Lower the Risk, Higher the Returns?
Typically, investors expect higher returns from high risk investments compared to low risk ones. However, realized returns are the opposite of what they expect.
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/a8cfbf14103efba8718586eaf25087b51-1024x585.png)
This anomaly, where lower risk systematically results in higher returns, has spawned a number of “betting against beta” strategies. A common approach is to rank a universe of stocks by volatility and create a portfolio off the top-N. However, this approach could lead to a highly volatile portfolio if relative correlations are not considered.
1+1 = 0
Here are two stocks with their volatility plotted against time:
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/vol1-1024x512.png)
If you create a portfolio off these two stocks, what happens to portfolio volatility?
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/vol2-1024x512.png)
In the worst case scenario, where all the volatilities are correlated, portfolio volatility can end up being a sum of all component volatility.
If low-vol stocks can create a high-vol portfolio, can high-vol stocks create a low-vol portfolio? Yes! It all depends on how the volatilities are correlated.
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/vol3-1024x512.png)
In the best case scenario, portfolio volatility can be a very low constant value if the components are inversely correlated.
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/vol4-1024x512.png)
It doesn’t matter if individual volatilities are high or low. What matters is the correlation of volatilities.
Portfolio Optimization
A simple ranking of stocks will not help in creating a low-vol portfolio. What we need is a holistic approach that considers the correlation of volatilities and optimizes the entire portfolio.
One way to go about this is to use gradient descent. Start with a random portfolio and go in the direction that minimizes variance (min-var) or expected tail loss (min-ETL)
![](https://portalvhds29z8xdrqhczq.blob.core.windows.net/wordpress/2020/01/min-var-etl-backtest-1024x585.png)
With a monthly rebalance, the chances of the portfolio getting trapped in a local-minima are low. And the backtest looks promising.
Investing in Low-Volatility Portfolios
Equity investors can map our Minimum Variance and Minimum ETL Themes to their portfolios to gain exposure to these low-vol strategies.
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