In the prior post we calculated the impact of Hurricane Harvey on U.S. P&C (re)insurer stock prices using the actual change in stock price from August 23 through September 1. It is a reasonable proxy for the impact of an event on the stock price, but we can do better.
This post does a proper event study using a Google developed package called CausalImpact. The goal of the analysis is to estimate what the stock prices would have been had the event, in this case Hurricane Harvey, had not occurred (this is called the counterfactual). There are many ways that we could estimate this counterfactual, but the key is to use variables that were themselves not affected by the event. In this case, we use the change in the S&P 500 to estimate what our returns would have been, similar to a traditional capital asset pricing model beta style approach. The CausalImpact package uses fancy statistical methods to help us to this and access reliability of our results.
Estimating what could have been
We will use TRV as an example to illustrate the methodology. The graph below shows the daily returns for TRV stock and the S&P 500 (SPY) over the six weeks prior to September 1. We need to estimate what returns could have been for the eight days highlighted in gray using the actual returns from SPY over those days.
The graph below shows the data that we will use to estimate the returns. The cumulative index returns since January 2017 show that TRV stock does broadly move with the S&P 500. The linear correlation coefficient between the TRV and S&P 500 daily returns for this time period is around 30%.
You can clearly see the divergence in the two time series in the gray box representing the Hurricane Harvey time period.
Now we can apply the statistical method to the data and derive an estimate of the impact of Harvey. The graph below shows the fitted data versus the actual stock price. The fit is good enough for our purposes. The key piece of information is the actual versus fitted results after the vertical line on August 23. You can see that the fitted results as shown by the dotted line indicate a slight increase in stock price over the event time period. In reality, the stock price decreased throughout this period. The difference between actual and expected during the event period is the estimated impact of Harvey. The bottom graph shows this difference, which is just under $10 by September 1, or 7%.
This method also provides us a measure of the uncertainty of our estimates, shown by the gray ribbons in the graphs. In this example, the actual stock price falls outside of the gray ribbon, indicating greater likelihood that the impact we estimate is real and not just random noise.
|Ticker||Company||Estimated||Lower bound||Upper bound||Estimated||Lower bound||Upper bound|
|TRV||The Travelers Companies, Inc.||-7%||-8.9%||-5.2%||-2,473.1||-3,120.5||-1,847.3|
The table above summarizes the results for TRV. It provides the estimated mean outcome (7%) as well as a 90% credible interval which reflects the uncertainty in our estimation. We can also see the impact to TRV’s market capitalization.
Next we replicate the same analysis for every other U.S. P&C (re)insurer stock.
The largest impact is AFSI. However, the uncertainty interval is very large indicating that our model was not appropriate for this stock. That is not surprising given the volatility of AFSI’s stock. The other companies with the largest impacts are as expected. Companies such as XL, NGHC, and RE had meaninfully positive expected returns given our fitted model, so their actual price decreases result in a greater event impact than all other companies.
This analysis highlights the impact that catastrophe losses - in this case still perceived losses - can have on P&C (re)insurer stock prices. The estimated total market value lost is $18.67B. Granted this is likely a short term reaction that will reverse itself in the future, but it is still a big number.