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Estimating Future Stock Prices from Historical Seasonal Returns

Article Quant Q&A · Author: Haikal Yeo
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Summary

The document considers estimating the chance that a stock reaches a future price by examining returns over a matching calendar period in each of several prior years. It proposes using those returns to normalize past price moves to today’s price, then assessing their distribution. The response recommends including dividends in total returns and ensuring prices are adjusted for stock splits, so the measured outcomes reflect investor returns rather than corporate actions.

The answer cautions that a handful of annual observations is too small for reliable estimates of distribution shape, such as skewness or kurtosis. A small sample may still be used to estimate volatility under a strong simplifying assumption, such as normally distributed log returns with zero mean, but that assumption should be evaluated through backtesting. More frequent observations might improve volatility forecasts, though the document does not report a comparison or establish that they will. It also suggests examining stock performance relative to an index or risk factors, rather than interpreting standalone returns alone.

Key ideas

  • Use total returns that include dividends when measuring an investment’s outcome.
  • Adjust historical prices for splits to avoid treating corporate actions as market losses.
  • A few annual observations provide little basis for estimating skewness or kurtosis.
  • Historical volatility can be used under a distributional assumption, but its forecasts should be backtested.
  • Compare stock returns with a market index or factors to add context.

Tags

EquitiesStatisticsBacktestingFactor investing
Full text
# Find probability of stock reaching certain price in the future given current price today based on historical data


# Find probability of stock reaching certain price in the future given current price today based on historical data












Say I have historical data of a ticker for the past 5 years. I look at the price on the current date for each of the five years (e.g. today is 20 Jul 2023 so I will look at 20 Jul 2022, etc.) and then consider the returns for 3 months (60-80 business days) from that day.

Can I use this as the sample space to determine how the price will move based on historical data?

I'm thinking to use the return as a way to normalise the historical prices to current price and then work out the probability of the returns to answer this question.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/76178

It might make more sense to include any dividends in your returns. If a stock is \$5 now, you don't care whether in 3 months it's \$5.25, or still \$5 after paying \$0.25 dividend.

Ensure that the prices are adjusted for splits. Otherwise, what looks like a 50% price drop, might just be a 2-for-1 split.

It also might make sense to look at the returns not in isolation, but in comparison to some market index (i.e. CAPM) or factors.

If I understand correctly, you want to use just 5 annual data points per stock. If you were to analyze the historical distribution, calculate historical skewness and kurtosis, then I'd say, 5 is too few. But conversely, if you plan to simply assume that everything is (log)normal with mean 0, and just use the historical data to calculate historical standard deviations, then 5 may be enough. When you backtest how well such historical standard deviations predict the future, then you might observe that using more data points, e.g. quarterly or monthly frquency, predicts better, or you might not.

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.