Scaling a Volatility-Managed Portfolio to Match Benchmark Risk

Summary

The document gives a practical way to choose the scale constant in a volatility-managed portfolio whose next-period factor return is multiplied by a constant divided by recent realized variance. The proposed procedure begins with a trial value for the constant, applies the strategy over a historical sample, and measures the strategy’s return standard deviation alongside that of the unscaled buy-and-hold factor.

It then adjusts the constant by the ratio of benchmark volatility to trial-strategy volatility, multiplied by the initial guess. Because portfolio returns scale linearly with this constant under the stated setup, the adjustment is intended to make the managed portfolio’s historical standard deviation match the benchmark’s. The answer is a calibration recipe, not evidence that the strategy improves returns or risk-adjusted performance. It assumes the same sample and return construction for both volatility estimates, and does not discuss transaction costs, leverage constraints, estimation choices, or out-of-sample performance.

Key ideas

• A trial run provides a volatility estimate for the volatility-managed strategy.
• The scale constant can be adjusted by the ratio of benchmark volatility to trial-strategy volatility.
• Matching standard deviations calibrates historical risk but does not establish improved performance.
• The procedure depends on consistent return definitions and sample periods for both volatility estimates.
• Implementation frictions and out-of-sample behavior are not addressed.

Tags

# implementing Volatility Managed Portfolios


# implementing Volatility Managed Portfolios












How to I calculate the value of c in the vol-managed equation specified by Moreira & Muir Volatilty Managed Portfolios (2016) Equation 1?

Portfolio return in month t+1 =$$\frac{c}{RV_t^2}f_{t+1}$$

where $RV^2_t$ is the Realized variance over the past month , $f_{t+1}$ is the factor return in the next month.

## Answer by Alex C (score 2)

https://quant.stackexchange.com/a/42968

Here is a simple "how to do it" answer.

Run the Volatility Managed Strategy over some historical period using an initial guess for $c$, say $c_0=0.05$. I will call this the Trial Run.

Compute the standard deviation of the strategy returns $\sigma_0$ and the standard deviation of the buy and hold returns $\sigma_{BH}$ over the same period.

Now run the Volatility Managed Strategy again over the same period but using $c=\frac{\sigma_{BH}}{\sigma_0}c_0$. This is the final run; you can check that the standard deviation of the VMS will be exactly equal to the standard deviation of buy and hold. And you are finished.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.