# How to calculate unsystematic risk?

We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the unsystematic risk quantitatively? is there any formula or calculation that can be related to the measurement of unsystematic risk?

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You should specify a lot more details in your question. As it is I bet yuo get much answers. Regards – TheBridge Oct 20 '11 at 15:59
You mean the calculation of beta in the Capital Asset Pricing Model, no? As @Quant Guy mentioned, I was also puzzled by the "CAPM formula" in the question. – Feral Oink Oct 21 '11 at 1:30
Hi Norlyda, welcome to quant.SE. Systematic and idiosyncratic (unsystematic) risk are estimated simultaneously in a CAPM-type regression equation. I believe you are misunderstanding CAPM. Please read the relevant wikipedia pages and come back if you still have a question. As it is, this question may be off topic or not a real question. – Tal Fishman Oct 22 '11 at 23:37

I would use the identity that Total Variance = Systematic Variance + Unsystematic Variance. Therefore, you can calculate systematic variance via: Systematic Risk = beta * std(x), so , Systematic Variance = (Systematic Risk)^2, and then you can rearrange the identity above to get:

Unsystematic Variance = Total Variance - Systematic Variance, or if you want the number as "risk" (i.e. standard deviation), then:

Unsystematic Risk = sqrt(Total Variance - Systematic Variance).

NOTE: You're making assumptions here that that the Covariance of Unsystematic and Systematic is 0 (which in my experience holds up a good bit of the time).

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I'm not sure about the "CAPM formula" that you are referring to.

I assume you are referring to the estimated coefficient of a regression of a security on a market portfolio. That is to say

$$\beta_{security,market} = \frac{\sigma_{security,market}}{\sigma^2_{market}}$$

The idiosyncratic risk is the portion of risk unexplained by the market factor. The value of $1 - R^2$ of the regression will tell you this proportion.

Empirically, the idiosyncratic risk in a single-factor contemporaneous CAPM model with US equities is around 60-70%.

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