1. When Does Idiosyncratic Risk Really Matter?
Tony Ruan Qian Sun Yexiao Xu
Xiamen Univ. Fudan Univ UT Dallas
December 11, 2010
2010 NTU International Conference on Finance

2. What Is Idiosyncratic Risk?
Consider a factor model (e.g., the CAPM or APT) for stock returns
In this setup, only systematic risk is priced and idiosyncratic risk is not priced due to a full level of diversification. (Sharp (1964), Lintner (1965), Mossin (1966), Black (1972), Ross (1976)…).

3. Could Idiosyncratic Risk Be Priced?
Idiosyncratic risk may matter.
Divergence of opinion and short-sales constraints. (negatively, Miller (1977))
Imperfect information. (positively, Merton (1987))
Difference between effective and published supplies of securities. (positively, Malkiel and Xu (2002))
Loss aversion (positively, Barberis and Huang (2001)).

4. The Recent Empirical Debate and Research Question
Issues related to times-series empirical evidence
Idiosyncratic risk increased over the past decades (Campbell, Lettau, Malkiel, and Xu (2001), known as CLMX (2001)).
Idiosyncratic risk positively predicts future expected market premium (Goyal and Santa-Clara (2003), known as GS (2003)).
GS’s results are NOT robust to subsamples, alternative measures, and subperiods (Bali, Cakici, Yan, and Zhang (2005) and Wei and Zhang (2005)).
What could explain the seemingly ambiguous results?

5. Our Idea
In a market with frictions, investors in general hold under-diversified portfolios (Goetzmann and Kumar, 2008) so that investors should be exposed to idiosyncratic risk to the extent it is not diversified away.
Hence, researchers have used aggregate idiosyncratic risk measures that are too noisy to deliver consistent and robust results in a time-series predictive regression. We use a simple method to reduce the noise effect in the time-series test.

6. Merton (1987) Revisited Undiversified idiosyncratic risk
Aggregate measure of undiversified idiosyncratic risk
But only aggregate measures of idiosyncratic risk is observed.

7. A Simple Econometric Method

8. Correlation B/W Noises
Simple Simulations
Correlation B/W Noises
High
Low

9. Specifications for Time-Series Tests

10. How to Construct Different Measures of Aggregate Idiosyncratic Risk?
The premise is that small stocks have larger priced idiosyncratic risk components than large stocks.
Using different weighting schemes (i.e., equal-weighted and value-weighted)
to construct n-stock portfolios
to aggregate portfolio idiosyncratic risks

11. A Simple Test Using CRSP VW Index Excess Return
Signal measure - Equal-weighted idiosyncratic risk;
Noise measure - Value-weighted idiosyncratic risk;

12. Main Results (Using CRSP VW Index Excess Return)
Signal
Noise

13. Sharpe Ratios of Trading Strategies Based on Different Forecasts

14. Profitability of Trading Strategies Based on Different Forecasts
P-value

15. Conclusion
Our results suggest that in a time-series predictive regression idiosyncratic risk matters
when investors are under-diversified.
when researchers take into account the noise effect resulting from under-diversification in testing for the effect of idiosyncratic risk.