### 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: VarP = (wASDA)2 + (wBSDB)2 + 2 wAwBCovAB

Thus, CovAB = [(0.17)2 - (wASDA)2 - (wBSDB)2]/(2wAwB) = [0.0289 - 0.0174 - 0.0027]/0.48 = 0.0183.

CorrelationAB = CovAB/(SDASDB) = 0.0183/(0.22 x 0.13) = 0.64

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