# How to Measure Idiosyncratic Risk in a Stock Portfolio

The risk specific to a particular investment is called idiosyncratic or firm-specific risk. It is the danger associated with an individual business, location or asset class. For instance, a particular company might lose business and its shares might lose value in the wake of an earthquake or other natural disaster. This event only affects firms that operated near the earthquake, leaving other companies largely unaffected. Diversification can lower idiosyncratic risks like these.

Determine the beta of your stock portfolio. Beta is the co-movement of an asset with the market. You can look up beta values for your investments on websites like Yahoo Finance or Google Finance. Once you have these beta values, calculate a weighted beta average that accounts for the different dollar values of each holding. For each holding, multiply its beta value by the percent of the portfolio value it is worth. Add up the products of this multiplication for each holding. This sum is the average beta for the entire portfolio.

Calculate the market risk of the portfolio. To do this, multiply the average portfolio beta by the historical volatility of a diversified stock market index or fund. You can find the volatility listed either as “volatility” or “standard deviation” on financial websites. The index or fund you use as a proxy for all risk assets should have a beta value near 1.

Calculate the market variance of your portfolio by squaring the market risk of your portfolio as calculated in Step 2.

Determine the total risk of your portfolio. The total risk of your portfolio is estimated by calculating the standard deviation of your portfolio's historical returns. You can enter your portfolio holdings into a portfolio back-testing calculator, which will calculate volatility for you. It will report this value as "volatility," "risk" or "standard deviation."

Calculate the total variance of your portfolio by squaring the total volatility of your portfolio as determined in Step 4.

Calculate the idiosyncratic variance of your portfolio. The idiosyncratic variance is calculated by subtracting the square of your portfolio’s market volatility -- the sum you reached in Step 3 -- from the square of your portfolio’s total volatility -- the sum you reached in Step 5.

Take the square root of idiosyncratic variance calculated in Step 6 to calculate the idiosyncratic risk.

#### Tips

• This calculation uses the formula "Idiosyncratic Volatility = Total Variance – Market Variance," where each of the variances is the square of standard deviation or volatility.
• Use a similar, liquid stock as a surrogate for any stock you own that is thinly traded or that is not publicly traded. A surrogate that is traded frequently can give more accurate estimates for volatility and beta than the stale prices of an illiquid or privately traded stock.

#### Warning

• Beta and volatility are commonly measured using past returns. Past values do not guarantee future outcomes.

#### References

• Investments, Second Edition: William F. Sharpe