Easiest way to calculate Standard deviation of portfolio?

[ronzo]

Formula is very cumbersome and will take a little bit of time. I know there are shortcuts for the BAII. Wasn’t sure if there was one for the following example.

What is the standard deviation of a portfolio if you invest 30% in stock one(Standard deviation of 4.6%) and 70% in stock two(standard deviation of 7.8%) if the correlatio coefficient for the two stock is 0.45?

 

[waiguy]

wait, let me check with Markowitz.

 

[maratikus]

ronzo wrote:
Formula is very cumbersome and will take a little bit of time. I know there are shortcuts for the BAII. Wasn’t sure if there was one for the following example.

What is the standard deviation of a portfolio if you invest 30% in stock one(Standard deviation of 4.6%) and 70% in stock two(standard deviation of 7.8%) if the correlatio coefficient for the two stock is 0.45?

Here is one way to remember formula - hopefully, it will help.
1) (a+b)^2=a^2+b^2+2*a*b - easy to remember and it works assuming correlation of 1 and no weights.
2) now add weights a becomes w1*x, b becomes w2*y.
(w1*x+w2*y)^2 = w1^2*x^2+w2^2*y^2+2*w1*w2*x*y - weights are there but still assume correlation of 1
3) now add correlation rho - the formula changes to
Var(w1*x+w2*y) = w1^2*x^2+w2^2*y^2+2*w1*w2*x*y*rho
For your example, w1 = 0.3, w2 = 0.7, x =4.6%, y = 7.8%, rho = 0.45 -> Variance = 0.00385, StDev=sqrt(Variance)=6.2046%. Des this help?

 

[waiguy]

Two asset is simple enough. You should be happy its not three or four or five. Fair attempt to simplify it in above comment. Derives from algebraic formula.

 

[maratikus]

waiguy wrote:
Two asset is simple enough. You should be happy its not three or four or five. Fair attempt to simplify it in above comment. Derives from algebraic formula.

For multiple assets it’s really hard to explain formulas without introducing matrices. Some people find it easy to understand that sigma = sqrt(wT*Sigma*w), where w is the vector of weights (wT- row of weights) and Sigma is the covariance matrix while others are very uncomfortable with matrices.

 

[waiguy]

Yes i have put together a 6 by 6 cov matrix in excel using matrix function in excel. Its hard at first, but nevertheless saves a lot messy formula. Portfolio risk is all about matrices manipulation.