Volatility Targeting in Multi-Asset Portfolios

1. The Volatility-Return Relationship

Moreira and Muir (2017) demonstrated a striking empirical regularity: a strategy that scales its market exposure inversely with recent realised volatility — holding more when volatility is low and less when volatility is high — produces substantially better risk-adjusted returns than a constant-exposure strategy. The mechanism is the negative relationship between volatility and expected returns at the daily-to-monthly frequency: periods of high volatility tend to coincide with negative or below-average returns, while low-volatility periods tend to produce positive returns.

This relationship is not merely a consequence of the well-known leverage effect (negative returns cause volatility to rise). It persists in out-of-sample tests, across asset classes, and in international markets. For systematic traders, the implication is practical and immediate: scaling position sizes by inverse volatility is a free improvement to nearly any strategy.

2. Implementation

The implementation is simple. At each rebalancing date, compute the trailing realised volatility of each position using a short lookback window (We use 20 trading days as the baseline). Then scale the position size so that the ex-ante contribution to portfolio volatility equals the target:

where w_i^base is the unscaled weight and σ_i(t) is the trailing realised volatility of asset i. The total portfolio exposure is then adjusted so that the portfolio-level volatility matches the target:

import numpy as np

def volatility_target_weights(returns, base_weights,
                               vol_target=0.10, lookback=20):
    """
    Compute volatility-targeted weights for a multi-asset portfolio.

    Args:
        returns: (T, N) array of daily returns
        base_weights: (N,) array of base (signal) weights
        vol_target: annualised volatility target
        lookback: days for realised vol estimation
    Returns:
        (T, N) array of daily adjusted weights
    """
    T, N = returns.shape
    daily_target = vol_target / np.sqrt(252)
    adjusted = np.zeros_like(returns)

    for t in range(lookback, T):
        window = returns[t-lookback:t]

        # Per-asset realised volatility
        asset_vols = np.std(window, axis=0)

        # Scale individual positions
        inv_vol = np.where(asset_vols > 0, 1.0 / asset_vols, 0)
        scaled = base_weights * inv_vol

        # Portfolio-level scaling
        port_returns = window @ scaled
        port_vol = np.std(port_returns)

        if port_vol > 0:
            leverage = daily_target / port_vol
            adjusted[t] = scaled * leverage
        else:
            adjusted[t] = scaled

    return adjusted

3. Results Across Asset Classes

We apply volatility targeting to individual asset class portfolios (equities, bonds, commodities, FX) and to a diversified multi-asset portfolio containing all four. The baseline is an equal risk-weighted portfolio with fixed weights, rebalanced monthly. The evaluation period is 2005–2024.

Table 1: Impact of 10% volatility targeting on risk-adjusted performance. All figures use 20-day realised volatility for scaling.

The improvement is positive across every asset class, with the largest gains in commodities (+0.23 Sharpe) and the multi-asset portfolio (+0.24). The mechanism is consistent: volatility targeting reduces exposure during high-volatility drawdown periods, materially reducing maximum drawdown (38.4% to 22.7% for equity indices). The multi-asset portfolio achieves a Sharpe of 0.78 with a maximum drawdown of 12.8% — a risk-return profile that compares favourably to most systematic fund benchmarks.

4. Interaction with Momentum

A natural question is whether volatility targeting provides additive value when combined with momentum signals, which also reduce exposure during drawdowns (by going short or flat when recent returns are negative). We test a time-series momentum strategy (12-month look-back, 1-month holding period) with and without volatility targeting.

Table 2: Momentum and volatility targeting applied to the multi-asset portfolio. The combination produces a Sharpe ratio 27% higher than momentum alone.

The combination is substantially better than either component alone. Momentum and volatility targeting are complementary because they respond to different aspects of the return-generating process: momentum adjusts the direction of exposure based on recent price trends, while volatility targeting adjusts the magnitude of exposure based on recent risk. A momentum signal can correctly predict the direction of a move but still produce large losses if the position is too large relative to the current volatility regime. Volatility targeting provides this sizing discipline.

5. Choosing the Target Level

The choice of volatility target determines the portfolio's average leverage and risk level. We test targets from 5% to 20% annualised and compute the resulting performance metrics.

The Sharpe ratio is approximately constant across target levels from 5% to 15%, as expected — scaling a strategy up or down by a constant factor should not change its Sharpe ratio if returns scale linearly with exposure. Above 15%, the Sharpe ratio declines modestly because the strategy occasionally requires leverage above 3× to hit the target, and the cost of maintaining such leverage (margin requirements, borrowing costs) reduces net returns.

The practical choice of target depends on the trader's drawdown tolerance. A 10% target produces an expected maximum drawdown of approximately 13% over a 5-year horizon. A 15% target produces approximately 19%. A 5% target produces approximately 7% — attractive for risk-averse allocators but with correspondingly lower absolute returns.

6. Lookback Window Sensitivity

The choice of lookback window for realised volatility estimation affects the strategy's responsiveness. Short windows (10 days) respond quickly to volatility spikes but produce more turnover and are more sensitive to noise. Long windows (60 days) are smoother but respond slowly to regime changes.

We find that 20 days provides the best trade-off for daily-rebalanced strategies. The Sharpe ratio difference between 10-day and 60-day windows is approximately 0.08 in favour of the shorter window, but the 10-day window produces approximately 40% more turnover. For weekly or monthly rebalancing, a 40-day window is more appropriate because it averages over the less frequent rebalancing points.

An EWMA volatility estimator with a half-life of 10 days provides a smooth compromise between responsiveness and stability. We find that the EWMA estimator produces Sharpe ratios approximately 0.03 higher than the simple rolling window, with 15% less turnover — a modest but consistent improvement.

7. When Volatility Targeting Fails

Volatility targeting underperforms in two specific scenarios. First, sharp V-shaped recoveries after volatility spikes. When markets crash and then immediately reverse (as in March 2020), volatility targeting reduces exposure at the bottom — exactly when the expected return is highest. The strategy misses a significant portion of the recovery rally because it takes time for realised volatility to decline and for the exposure to ramp back up.

Second, gradual volatility increases during trending markets. In the 2022 rate-hiking environment, volatility increased gradually while equities declined steadily. Volatility targeting correctly reduced exposure during this period, but the gradual nature of the volatility increase meant the exposure reduction lagged the price decline, resulting in larger drawdowns than a faster-responding risk model would have produced.

These failure modes are inherent to any backward-looking risk model. They can be partially mitigated by incorporating implied volatility (which is forward-looking) into the volatility estimate, or by adding a momentum overlay that reduces exposure based on price trends as well as volatility.

8. Conclusion

Volatility targeting is one of the simplest and most robust improvements available to systematic traders. Applied to a diversified multi-asset futures portfolio, it improves the Sharpe ratio by 0.24 and reduces maximum drawdown by 40%. It combines effectively with momentum signals, producing a portfolio with a Sharpe of 0.91 and maximum drawdown under 11%. The optimal target for most practitioners is 10–15% annualised, estimated with a 20-day trailing window or an EWMA with 10-day half-life. The main cost is reduced participation in sharp recoveries — a trade-off that is favourable for most risk-averse investors.