Dynamic Position Sizing Based On Realized Volatility

When to Use

Invoke this skill when executing trend-following, mean-reversion, or multi-asset strategies where static capital allocation ($X%$ per trade) leads to unintentional risk concentration during high-volatility market regimes. Volatility targeting scales position size inversely to annualized realized volatility $\sigma_{\text{realized}}$, so a strategy consumes a constant ex-ante risk budget (e.g. $15%$ target annualized volatility) whether the VIX is at $12$ or $45$.

When NOT to Use

• As a stop-loss, drawdown control, or gap protection. The scalar is set from volatility already realized. It cannot anticipate a jump, and a position sized on calm data is full-size when the gap arrives. Pair it with an independent circuit breaker.
• On a return history shorter than the estimator's effective window. A $\lambda = 0.94$ EWMA consumes ~74 daily returns at a 1% tolerance (RiskMetrics Table 5.7). Below that the estimate mostly reflects the arbitrary seed, so the sizer raises rather than sizing.
• On intraday bars without changing annualization_factor. The default 252 is daily. Feeding 5-minute bars while leaving it at 252 understates volatility by roughly $\sqrt{78}$ and oversizes the position ~9×. The frequency cannot be inferred from a list of floats — you must set it.
• As portfolio construction. This sizes one asset at a time. Summing independently vol-targeted positions does not produce a vol-targeted portfolio; see correlation-aware-exposure-limits.
• When the constraint is liquidity or lot size rather than volatility — see liquidity-adjusted-position-sizing and minimum-fill-size-and-lot-rounding-logic.

Prerequisites

• Return series $r_t$ ending at the last completed observation before the bar being sized, sampled at one consistent frequency.
• annualization_factor = observations per year for that frequency (252 for daily bars).
• Target annualized volatility $\sigma_{\text{target}}$ (e.g. $0.15 = 15%$).
• Estimator choice: RiskMetrics EWMA ($\lambda = 0.94$ daily, $0.97$ monthly) or simple rolling sample standard deviation.

Workflow

1. Estimate Realized Volatility:

   • EWMA (RiskMetrics Eq. 5.3): $\sigma_t^2 = \lambda \sigma_{t-1}^2 + (1 - \lambda) r_t^2$, using raw squared returns — RiskMetrics centres on zero, not on the sample mean.
   • Annualize: $\sigma_{\text{ann}} = \sqrt{F} \times \sigma_t$, where $F$ is observations per year.
   • Decision point — check the history length before trusting the number. required_ewma_observations(λ, tolerance) gives the effective window ($\lambda=0.94 \Rightarrow 74$ at 1%). A shorter history is not a noisy estimate, it is largely the seed; the sizer raises instead of returning one.
   • Decision point — the two estimators are not interchangeable. EWMA assumes a zero mean; the rolling estimator subtracts the sample mean and applies the $(n-1)$ correction. They disagree on identical data. Pick one per strategy; do not compare their outputs or switch mid-backtest.

2. Compute Volatility Scalar: $$\text{Scalar} = \frac{\sigma_{\text{target}}}{\max(\sigma_{\text{floor}}, \sigma_{\text{ann}})}$$

   • Decision point — if vol_floor_binding is true, the size was set by the floor, not by measured volatility. That is a deliberate leverage brake on an abnormally quiet series, not a volatility reading; do not report it as one.

3. Apply Min/Max Multiplier Bounds: $$\text{FinalScalar} = \text{clip}(\text{Scalar}, \text{MinScalar}, \text{MaxScalar})$$

4. Calculate Volatility-Adjusted Allocation: $$\text{CapitalAllocation} = \text{BaseCapital} \times \text{FinalScalar}$$

   • Share count is floored, never rounded up, so the position cannot exceed the risk budget.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

• Sizing on corrupt data: a single NaN in the return series collapses a naive variance calculation to zero, which the volatility floor then converts into the maximum leverage scalar — the largest possible position produced by the worst possible data. Reject non-finite returns before estimating; never let them reach the estimator.
• Silently sizing with no data: returning the target volatility as a fallback yields a scalar of exactly $1.0$ — a full-size position justified by nothing. Absent or too-short history must raise, not default.
• Including the current bar's return: the volatility used to size period $t$ must be built from returns through $t-1$ (RiskMetrics Eq. 5.37). Including the bar being sized leaks its outcome into the size and flatters every backtest.
• Mismatched annualization: intraday returns annualized with 252 understate volatility by $\sqrt{\text{bars per day}}$, producing a position several times larger than intended.
• Reporting the floored volatility as realized volatility: when the floor binds it is a sizing guard, not a measurement; conflating the two overstates a genuinely quiet asset's risk in every downstream report.
• Lagged Volatility Response During Crashing Markets: a 60-day simple estimator reacts too slowly during a sudden crash, leaving positions oversized. Faster $\lambda$ reacts sooner but consumes less data — the trade-off is explicit in RiskMetrics Table 5.7.
• Hyper-Leveraging in Ultra-Quiet Regimes: allowing the scalar to reach $10\times$ during abnormally low vol without enforcing a MaxScalar cap.
• Assuming the floor caps leverage: with $\sigma_{\text{target}}=15%$ and $\sigma_{\text{floor}}=5%$ the floor permits a raw scalar of $3.0$, so with MaxScalar $=2.0$ it is the cap, not the floor, that binds. Set both deliberately.

Verification

• Instantiate RealizedVolPositionSizer(target_annualized_vol=0.15, min_scalar=0.20, max_scalar=2.00, vol_floor=0.05). Feed an alternating $\pm d$ return series with $d = 0.60/\sqrt{252}$ (100 observations, exactly 60% annualized): verify realized_annualized_vol $= 0.60$, bounded_vol_scalar $= 0.25$, and adjusted_capital_usd $= $25{,}000$ on $$100{,}000$ base. Repeat at 4% annualized: verify the raw scalar is $3.0$ (floor-bound, not $3.75$), clipped to the $2.0$ cap, with vol_floor_binding true.
• Verify required_ewma_observations(0.94, 0.01) == 74 and (0.97, 0.01) == 151, reproducing RiskMetrics Table 5.7.
• Negative checks: an empty history, a 1-element history, a 73-element history at $\lambda=0.94$, a NaN return, and a negative base_capital_usd must each raise.
• Run python -m unittest discover -s skills/dynamic-position-sizing-based-on-realized-volatility/scripts and confirm 100% pass rate.

Related Skills

• correlation-aware-exposure-limits
• liquidity-adjusted-position-sizing
• value-at-risk-var-live-monitoring
• kill-switch-and-drawdown-circuit-breakers