**Please note that this article may contain technical language. For this reason, it is not recommended to readers without professional investment experience.**

**Traditional finance theory assumes that the volatility of assets is constant over time. But in real life, the volatility of assets changes over time. Strategies that target constant volatility – also known as target-volatility strategies – can be shown to generate higher returns for each unit of risk. This is because volatility tends to be easier to forecast than returns. And because the returns tend to be negatively correlated with volatility. Thus, we believe, investors should think in terms of an allocation to volatility instead of an allocation of amounts.**

**Meet the two volatility regimes!**

Rather than being constant, the volatility of asset classes tends to fall into one of two distinct regimes: one with higher average volatility and lower average return and one with lower average volatility and higher average return.

In Exhibit 1 (below), we show the average volatility of returns and the average returns of different asset classes conditional to its respective volatility regimes. In the top of the table, we can see that in the higher volatility regime, average asset class returns tend to be lower, often even negative, while in the low volatility regime, average returns tend to be higher and positive.

**Exhibit 1: Average volatility of returns and the average returns of different asset classes conditional to its respective volatility regimes**

###### Source : Financial Engineering BNP Paribas Investment Partners

*(Estimated parameters of a two-regime **Hidden Markov Model** applied to the time series of the daily total returns in USD of different asset classes. The parameters were obtained from **maximum likelihood estimation** using data from 1 January 1988 through 31 December 2013).*

The differences in average volatility between regimes are larger for asset classes such as equities, e.g. Russell 1000, than for fixed income, e.g. US 10-year government bonds. The differences in average returns are also larger for equities than for fixed income. Finally, volatility is in a higher-volatility regime for 20% to 37% of the time, depending on the asset class considered, and 80% to 63% in a lower-volatility regime.

**What makes a target volatility strategy successful?**

In a recent paper “*Predicting the success of volatility targeting strategies: Application to equities and other asset classes*”, which will appear in the Journal of Alternative Investments in December 2015, we investigate target risk strategies in detail and give the reasons why such strategies can deliver superior returns.

We show that when volatility is not constant and can be forecast, that is already enough to explain the higher Sharpe ratio. Since this is the case for most asset classes, this provides a first explanation of the returns. Indeed, large changes in returns tend to be followed by more large changes in returns (in either direction) and small changes in returns tend to be followed by more small changes.

The volatility of returns then forms the two regimes mentioned above and can be forecast with a certain degree of success. The probability that it jumps from one regime to the other is smaller than the probability that it stays in the same regime.

But this effect alone does not explain in full the returns to target-volatility strategies.

**Fat tails can add value**

In fact, we also find that the asset class returns include fat tails and then the target-volatility strategy can add even more value. When this is the case, we see a clear drop in the largest return drawdowns.

As seen above, the average returns in the lower volatility regimes are much higher than the average returns in the higher volatility regimes, for most of the asset classes. This negative relationship between average returns and volatility explains why the Sharpe ratio from target-volatility strategies is even higher. Such a strategy simply reduces the amount invested in an asset when its volatility is higher and the average return earned is lower, sometimes even negative, for many asset classes.

**Using GARCH models to forecast volatility**

A target-volatility strategy requires the best possible volatility forecasts. GARCH models can capture most of the volatility features of asset classes and have a remarkably high forecasting power.

We have compared the *ex-post* volatility of target-volatility strategies using daily returns to the pre-defined level of target volatility using historical simulations (see Exhibit 2 below). Using GARCH models, we could get target-volatility strategies to deliver an ex-post volatility well in line with pre-defined target levels for all asset classes.

**Exhibit 2: Comparison between the ***ex-post* volatility of target-volatility strategies using daily returns and the pre-defined level of target volatility using historical simulations

*ex-post*volatility of target-volatility strategies using daily returns and the pre-defined level of target volatility using historical simulations

###### Source: R Perchet, R Leote de Carvalho, T Heckel and P Moulin, *“Predicting the success of volatility targeting strategies: Application to equities and other asset classes” *Journal of Alternative Investments, December 2015

**Can transation costs spoil the party? **

The performance is resilient to changes in the frequency with which the portfolio is rebalanced, irrespective of whether this is done daily or weekly. In practical terms, the effect of turnover is acceptable in the case of weekly rebalancing (see Exhibit 3 below). Turnover can be reduced further when volatility is monitored daily and rebalanced only when the volatility changes significantly.

**Exhibit 3: The effect of turnover on the improvement of the Sharpe ratio**

###### Source: R Perchet, R Leote de Carvalho, T Heckel and P Moulin, *“Predicting the success of volatility targeting strategies: Application to equities and other asset classes” *Journal of Alternative Investments, December 2015

**Target-volatility: more effective for some asset classes?**

We looked at the application of the target-volatility strategy to different asset classes.

Larger differences in the average volatility of regimes, larger differences in the average returns of each volatility regime, stronger persistence of volatility to stay in a given regime and the presence of fat tails in the distribution of returns (e.g. high-yield bonds) lead to the most significant improvement in the Sharpe ratio (see Exhibit 4 below).

For investment-grade corporate bonds and government bonds, the differences in the average volatility of regimes and in the average returns in each volatility regime are not large enough to lead to a significant improvement in the Sharpe ratio (at least not in the last 20 years).

**Exhibit 4:**

###### Source: R Perchet, R Leote de Carvalho, T Heckel and P Moulin, *“Predicting the success of volatility targeting strategies: Application to equities and other asset classes” *Journal of Alternative Investments, December 2015

**Controlling volatility can add to multi-asset returns**

In our view, investors should pay attention to the risk management component of multi-asset, or all-in-one, portfolios. Not only can volatility be forecast to a great extent, controlling it can add substantially to returns, using target-volatility strategies, even after transaction costs. In our view, investors should think in terms of allocating a volatility budget to asset classes rather than a given amount of wealth.

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