Naive Backtesting
This article presents a traditional expanding window backtest of CVaR and variance optimization.
I am occasionally asked about historical backtests “proving” that CVaR is a better risk measure than variance.
I provide such a backtest in Section 2.6 of the Portfolio Construction and Risk Management book1 and explain why it is naive (see the PDF at the bottom of this article).
Although many people are familiar with backtest overfitting and various dangers of generalizing results based on one historical realization, many still happily make conclusions about the quality of different risk measures based on such analysis.
I could have done the same. The backtest after all shows what I think are accurate characteristics of CVaR compared to variance optimization, i.e., that CVaR optimization is likely to result in better performance characteristics given the stylized market facts and investor preferences for avoiding large losses.
However, I am not going to make that conclusion using just this backtest as the only argument. In Chapter 2 of the Portfolio Construction and Risk Management book, I give logical arguments for why this must be the case.
In Section 3.5, I present a better approach for making generalized conclusions using backtests. It contains elements of synthetic market simulation, similar to the Tactical Asset Allocation Performance Lower Bound article2 but with additional nuances.
You can see the results of the historical backtest and my analysis of it in the PDF below. For more information about the book, see the Portfolio Construction and Risk Management Update3.
Portfolio Construction and Risk Management book crowdfunding: https://igg.me/at/pcrm-book
Tactical Asset Allocation Performance Lower Bound Substack post: https://antonvorobets.substack.com/p/tactical-asset-allocation-performance
Portfolio Construction and Risk Management Update Substack post: https://antonvorobets.substack.com/p/portfolio-construction-and-risk-management