### Acknowledgements

This article extends the work Cliff Smith presented on 11 July 2016, and none of this would have existed if he hadn’t put in the time and effort to write that great article. As such, I feel it necessary to start off by drawing attention to his work and to give thanks to him for turning me onto this strategy and for inspiring me to explore the field of volatility targeting.

### Overview

This article extends upon Cliff Smith’s work with Volatility Targeting Strategies using 3X Leveraged ETFs by generating synthetic backtest data that approximate the returns 3X leveraged S&P 500 Index and 30 Year Treasury Bonds would have yielded from 1986 to present. To generate the data, the daily returns for VFINX and VUSTX were multiplied by 3 to create a synthetic leveraged index.

The extended strategy seeks to provide a portfolio that targets 12% annualized volatility. From 1986 to present, this leveraged strategy produces a compound annual growth rate [CAGR] of 20.17% with a maximum drawdown [MaxDD] of -25.96%. The risk adjusted return-to-drawdown ratio MAR [CAGR/MaxDD] is 0.78.

### Introduction

As a young[ish] investor, I am always on the search for strategies that offer higher returns without taking on inordinate levels of risk. Trading volatility directly—such as XIV, VXX, and other leveraged volatility ETFs—has shown risk-adjusted returns that are unacceptable for the typical investor, and using a typical 60/40 allocation of stocks and bonds yields reduced returns for a negligible increase in risk-adjusted returns. Thus, the non-institutional investor must look to allocating assets towards leveraged instruments if he or she wishes to increase real returns. In this article, I extend upon Cliff Smith’s work by backtesting a target volatility strategy from 1987 to present and show that one can significantly increase returns without taking on significant risk.Many strategies posted online—whether at SA or otherwise—are guilty of the Backtest Bias. Some backtests go back less than 10 years. Other backtests adjust parameters so that overfitting takes place. Each parameter of a backtest should have some significance, and arbitrary parameter values should be avoided. For example, in Cliff’s article, he discusses the lookback periods for momentum strategies and how the optimal lookback period varies from decade to decade. In this strategy, the parameter value used—target volatility—is 14.4%. This value is chosen because that is the average annualized historic volatility of the S&P 500.

### Target Volatility

By setting a desired level of portfolio volatility, investors can optimize returns for desired levels of risk. Risk Parity and Efficient Frontier are two examples of such optimization. In this method, we take the previous month’s volatility and adjust the current month’s allocations to—hopefully—target an annualized volatility with which we are comfortable. Calculating monthly asset allocations is as follows:

- Assume the portfolio is 60% 3X leveraged stocks—e.g. SPXL—and 40% 3X leveraged long term bonds—e.g. TMF.
- Calculate the portfolio daily returns for the month. [0.01, -0.005, 0.008, …]
- Calculate the annualized volatility of the 3X60/40 portfolio. [STDEV(MONTH_RETURNS)*SQRT(252)]
- Divide the target volatility by the portfolio’s current month annualized volatility. [TAR_VOL/POR_VOL]
- Multiply the ratio calculated from (4) by 60% and 40%.
- The two numbers calculated in (5) tell us how much to allocate to SPXL and TMF, respectively.
- Allocate the rest to a risk-off asset—e.g. MBB.

An argument for volatility targeting is that the market contains clusters of volatile times and clusters of non-volatile times. Keeping in mind these clusters, we can use a 1 month lookback period, to lower portfolio allocations in times of high volatility and raise allocations in times of low volatility.

### Backtest Results

The Portfolio Visualizer link for this backtest can be found here.

Keeping target volatility and portfolio allocation but leveraging to 3x yields the following results:

### Discussion

Utilizing leveraged instruments and volatility targeting provides a model to increase returns, maintain or lower risk, and minimize drawdowns. By extending on Cliff’s work, we showed that the model performs well as far back as 1987.

Though the model did well and the data support a volatility targeting strategy using leveraged instruments, it is not without its limitations. First and foremost, the obvious limitation of synthetic data cannot be understated. Due to its nature, synthetic data cannot provide real world results. Comparing the synthetic data to the current SPXL/TMF volatility targeting strategy results in similar—but not exact—asset allocations. Second, even though we pushed the backtest start date to 1987, it still does not provide us with complete confidence that such a strategy will perform well over the long term. I agree with Cliff that we ought to aim for the half century backtest before confidence levels are sufficiently high. Third, I mention that backtest parameters are often chosen arbitrarily or adapted to fit the data, and then I choose a seemingly arbitrary target volatility parameter. There may be better methods for determining this parameter—perhaps mathematically determining optimal target volatility for some level of return. Perhaps by maximizing the Sharpe Ratio or some other metric.

In the original article, Cliff stated that the strategy is geared towards young investors willing to take on high risk, high reward opportunities. I argue that this strategy can be utilized by investors willing to take on medium to high levels of risk and should not be exclusive to young investors. If we define “risk” as the level of volatility in a portfolio, then the backtest results from this study show that a 3X leveraged volatility targeting strategy does not take on much more risk than simply investing in the S&P 500; risk-adjusted returns for the strategy are much greater than those of the S&P 500. If you had to choose between two portfolios with similar levels of risk, the portfolio with higher returns and a lower drawdown would be the optimal choice—assuming both portfolios are growth/equity focused.

In conclusion, more research into Target Volatility strategies can be done, and the parameters and base portfolio allocations need not be chosen arbitrarily. For example, a combination of Risk Parity and Target Volatilty may yield alternate results—for better or worse.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.