# Std Dev - Tricky or did I goof it up ?

There was a question in Part-2 actual CFA exam. For confidentiality reasons, I cannot post the actual question but it was something like. There were 2 stocks X & Y in a portfolio (50% each) with returns 3 & 5% respectively. The std dev were 4 and 6 respectively. Find the standard deviation of the portfolio ? My question is that do we need to worry about individual standard deviaiton in the calculation of portfolio standard deviation. I reckon that we need to first compute mean and then variance and finally taking square root to calculate std dev of the combined portfolio. Do we need to worry about individual standard deviations of X & Y in this question? Thanks, DD

yes, you needed them and then you use the formula for std dev of a portfolio (weight squared * variance for each stock + 2*w1*w2*stdev1*stdev2*correlation)

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There was a standard formula for that in the quants book. The above mentioned formula with square root is correct. It was not a tricky question. I think the answer was 3.5%. It was the last but 2 question I guess.

rpradeephere Wrote: ------------------------------------------------------- > There was a standard formula for that in the > quants book. The above mentioned formula with > square root is correct. It was not a tricky > question. I think the answer was 3.5%. It was the > last but 2 question I guess. thanks Pradeep ! I have the same vague souvenir of ticking the 3.5% bubble

This was a very straightfoward question… wise all the questions were like that.

Thanks guys. I got confused a bit during the exams but I remember clearly that I marked 3.5 as well using some common-sense (as I didnt remember the formula)

willispierre Wrote: ------------------------------------------------------- > yes, you needed them and then you use the formula > for std dev of a portfolio (weight squared * > variance for each stock + > 2*w1*w2*stdev1*stdev2*correlation) Bingo. The ‘trick’ they try on you in this question is that they say the positions are equally weighted, and if you fall for it you just find the arithmetic mean of the std devs. Since you can’t do that to find std dev of a portfolio, you have to use the above formula.

I had trouble with that Q too. I know the formula, but for some reason , I kept getting 5.3 as the answer. I kept repeating my calc like for 10 mins and never got it right . Not sure what silly stuff I was doing.

Tthe calculation for the std of two portfolios (assets, positions, etc) is nonlinear (i.e., use the formula!). The only exception is when the correlation is 0 may you use a straight weighted average.