Size-Adjusted and Value-Weighted Returns for Event Studies

Summary

The document clarifies two return calculations used when measuring event-study abnormal returns. A stock’s size-adjusted return for a day is its own return minus the equal-weighted return of stocks in the same size decile. The described reference group uses NYSE size breakpoints, while membership in the corresponding decile may include stocks from outside NYSE. For an event sample containing multiple companies, the equal-weighted size-adjusted return is the average of those company-level adjusted returns.

The second measure is a value-weighted return across the included companies: each stock’s return is weighted by its market capitalization, calculated from price and shares outstanding, and weights are normalized by total included capitalization. These are distinct aggregation choices: the size-adjustment benchmark is formed within size groups, while value weighting emphasizes larger firms in the selected portfolio or sample. The post gives definitions rather than a full event-study procedure, so it does not specify return timing, missing-data handling, or the exact market-cap measurement date; those choices should be made consistently in an implementation.

Key ideas

• A size-adjusted return subtracts the same-day equal-weighted return of the stock’s size-decile group.
• The size groups are defined using NYSE size deciles, with the example benchmark including other listed stocks in the matching group.
• For multiple event firms, the equal-weighted size-adjusted return averages their individual adjusted returns.
• A value-weighted return uses each included firm’s market capitalization as its weight.
• Consistent timing and data conventions are needed when implementing either measure.

Tags

# Daily value weighted return and equally weighted size adjusted


# Daily value weighted return and equally weighted size adjusted












For an event study, can anyone explain me the daily value weighted return for a benchmark and the equally weighted return size adjusted for measuring the EARs and how to calculate both weights? Regards,

## Answer by Alex C (score 1, accepted)

https://quant.stackexchange.com/a/35108

"Size adjusted return for company X" on day t is defined as the return of company X on day t minus the equal weighted return of all stocks in the same size decile as company X. So for example if company X is in the third NYSE size decile, you average together the returns of all third size decile companies (whether NYSE or not) on day t and you subtract this from the return of company X.

If you have several companies X, Y, Z, etc. then the "equal weighted size adjusted return" means you average together the size adjusted returns (computed as described above) for the companies X, Y, Z, etc.

The "value weighted return" for companies X, Y, Z, etc. is a weighted average of the returns of these companies, where the weights are the market capitalizations (price times shares outstanding) of these companies and the denominator is the total market capitalization of all included companies.

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.