Why Modeling Cannot Reliably Remove Survivorship Bias
Summary
The document considers a proposed adjustment for a stock dataset that omits delisted and bankrupt companies. The proposal models bankruptcy likelihood as dependent on volatility, assigns a distribution of losses at bankruptcy, removes subsequent returns, and duplicates the surviving historical data to retain more observations. The stated research aim is to estimate annual multiplicative returns conditional on starting volatility and the risk-free rate.
The accepted answer cautions that a model-based reconstruction cannot reliably undo survivorship bias without access to the original unbiased dataset. Such an adjustment may replace some survivorship bias with model bias, and its severity cannot be assessed from the biased sample alone. The answer recommends obtaining data with little survivorship bias for serious historical research. It gives no validation of the proposed bankruptcy model or duplication method, so the suggested adjustment should not be treated as a dependable correction.
Key ideas
- A dataset omitting delisted and bankrupt stocks can bias historical return estimates.
- The proposed adjustment models bankruptcy risk by volatility and applies losses before removing future observations.
- Duplicating existing observations does not recover the missing historical companies.
- A model-based correction can introduce additional bias that cannot be measured from the biased dataset alone.
- Reliable research requires access to historical data with little survivorship bias.
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Full text
# How to remove survivorship bias from historical data?
# How to remove survivorship bias from historical data?
I have biased data, missing delisted stocks after the bankruptcies. How to adjust the data to avoid survivorship bias? A simple approach but more or less reasonable one?
The dataset N stocks (250), current volatility and future annual log returns for N years (all stocks start from 1972 and end in 2025).
The bancruptcy probability conditional on company volatility $P(b|σ)$. Defined as PMF in table below for each quantile, table derived from $logit P(b∣σ)=α+βσ$, with β~3-4 and α = total bankruptcy probability per year = 0.5%.
The drop magnitude, most bankruptsies cause 100% loss, the detailed PMF defined in table below.
After the bankruptcy event all future returns of stock removed from the dataset.
To avoid loosing valuable historical data, the original data multiplied, by copying it x10 times. It would distort credible intervals and cross sectional dispersion, but not loosing the data is more important.
Does such approach looks reasonable?
Bankruptcy probability, conditioned on volatility quantile, PMF:
```
q p
0.1: 0.11
0.2: 0.13
0.3: 0.16
0.4: 0.19
0.5: 0.22
0.6: 0.26
0.7: 0.38
0.8: 0.53
0.9: 0.90
1.0: 2.12
```
The drop magnitude, defined as PMF of returns:
```
r p
0.01 0.75
0.05 0.11
0.10 0.05
0.20 0.04
0.30 0.03
0.40 0.02
0.50 0.01
```
P.S.
The main goal - avoid bias in estimation of the annual mean return, conditioned on stock volatility and risk free rate:
$E[S_{365}/S_0|\sigma_0,r_{\text{rf},0}]$
The return - the multiplicative return, like x1.11 it doesn't require drift correction like log return. I want to test if volatile stocks historically had slightly higher expected returns, or not.
## Answer by Chris Taylor (score 5, accepted)
https://quant.stackexchange.com/a/82514
If you have data which is contaminated with survivorship bias, there is no reliable way to un-bias the data without access to the original, un-biased data set.
Your current dataset has survivorship bias. If you try to adjust it with a model, you will now have a dataset containing both survivorship bias and model bias. It is possible that the model bias will partially offset some of the survivorship bias, but it will add new biases of its own, and you have no way to judge how severe those biases are without access to the original, un-biased data set.
If you are serious about doing research into historical stock prices, you need to pay for access to a dataset which does not have (much) survivorship bias. There are no shortcuts.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.