17 – M4 L3b 17 IVol Idiosyncratic Volatility V2

Remember from our prior discussions, especially the one about risk models, the returns can be broken up into a systematic and idiosyncratic component. Likewise, the volatility of returns can be broken up into systematic and idiosyncratic components. Idiosyncratic risk maybe a more helpful indicator of arbitrage risk. Why is this? Because market participants who pursue strategies to capture relative mispricings will seek to eliminate common factor risks leaving them bearing idiosyncratic risks only. As such, when we think about the risks to arbitrage, we likely should consider only the idiosyncratic risks. Recall that the systematic component of a stock’s risk can be attributed to movements in major risk factors. For example, using the CAPM model, a part of a stock’s movement can be attributed to the movement of the market as a whole. The rest of the stock’s return that cannot be attributed to major risk factors is the idiosyncratic component of its return. One way to isolate the idiosyncratic return, is by fitting a multiple regression using the risk factors. In this research paper, the authors use the Fama-French model. The model gives a prediction of the return due to the model factors. Since the model factors do not fully explain the stock’s returns, there will be a difference between the actual and modeled returns. This difference is called the residual. If we take the standard deviation of the residual return, we get the idiosyncratic volatility which is also called the idiosyncratic risk. In short, the idiosyncratic volatility or iVol is the volatility that is specific to the stock, and not explained by the risk factors. This is useful for us because when we want to measure a stock’s arbitrage risk, what we’re interested in is the specific or idiosyncratic risk of that stock, and not the systematic risk that exists broadly among all stocks.

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