Information arrival as price jumps

Abstract

We propose two new risk measures (i-beta and i-gamma) for a stock, which aim to distinguish between noise and information. Noise allows the stock price evolution to happen along a continuous path. Market wide economic information is transmitted via price jumps. Noise is idiosyncratic and does not propagate across securities. The main contribution is the development of an exact closed-form non-parametric jump risk estimator that boosts the ‘signal-to-noise’ ratio by utilizing co-skew moments. Empirically, the procedure is used to extract the i-beta and i-gamma for Google and Yahoo on NASDAQ, and provide a possible explanation of their seemingly low Sharpe ratio during the 2006–2008 period based on their asymmetrically high i-beta value.

Keywords:

• stock beta
• price jump
• Lévy process
• noise trading
• information
• return skew
• asymmetric beta

AMS Subject Classifications::

• 91G10
• 91G70
• 91B25
• 91B30
• 60G51

Notes

Notes

1. Even though for most stocks β and γ will be positive, the estimator here does not depend on the β and γ signs. Albeit rare, one may consider a particular company for which good news for the economy is bad news for the stock (β < 0).

2. Mathematically, the choice of the index that represents the market is irrelevant. In reality, the econometrician would want to consider using as the market any index that has minimal idiosyncratic noise component q.

3. When obvious, we drop the i subscripts.

4. With time homogeneous Lévy process conditioning information in expectation does not matter.