Question

Consider the following information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is .97. |

Year | Fund | Market | Risk-Free | |||

2008 | –15.2 | % | –24.5 | % | 1 | % |

2009 | 25.1 | 19.5 | 3 | |||

2010 | 12.4 | 9.4 | 2 | |||

2011 | 6.2 | 7.6 | 4 | |||

2012 | –1.2 | –2.2 | 2 | |||

What are the Sharpe and Treynor ratios for the fund? |

Sharpe ratio | |

Treynor ratio | |

Answer #1

Fund | Market | Risk-free | |

2008 | -15.20% | -24.50% | 1% |

2009 | 25.10% | 19.50% | 3% |

2010 | 12.40% | 9.40% | 2% |

2011 | 6.20% | 7.60% | 4% |

2012 | -1.20% | -2.20% | 2% |

Average | 4.58% | 0.76% | 2.39% |

Std. Dev. | 15.05% | 16.68% | |

Sharpe | 0.1454 | ||

Treynor | 0.0250 |

Calculate Geometric Average Return using following formula:

(1 + R)^5 = (1 + R1) x (1 + R2) x... x (1 + R5)

For Fund, Rp = 4.58% and for Risk-free rate, Rf = 2.39%

Standard deviation can be calculated using STDEV.S function in excel.

Std. Dev. of Fund, SDp = 15.05% and that for Market, SDm = 16.68%

Sharpe Ratio = (Rp - Rf) / SDp = (4.58% - 2.39%) / 15.05% = 0.1454

Beta = Correlation x SDp / SDm = 0.97 x 15.05% / 16.68% = 0.875

Treynor Ratio = (Rp - Rf) / beta = (4.58% - 2.39%) / 0.875 = 0.0250

Consider the following information for a mutual fund, the market
index, and the risk-free rate. You also know that the return
correlation between the fund and the market is .97. Year Fund
Market Risk-Free 2008 –18.20 % –35.5 % 2 % 2009 25.1 20.6 5 2010
13.5 12.7 2 2011 6.8 8.4 6 2012 –1.86 –4.2 3 What are the Sharpe
and Treynor ratios for the fund? (Do not round intermediate
calculations. Round your answers to 4 decimal places.) Sharpe...

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–21.2
%
–40.5
%
2
%
2012
25.1
21.1
4
2013
14.0
14.2
2
2014
6.2
8.8
4
2015
–2.16
–5.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–15.06
%
–26.5
%
3
%
2012
25.1
19.7
5
2013
12.6
10.0
2
2014
6.6
7.6
4
2015
–1.32
–2.2
3
What are the Sharpe and Treynor ratios for the fund?

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–15.06
%
–26.5
%
3
%
2012
25.1
19.7
5
2013
12.6
10.0
2
2014
6.6
7.6
4
2015
–1.32
–2.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
.97.
Year
Fund
Market
Risk-Free
2015
−17.6
%
−34.5
%
2
%
2016
25.1
20.5
4
2017
13.4
12.4
2
2018
6.6
8.4
5
2019
−1.8
−4.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
.97.
Year
Fund
Market
Risk-Free
2015
−16.4
%
−32.5
%
3
%
2016
25.1
20.3
4
2017
13.2
11.8
2
2018
6.2
8.0
5
2019
−1.68
−3.2
3
What are the Sharpe and Treynor ratios for the fund?
Sharpe ratio
Treynor ratio

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–21.8
%
–41.5
%
3
%
2012
25.1
21.2
4
2013
14.1
14.5
2
2014
6.4
8.8
4
2015
–2.22
–5.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–21.2
%
–40.5
%
2
%
2012
25.1
21.1
4
2013
14.0
14.2
2
2014
6.2
8.8
4
2015
–2.16
–5.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

You have been given
the following return information for a mutual fund, the market
index, and the risk-free rate. You also know that the return
correlation between the fund and the market is 0.97.
Year
Fund
Market
Risk-Free
2011
–17.0
%
–33.5
%
2
%
2012
25.1
20.4
6
2013
13.3
12.1
2
2014
6.4
8.0
5
2015
–1.74
–3.2
3
What are the Sharpe
and Treynor ratios for the fund?

You have been given the following return information for a
mutual fund, the market index, and the risk-free rate. You also
know that the return correlation between the fund and the market is
0.97.
Year
Fund
Market
Risk-Free
2011
–22.4
%
–42.5
%
3
%
2012
25.1
21.3
5
2013
14.2
14.8
2
2014
6.6
8.8
6
2015
–2.28
–5.2
3
What are the Sharpe and Treynor ratios for the fund? (Do
not round intermediate calculations. Round your answers to...

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