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**CFA Practice Question**

A portfolio manager has identified two securities for her portfolio. Their expected returns and standard deviations are given below:

Security A - returns: 0.12; Standard Deviation: 0.22

Security B - returns: 0.08; Standard Deviation: 0.13

The manager weights securities A and B in proportions of 3/5th and 2/5th respectively. What is the correlation between A and B if the portfolio standard deviation is 17%?

A. 1.00

B. 0.64

C. 0.50

**Explanation:**For a two-asset portfolio: Var

_{P}= (w

_{A}SD

_{A})

^{2}+ (w

_{B}SD

_{B})

^{2}+ 2 w

_{A}w

_{B}Cov

_{AB}

Thus, Cov

_{AB}= [(0.17)

^{2}- (w

_{A}SD

_{A})

^{2}- (w

_{B}SD

_{B})

^{2}]/(2w

_{A}w

_{B}) = [0.0289 - 0.0174 - 0.0027]/0.48 = 0.0183.

Correlation

_{AB}= Cov

_{AB}/(SD

_{A}SD

_{B}) = 0.0183/(0.22 x 0.13) = 0.64

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**User Contributed Comments**
13

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

dimanyc |
I don't know how it is possible to do such a tedious calculation in 90 sec. |

uberstyle |
some take more than 90, some less. use your time wisely! |

Frehner |
Got it! and it only took me ten minutes...after I looked at the answer. |

copus |
not even Einstein could do this in 90 seconds! |

boddunah |
well well.i wish i was space alien. aliens from different planet could them . |

frants54 |
lol! leave this one |

endurance |
A little risky, but calculations is not nessecary if you are in a hurry. Both assets are increasing but because of different weightings (60% and 40%) and higher stddev of A, this implies more than the 0.5 in correlation coefficient. They are not perfectly correlated, so B seems obvious. |

Sam123456 |
Nice one, endurance, that's the way to do it! |

Sam123456 |
To do this question in time, you can't really write it down, you have to remember the formula and use your memory buttons on the calculator and hope that after you punch in the numbers you get one of those choices! |

cfastudypl |
Similar to endurance's, I simply use the weightings and by foresight, knew that it has to be option B, needless to bother about the calculations. |

ashish100 |
var = (Wa*SDa)^2 + ( Wb*SDb)^2 + 2*Wa*Wb*CoVar Wus good yo.. just typed that without looking. Got that shit down pat now |

ashish100 |
Correlation = CoVar/(SDa*SDb) That too. set for life |

pigletin |
just be familiar with the formula and it will take less than 60 seconds to solve this one |