# Finding Standard Deviation Of 2 Corner Portfolios

This is Study Session 8, Reading 26. When finding the standard deviation of a portfolio consisting of two corner portfolios, why are we using a weighted average of the standard deviations from each corner portfolio? (SD§ = W(a)*SD(a) + W(b)*SD(b)) **Why are we not using the formula for standard deviation of a two asset portfolio? Because that is what this is: (SD§ = SQRT[W(a)^2*SD(a)^2 + W(b)^2*SD(b)^2 + 2*W(a)*W(b)*SD(a)*SD(b)*Corr(a,b)]) Assuming Corr(a,b) = 0, this simplifies to: (SD§ = SQRT[W(a)^2*SD(a)^2 + W(b)^2*SD(b)^2])

…being conservative by assuming the correlation coeff = 1.

The weighted average is just an approximation for the more complicated formula. The approximation overstates the level of portfolio risk because it doesnt account for the correlations. You can’t use the more complicate formula because each corner portfolio is composed of various different asset classes.

Deriv108, how can correlation = 1? Each corner portfolio is composed of totally different asset classes. qqqqqq, wouldn’t the weighted average understate the risk because it assumes correlation = 0? Each corner portfolio is composed of various different asset classes. Why does this mean that I can’t use the more complicated formula? They still have correlations with each other and most of time, the question doesn’t provide correlation or even covariance. I am specifically talking about Schweser 2010 Practice Exam 2 AM, question 6B.

It’s a simplifying assumption, just take it as is. Would you rather waste more time using the more complicated formula?

It would be the weighted correlation coefficient of a multivariate portfolio. You would need covariance of all the asset classes to find the true the SD. In a 4 asset portfolio the calculation is too long to complete more than likely. 1x2, 1x3, 1x4, 2x3, 2x4, 3x4 and remaining squaring of deviations. Assume correlation is 1 between portfolios and state that this is “The Maximum Standard Deviation is xxx.”

I still do not understand how can correlation = 1? Each corner portfolio is composed of totally different asset classes. Or they should give us the correlation on the exam.

AndyPettitteIsGreat Wrote: ------------------------------------------------------- > I still do not understand how can correlation = 1? > Each corner portfolio is composed of totally > different asset classes. Or they should give us > the correlation on the exam. If correlation is not given assume 1 and write maximum. If correlation between portfolios is given you could work it out but I definitely wouldn’t take the time to do a weighted correlation among asset classes.

AndyPettitteIsGreat Wrote: ------------------------------------------------------- > I still do not understand how can correlation = 1? > Each corner portfolio is composed of totally > different asset classes. Or they should give us > the correlation on the exam. With computers, you can do this outside of the exam. For test purposes, this doesn’t seem practical.