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# 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?

### 5 Answers

- NCLv 71 decade agoFavorite Answer
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 = ((x1^2)*v1) + (x2^2)*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.

- 1 decade ago
Please see answers below **

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?

** Unfortunately, no. To determine portfolio risk we need to introduce the concept of correlation. Take an extreme example: if a portfolio has two securities, and they both have the same standard deviation. But, the securities were perfectly inverse correlated, when one went up, the other went down by the same amount. This portfolio would have no volatilty. To determine portfolio risk, there are unfortunately more complicated techniques required that are available in portfolio management software packages.

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?

** ** Again, no. To project a range of expected returns using historical returns, in addition to correlation, we need to take into account the fact that past performance is only one possible path through time, and, similation techniques will provide a better probability based range and disperstion of returns which can then be used to estimate drawdown.

- Anonymous1 decade ago
To calculate the std of a portfolio, you need to take the sqrt of the portfolio variance, which for a 20 asset portfolio is quite complicated to calculate without a spreadsheet model. Check out this Wikipedia site for more info on the actual calculation: http://en.wikipedia.org/wiki/Modern_portfolio_theo...

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