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Single-Asset Adaptive Leveraged Volatility Control

Nikhil Devanathan, Dylan Rueter, Stephen Boyd, Emmanuel Candès, Trevor Hastie, Mykel J. Kochenderfer, Arpit Apoorv, David Soronow, Igor Zamkovsky

Abstract

This paper introduces methodologies for constructing an index composed of a risky asset and a risk-free asset that achieves a fixed target volatility. We propose a simple proportional-control-based approach for setting the index weights, and we demonstrate in simulation that this method is more effective at consistently achieving the target volatility than an open-loop approach. We additionally present a modification to our proportional control approach that reduces index drawdowns in simulation.

Single-Asset Adaptive Leveraged Volatility Control

Abstract

This paper introduces methodologies for constructing an index composed of a risky asset and a risk-free asset that achieves a fixed target volatility. We propose a simple proportional-control-based approach for setting the index weights, and we demonstrate in simulation that this method is more effective at consistently achieving the target volatility than an open-loop approach. We additionally present a modification to our proportional control approach that reduces index drawdowns in simulation.
Paper Structure (15 sections, 14 equations, 4 figures, 1 table, 3 algorithms)

This paper contains 15 sections, 14 equations, 4 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Index weights and returns.
  4. Realized volatility.
  5. Realized index volatility.
  6. Tracking error.
  7. The volatility control problem.
  8. Open-loop approach
  9. Volatility control
  10. Leverage control
  11. Results
  12. Simulation details.
  13. Discussion.
  14. Evaluation
  15. Example

Figures (4)

  • Figure 1: Cumulative returns of four indices.
  • Figure 2: Running annualized estimated volatility of four indices. 15% target volatility is shown as a solid black line. A 90% confidence interval for the running volatility estimate of an asset with a true volatility of $15\%$ is shown as a shaded region.
  • Figure 3: Approximate standard deviation of the ideal EWMA volatility estimate $\sigma^\text{synth}$ as a function of halflife $h$ for $\sigma^{\text{tar}}=0.15/\sqrt{252}$.
  • Figure 4: Distribution of EWMA volatility estimates $\sigma^\text{synth}$ from Monte Carlo simulation with $N=10000$ samples and the first $n=252$ discarded. The dashed lines show the approximate distribution of $\sigma^\text{synth}$ for halflives $h=21,126$.