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**CFA Practice Question**

A sample size of 24 was put together for estimation of correlation between an index and a portfolio. Covariance was estimated as 354, with the portfolio and index standard deviations being estimated as 35 and 22. What is the value of the correlation co-efficient, and is it significantly different from 0.5 at 5% alpha?

A. 0.10; Yes

B. 0.46; Yes

C. 0.46; No

**Explanation:**Correlation co-efficient = r = 354/(35 x 22) = 0.46. Its standard error is given as: [(1 - r

^{2})/(n - 2)]

^{1/2}, where n is the sample size.

Std. error = [(1 - 0.46

^{2})/(24 - 2)]

^{1/2}= 0.1893, t = (0.46 - 0.50)/0.1893 = -0.21

The absolute value of calculated t is less than the critical t-value of 2.074 (two-tailed). Thus, the estimated correlation is not significantly different from 0.5.

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**User Contributed Comments**
21

User |
Comment |
---|---|

danlan |
Where can I get std. error=sqrt((1-r*r)/(n-2)) ? |

MUSK |
I thought we have to use r*sqrt(n-2) / sqrt (1-r^2). Can some one please explain why we are not using this and do answer danlan's question too. |

PedroEdmundo |
If u carefully pay attention u will realize that they ask different from 0.5 while we have the formula for different from 0. Keep in mind the formula of the test statistic and u will undertand that formula too. |

malley |
MUSK, the formula you gave is to test whether the correlation coefficient is statistically different from zero. As pedro pointed out, the question asks whether the coefficient is statistically different from 0.5. |

achu |
Looking carefully at this you can see that the formula given is just the special case of the general usage of (r- r0)/ [std error] in which r0 = ZERO. This was a HARD question, however; not sure we'd get one like this. |

pjdeschenes |
What section of the material is the standard error for a sample ocrrelation coefficient in? What is the formula? How is the critical value selected? |

sagania |
How does everybody deal with the TIME? For me it remains the biggest issue,,, |

CjjCjj |
are they seriously going to ask this many long compuational questions.. this exam seems like theres no way you could complete this in 3 hours.. there were a lot more long questions than short in my opinion. |

cong |
I don't think this std error formula is requried for the exam. |

Rob09 |
how do we find the critical t-value of 2.074? I understand how to find 2.074 (a t-test chart)...but why is the standard error formula the inverse of the Spearman's rank formula on pg 491 of book 1? |

trikee01 |
i can't remember these formulas |

jonnyp |
they do give us a z-table and t-table at the exam right? I have no idea how to do this on a calculator. |

Mgtw |
No they don't. But they will probably give you a few values one of which is what you'll need. |

Insipidity |
Agree with CjjCjj .... :( |

bsm9 |
This sucks. I hate this. I would rather be out with friends. I deserve better. This exam is a time waster; better to network/market. And there are two more levels? |

change2010 |
haha agreed bsm9! |

Sam123456 |
I've been asking myself that same question bsm9! |

Oksanata |
i think this is not that hard question unless they do not give us t-value..the issue is with standard error: i thought the formula is S/n^1/2..anyone knows where to look for that another formula? |

mpeterson |
I'm going to go ahead and plan on missing this question on the exam. |

jeeychung |
Where does the formula about sd error come from? lol |

jstid40 |
Am I looking at this wrong? This should be with 23 degrees of freedom and thus 2.069 correct? |