is

Ti = 0.135 – 0.07 /0.8 = 0.08125

This indicates that portfolio manager Y outperformed portfolio manager X on a risk-adjusted basis