Assessing a Smoothed Volatility-Targeting Position-Size Rule
Summary
The document examines a proposed position-sizing rule that scales exposure using portfolio capital, a target volatility, instrument volatility and price, and a portfolio-level multiplier. That multiplier is based on the ratio of target volatility to lagged realized portfolio volatility, then smoothed using an average of prior multiplier values. The author questions whether this smoothing is necessary and whether it compensates for omitting an explicit covariance matrix.
The author reports that their experiments undershot the volatility target when the historical average multiplier was omitted, while including it brought realized volatility closer to the target. These observations motivate the question, but the document provides no experimental setup, asset universe, estimation details, or robustness analysis, so they do not establish that the rule is generally valid. It also does not provide a definitive alternative or attribution for the smoothing technique. The main lesson is that a portfolio-level volatility feedback term and its smoothing can materially affect realized exposure and need careful evaluation.
Key ideas
- The proposed sizing rule scales instrument exposure using target and estimated volatility, capital, and price.
- A portfolio multiplier adjusts exposure according to target volatility relative to lagged realized volatility.
- The multiplier is further smoothed by averaging its previous values.
- The author reports better target tracking in experiments when this smoothing is included.
- The document gives no experiment details sufficient to establish general validity or compare alternatives.
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Full text
# Is this a valid implementation for volatility targeting?
# Is this a valid implementation for volatility targeting?
Let positions size for the instrument be
$$K_t \frac{V_t \Sigma^{target}}{\tilde{N_t}} \frac{1}{\sigma_t P_t}$$
where $$K_t = \bar{K}_{t-1} \frac{\Sigma^{target}}{\Sigma^{realized}_{t-1}}$$
where
$V_t$ is portfolio capital $\Sigma^{target}$ is target annualized volatility $\tilde{N}_t$ is the number of positions to be in $\sigma_t$ is annualized volatility of instrument $P_t$ is price of instrument $\bar{K}_{t-1}$ is the average of the previous $K_t$'s for the past M periods and $\Sigma^{realized}_{t-1}$ is the realized annualized volatility of the portfolio.
I found this implementation in a blog (https://hangukquant.substack.com/p/volatility-targeting-the-strategy and https://hangukquant.substack.com/p/volatility-targeting-the-asset-level). I have changed the notation a bit for simplicity.
The math adds up for me but I'm unsure about using a moving average of previous values to calculate $K_t$. He seems to reason that it's an empirical approach that bypasses the need for calculating the covariance matrix, but I would think that simply setting $$K_t = \frac{\Sigma^{target}}{\Sigma^{realized}_{t-1}}$$ would take care of that; while multiplying by $\bar{K}_{t-1}$ would simply stablize/smooth out the values of $K_t$ through time.
I ran some experiments and it appears that not multiplying by the $\bar{K}_{t-1}$ term tends to undershoot the vol target by about 40%, while multiplying by the $\bar{K}_{t-1}$ term actually gets you pretty close to the vol target.
Is this a valid implementation? Is there a better implementation I should look at? Did this guy invent the use of the moving average for $K_t$ in this context or did he take it from somewhere else? The papers he's cited don't use this implementation and I haven't seen it anywhere else either.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.