Estimating One-Day Earnings Returns from Event Volatility

Summary

This document asks how to translate an earnings event volatility estimate into an implied one-day expected return using a formula from a volatility trading text. The formula combines the exponential of half the event variance with the normal cumulative distribution function evaluated at the volatility. The question specifically concerns how to interpret that distribution term and whether Monte Carlo simulation or the expected value of a straddle is needed; the document does not resolve this question.

It also gives a variance-based method for isolating jump volatility: combine total implied variance through an expiry after the event with an estimate of diffusive variance over the non-event period. The resulting jump component is intended to represent event-related uncertainty. The text supplies no numerical calculation or empirical validation, and it does not explain assumptions behind the return formula, how to choose inputs, or how well the method predicts realized earnings moves. Treat the formulas as a setup for analysis rather than evidence of a reliable forecast.

Key ideas

• The stated expected-return formula uses event volatility and the normal cumulative distribution function evaluated at that volatility.
• The document asks whether simulation or straddle valuation is needed to interpret the formula but provides no answer.
• Jump volatility is estimated by separating diffusive variance from total implied variance through an expiry after the event.
• The method depends on the chosen diffusive volatility and expiry horizon, neither of which is empirically assessed here.

Tags

# How To Calculate The Implied One Day Expected Return For Earnings


# How To Calculate The Implied One Day Expected Return For Earnings












I am trying to figure out how to calculate the one day expected return given I have the event volatility. In his book Trading Volatility, Correlation, Term Structure and Skew, Collin Bennet (link) explains how to calculate the one day expected return given we already calculated the event volatility. However, I am not too sure how to use the $N(\sigma)$ in the formula on Page 247:

$$\operatorname{Expected daily return} = e^{\frac{\sigma^2}{2}} \left[ 2 \cdot N(\sigma) -1 \right]$$

Do I have to run simulations and calculate the expected value of the straddle?

Assuming our event volatility is 100% would someone be able to help me make sense of this formula?

The event volatility was calculated by solving for non-event vol and subtracting it from current ivol. Below is the formula from Page 180.

$$\sigma_{\operatorname{Jump}} = \sqrt{\sigma_{\operatorname{Expiry after Jump}}^2 \cdot T - \sigma_{\operatorname{Diffusive}}^2 \cdot (T-1)}$$

where $\sigma_{\operatorname{Expiry after Jump}}$ denotes the implied volatility of an option whose expiry is after the jump, $T$ is the time to the expiry after jump ($=T_1$), $\sigma_{\operatorname{Diffusive}}$ is the diffusive volatility and $\sigma_{\operatorname{Jump}}$ is the implied volatility due to the jump.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.