When Does Idiosyncratic Risk Really Matter Tony Ruan
- Slides: 15
When Does Idiosyncratic Risk Really Matter? Tony Ruan Xiamen Univ. Qian Sun Fudan Univ. Yexiao Xu UT Dallas December 11, 2010 NTU International Conference on Finance 1
What Is Idiosyncratic Risk? 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), n Consider a factor model (e. g. , the CAPM or. Mossin APT) for 2 (1966), (1972), Ross (1976)…). stock. Black returns
Could Idiosyncratic Risk Be Priced? n Idiosyncratic risk may matter. n Divergence of opinion and short-sales constraints. (negatively, Miller (1977)) n Imperfect information. (positively, Merton (1987)) n Difference between effective and published supplies of securities. (positively, Malkiel and Xu (2002)) n Loss aversion (positively, Barberis and Huang (2001)). 3
The Recent Empirical Debate and Research Question n n Issues related to times-series empirical evidence n Idiosyncratic risk increased over the past decades (Campbell, Lettau, Malkiel, and Xu (2001), known as CLMX (2001)). n Idiosyncratic risk positively predicts future expected market premium (Goyal and Santa-Clara (2003), known as GS (2003)). n 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? 4
Our Idea n 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. n 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. 5
Merton (1987) Revisited Undiversified idiosyncratic risk Aggregate measure of undiversified idiosyncratic risk But only aggregate measures of idiosyncratic risk is observed. 6
A Simple Econometric Method 7
Simple Simulations High Correlation B/W Noises Low 8
Specifications for Time-Series Tests 9
How to Construct Different Measures of Aggregate Idiosyncratic Risk? n n The premise is that small stocks have larger priced idiosyncratic risk components than large stocks. Using different weighting schemes (i. e. , equalweighted and value-weighted) to construct n-stock portfolios n to aggregate portfolio idiosyncratic risks n 10
A Simple Test Using CRSP VW Index Excess Return Signal measure - Equal-weighted idiosyncratic risk; Noise measure - Value-weighted idiosyncratic risk; 11
Main Results (Using CRSP VW Index Excess Return) Signal Noise 12
Sharpe Ratios of Trading Strategies Based on Different Forecasts 13
Profitability of Trading Strategies Based on Different Forecasts P-value 14
Conclusion n Our results suggest that in a time-series predictive regression idiosyncratic risk matters when investors are under-diversified. n when researchers take into account the noise effect resulting from under-diversification in testing for the effect of idiosyncratic risk. n 15
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