## Enhancing MinVol Strategies with Multiple Risk Models

Minimum Volatility strategies have historically delivered portfolios with significant excess returns and much lower volatility compared with broader benchmarks. Quant portfolio managers have been exploiting this anomaly for decades, and this strategy does not seem to be fading away.

Of course, MinVol strategies do not outperform all the time. I was curious – is there a way to create a better MinVol strategy?

I believed there is and created a sample portfolio to explore my hypothesis. As can be seen from the graph, the alpha generated by a European Pure MinVol strategy was highly significant (Alpha = 0.37%/mth or 4.41%/year, t=2.05) [1]. It does tend to outperform in down markets because of its alpha and the low beta, which clearly helps reduce losses.

In a market that is moving slightly upwards, the alpha tends to be larger than the loss from the low beta position. It is only in strong bull markets that the loss from its low beta will be larger than the alpha.

When building MinVol strategies, I can choose between Axioma’s risk models: fundamental or statistical, as well as medium- and short-horizon models. A shorter horizon model will unduly increase turnover, so I used Axioma’s European medium-horizon risk model to perform a 10-year backtest.

**10-year backtest of a Europe MinVol strategy**

The test showed the results would have been the same whether I used our fundamental or our statistical risk model. While the risk of the benchmark was at 15.54% over that period, the two MinVol portfolios generated similar risk reduction with ex-post risk of 9.66% (fundamental) and 9.71% (statistical). In itself, this huge risk reduction makes the MinVol product quite attractive.

The benefits of a MinVol strategy do not stop at risk reduction though. As the volatility factor tends to have a negative drift in its performance, MinVol strategies that are exposed to lower volatility stocks tend to generate alpha. And they did. While the index returned 3.68%, the MinVol portfolio delivered around 5.8% or 2.1% in increased return.

The end result is a significant increase in the Sharpe Ratio from 0.24 (index) to approximately 0.60 for the two MinVol strategies.

I was surprised to see both the fundamental and the statistical risk models delivered very similar results. I suspected that it may vary over time with the fundamental and/or the statistical risk model outperforming at different periods. Axioma’s risk models do an incredible job at delivering portfolios with a much lower volatility than the benchmark. If both risk models deliver a very good estimate of risk, how can I improve from two great risk estimates?

In alpha forecasting, we know that if one has two great, yet highly correlated, alpha signals, some weighted average will beat any of them over time. The same rule applies to risk estimates. If one averages two very good estimates of risk, this average should be superior to any of these two individual estimates.

**Mixing two very good estimates of risk in the same MinVol optimisation**

I thus redid my 10-year backtest. This time, the objective function was to minimize the average risk estimate from both the fundamental and statistical risk models. Axioma’s Optimizer is very flexible in accommodating this.

Results were as expected. There was a slight, yet significant reduction of ex-post risk (which is the thing we were minimizing) to 9.25%. Return was also slightly improved further to 6.14%. The net effect was a significant improvement by about 10% of the Sharpe ratio from 0.6 to 0.66.

With this result, I had answered my initial question. Using more than one risk model can lead to a better MinVol strategy.

Of course, more research is required. My analysis can be region, benchmark, and time dependent. In any case, having access to multiple risk models opens up more possibilities for significantly improving MinVol strategies.

If you’d like to learn more about how multiple risk models can help improve your MinVol portfolios, please contact us

[1] *To be more precise, I should have deducted the risk-free rate from these returns – the Beta estimate is unaffected.*

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