Calculating portfolio risk

A question from Yahoo! Answers:

Can I calculate total portfolio risk by using the weighted average of the std (risk) of each stock?

Let’s say I have a portfolio made up of 20 mutual funds. I have the std (risk) of each fund. I want to calculate the over risk of the portfolio. Is it statistically correct to calculate the weighted average of the standard deviations (sum of (std * dollars at that std)/ N) in order to obtain a approximation of the overall portfolio risk? Can I then do the same with historical returns and use (weighted std * weighted return * porfolio value) to obtain the range of expected returns? How can this information then be used to calculate the expected draw down at one and two standard deviations?

No. The formula is much more complex. For a two-asset portfolio, the variance of the portfolio, vp, will be a function of the proportions invested in the assets (x1 and x2), their return variances (v1 and v2), and the covariance between their returns (c12):

vp = ((x12)*v1) + (x22)*v2) + 2*x1*x2*c12

With 20 assets, the formula will be even more confusing (about 20 times so).

You need to employ an alternative strategy. Build a time series of your portfolio value, compute periodic changes in that value, and calculate standard deviation of that change.

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