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Handling Short Histories in Mean-Variance Portfolios

Article Quant Q&A · Author: Xiaowan Wen
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Summary

The document considers how to estimate risk and correlation when one asset has far less price history than the rest of a portfolio. It outlines two approaches: exclude assets with histories too short for reliable estimation, or estimate their covariances with a model. Simply forcing the other assets to use the short sample is presented as unnecessary; filling missing observations with zero is not recommended.

For modeled estimates, it describes a factor-based approach: predict an asset’s relationships to a small set of market-driving factors using fundamentals, including for a newly listed company with no trading history. The discussion cites a commercial predicted-beta framework as an example, but gives no formula, validation results, or implementation detail. The choice depends on the researcher's ability to tolerate exclusions or build a credible model, and the suggested factor approach does not directly estimate every pairwise covariance.

Key ideas

  • Short asset histories can make direct covariance estimates unreliable.
  • One option is to exclude assets whose available history is inadequate.
  • A factor model can estimate risk relationships using fundamentals even when an asset has no price history.
  • The described factor approach predicts relationships to a limited set of factors rather than every other asset.

Tags

Portfolio constructionStatisticsRisk management
Full text
# How to deal with securities that has short historical data when performing mean-variance portfolio analysis?


# How to deal with securities that has short historical data when performing mean-variance portfolio analysis?












I am trying calculate expected return and risk (stdev) based on historical data using Mean Variance Analysis framework. Let's say the portfolio has 10 stocks, 9 of them have more than 10 years history but one of them only have 1 month historical data. If I want every stock has the same length of historical data for correlation matrix, shall i just use 1 month of data to estimate? or fill the one with short historical data with 0?

## Answer by Dimitri Vulis (score 2, accepted)

https://quant.stackexchange.com/a/63755

There are two common solutions.

- You exclude from your universe stocks whose history is too short (i.e. only recently went public). Sometimes it breaks your heart to do that, because you really like the stock. (If the time series is long enough, but still has small gaps, there are ways to "fix" the covariance matrix.)

- You use models to predict the covariance. The most famous example of this approach is MSCI Barra predicted beta (see, for example, https://doi.org/10.3905/jpm.2014.41.1.057 for its description). However they don't try to predict the covarance to all other stocks. Rather, they use multifactor model, and predict, based on fundamentals, the correlation to the few factors that they assume to drive the market. They do it right at IPO time with no history.

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.