Analysing Impact of CEO Change on Company Share Price

Applications of Change-point Detection, Cox Regression, and Bayesian Hierarchical Models

A company’s performance relative to its peers will be ultimately driven by management’s strategic decision making ability to drive growth and position the organisation for changing market conditions.

Depending on where you went short at in this example, you could have either made or lost a lot of money — even if you knew about the accounting scandal well in advance.

How long does it take for the replacement of the CEO of a US public company to impact on the company’s performance / share price?

Some Assumptions

Defining The Approach

Isolating Management Impact

Identifying Impact Event Quarter

I think it's pretty clear to anyone looking at the TSLA chart that the major management change impact occurs after around day 2200 (a long time). In ABBV it's less clear but looks like there's a temporary effect at around 1000 until 1300 days.

Change-point Detection Algorithm

The Cumulative Returns (In excess of the stocks GICS sector index) can be modeled as having a linear trend that changes after time ‘b’ due to the impact of the new CEO’s decisions.
In practice, we can easily solve this problem by choosing breakpoint “b” to maximize the likelihood that we observed all the data before time b under model 1 and all the data after time b under model 2.
The likelihoods for both models will be simply the likelihood that the residuals (epsilon_t) were drawn from the normal distribution specified and multiplying all the likelihoods for all time-points together. It's clear that we can’t take derivatives with respect to b here so we will have to solve this with a numerical approach.
You can see the first red dashed line indicating the first change-point (the “Impact Event”), where the management effect started to take hold. The second change-point is mostly irrelevant but helps us also approximately the percentage improvement / dis-improvement due to the new CEO’s decision making which will be useful later we will refer to this as the “Performance Impact Metric”.

Aggregating To Sector Level

Sample of data processing so far.

Crude Poisson Models

The “S” subscript denotes the sector (Eg. Financials, Utilities, Tech etc.), this will be useful later…

Kaplan-Meier Estimator Based on Crude Rates (And Associated Issues)

The Capital Pi is the multiplication of all (1-mu_q) for all quarters up to and including quarter q. The estimator of the survival function is called the Kaplan Meier Estimator and is constant for all times between quarter q and q+1 (exclusive of q+1)
Hazard Rates (Left), Survival Functions (Right) — Dashed lines are the missing data curves.
Some sectors have a lot fewer quarters with good data available.

Bayesian / Survival Modelling

We can see in red the telecommunications sector barely has any observations after about 30 quarters, whereas at market level there is still plenty of information available. The goal is to use or transfer information from the market level as the best guess when no rates or only very noisy rates estimated from a small sample are present.

Results of Bayesian Model

We can see loads of missing data and extreme values past 30 quarters, so we manage to impute some reasonable hazards from market data!

Cox Regression (Proportional Hazards Model)

Choice of Covariates

Results of Cox Model

To interpret this plot simply follow the same fixed colour along each plot to get the hazard when the PI metric covariate is set according to the scale on the plot.

In summary In this article we have isolated effect of management impact on company share prices and identified pivotal change points in the stocks trend. We then used these to create a bayesian model which smooths and imputes crude rates to create a survival function, indicating the probability of management impacts influencing the stock’s trend after a number of quarters since the CEO replacement. I then employed a Cox Model to identify that negative impacts are likely to materialise sooner after the CEO change and that investors should be more patient for positive changes to materialise.

Below i’ve attached some a Github gist for how to do the bayesian modelling from this article.

Some Additional Comments On Robustness

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