# Scaling crypto exposure by volatility does not beat buy-and-hold

> Sizing daily Bitcoin and Ether exposure inversely to recent volatility changed the out-of-sample Sharpe ratio by -0.20 to +0.05 against buy-and-hold across 12 variants, and all 12 bootstrap intervals include zero.

E024 · Verdict: KILL · Cause: No signal · Market: Crypto & DeFi · Mechanism: Risk premium · Horizon: 1d · Tested: October 2026

Source: https://alphanotfound.eu/experiments/E024-volatility-managed-bitcoin-ether-exposure

A well-known idea says to hold less of an asset when it is turbulent and more when it is calm, which raises the return per unit of risk. We tested it on Bitcoin and Ether perpetual futures: each day the position was set inversely to the previous 10, 20 or 60 days of volatility, capped at 1x or 2x, with 7 bp paid on every change. From 2024-06 on, the Sharpe ratio differed from buy-and-hold by -0.20 to +0.05 across 12 variants. Every 95% interval included zero, and the 2x cap made the worst drawdown deeper in all six cases.

## Key numbers

- **Sharpe difference vs buy-and-hold:** -0.20 to +0.05 (12 variants, 2024-06 onward, after 7 bp per unit of turnover)
- **Intervals that exclude zero:** 0 of 12 (95% moving-block bootstrap, 3,000 resamples)
- **Buy-and-hold Sharpe, same window:** 0.41 / 0.07 (Bitcoin / Ether)
- **Worst drawdown at the 2x cap:** 6.1 to 21.4 points deeper (in all 6 variants, versus buy-and-hold)

## The idea being tested

**Belief:** Hold less of an asset when its volatility is high and more when it is low, and the return per unit of risk improves.

**Why people believe it:** People argue that volatility is the most persistent thing in a price series: calm days follow calm days and turbulent days follow turbulent days. Yesterday's volatility would then say how risky tomorrow is, while the expected return does not rise in proportion. Cutting the position in storms and restoring it in calm would keep the average return and lower the risk. The idea is stated as sizing, not as a forecast of direction.

**Why it would persist:** The belief is that it needs no view on direction and uses only public prices, so it would not be arbitraged away.

## How it was tested

Each day at 00:00 UTC we set the position in Bitcoin (or Ether) to a weight. The weight is a scale factor divided by the asset's volatility over the previous 10, 20 or 60 days, and it is never above a cap of 1x or 2x of the account. The scale factor is re-estimated every day from past data only, so that the managed position's volatility matches that of simply holding the asset. We paid 7 bp on every change of weight, and compared the Sharpe ratio (return divided by volatility, annualised) of the managed position with buy-and-hold on the same days. A bootstrap gave a 95% interval for the difference. The idea passes only if that interval is entirely above zero.

**Pre-registered:** no

**Data:** Hourly closing prices of the Bitcoin and Ether USDT-margined perpetual futures, aggregated to daily 00:00 UTC closes (the largest USD-margined crypto perpetual venue, public historical klines; 1 hour, aggregated to daily; 2020-01..2026-10)

**Universe:** Bitcoin and Ether perpetuals, one at a time. 2 assets x 3 volatility lookbacks (10, 20, 60 days) x 2 caps (1x, 2x) = 12 variants.

**Signal:** r(t) is the simple daily return. sigma(t) is the standard deviation of r over the previous L days (L = 10, 20 or 60), known before the rebalance. Raw weight is 1 / sigma(t). The weight is w(t) = min(cap, c(t) / sigma(t)), long only and set to 0 until defined. c(t) is chosen in real time from the expanding history up to the day before: the ratio of the standard deviation of buy-and-hold returns to that of the unscaled managed series, so the managed series has the same volatility as buy-and-hold in the past.

**Execution:** Rebalance once per day at the 00:00 UTC close; the weight set at a close earns the following day's simple return.

**Costs:** 7 bp times the absolute change of weight each day (the first day pays on the full weight). Buy-and-hold pays nothing. Funding payments are not modelled.

**Controls:** Buy-and-hold of the same asset over the same days. Sharpe difference = managed Sharpe minus buy-and-hold Sharpe, with Sharpe = mean / standard deviation x square root of 365.

**Sample split:** Evaluation window from 2024-06 to 2026-10, with a 95% moving-block bootstrap interval on the Sharpe difference (block length 10 days, 3,000 resamples, fixed seed, 2.5th and 97.5th percentiles). A full-sample difference over 2020-01..2026-10 is reported without an interval. The scale factor uses expanding history, so earlier data only calibrates it.

**Pass criterion:** Reconstructed after the test; no criteria were fixed in advance. The 95% interval of the Sharpe difference against buy-and-hold lies entirely above zero in the evaluation window.

**Kill criterion:** Reconstructed after the test; no criteria were fixed in advance. No variant has an interval of the Sharpe difference excluding zero.

**Power:** Not computed in advance. The 12 evaluation-window intervals are 0.06 to 0.74 Sharpe units wide, so differences smaller than their half-widths, 0.03 to 0.37, could not be told from zero.

## Result

**Why it was rejected:** No variant has a 95% interval for the Sharpe difference against buy-and-hold that excludes zero; the point estimates run from -0.20 to +0.05.

**Observations:** 12

**Net mean:** —

**Median:** -0.03

**Worst:** -0.2

- In the evaluation window (2024-06 onward), the Sharpe difference against buy-and-hold ranged from -0.204 to +0.045 across the 12 variants, with a median of -0.033 (positive means the managed position had the higher Sharpe). 10 of 12 were below zero.
- All 12 bootstrap 95% intervals include zero. The narrowest, Bitcoin with a 60-day lookback and a 1x cap, runs from -0.034 to +0.030; the widest, Ether with a 10-day lookback and a 2x cap, from -0.329 to +0.414.
- Buy-and-hold Sharpe in the window was 0.41 for Bitcoin and 0.07 for Ether. Managed Sharpe ranged from 0.20 to 0.40 for Bitcoin and from -0.09 to 0.12 for Ether.
- Over the full sample, 2020-01 to 2026-10, the Sharpe difference ranged from -0.140 to +0.157, with 4 of 12 positive. These full-sample figures have no interval and are descriptive only. Buy-and-hold Sharpe was 0.90 for Bitcoin and 0.95 for Ether.
- At the 1x cap the worst drawdown in the evaluation window ranged from 0.7 points deeper to 3.9 points shallower than buy-and-hold (Bitcoin buy-and-hold -53.0%, Ether -67.6%). At the 2x cap it was deeper in all 6 variants, by 6.1 to 21.4 points.
- Average weight was 0.91 to 0.99 at the 1x cap and 1.19 to 1.37 at the 2x cap in the evaluation window, so the managed position was on average about as large as buy-and-hold at 1x and about 1.3 times as large at 2x.

### Every interval for the Sharpe difference includes zero (Sharpe difference vs buy-and-hold)

Managed Sharpe minus buy-and-hold Sharpe, 2024-06 onward, with 95% bootstrap intervals, one row per variant. All 12 intervals cross zero, and 10 of 12 point estimates are below it. The idea needed an interval entirely above zero.

|   | Mean | 95% low | 95% high |
| --- | --- | --- | --- |
| BTC 10d, 1x cap | -0.024 | -0.168 | 0.125 |
| BTC 10d, 2x cap | -0.158 | -0.505 | 0.158 |
| BTC 20d, 1x cap | -0.031 | -0.133 | 0.067 |
| BTC 20d, 2x cap | -0.204 | -0.489 | 0.102 |
| BTC 60d, 1x cap | -0.005 | -0.034 | 0.03 |
| BTC 60d, 2x cap | -0.129 | -0.374 | 0.127 |
| ETH 10d, 1x cap | 0.014 | -0.164 | 0.209 |
| ETH 10d, 2x cap | 0.045 | -0.329 | 0.414 |
| ETH 20d, 1x cap | -0.036 | -0.147 | 0.091 |
| ETH 20d, 2x cap | -0.164 | -0.484 | 0.145 |
| ETH 60d, 1x cap | -0.022 | -0.066 | 0.019 |
| ETH 60d, 2x cap | -0.062 | -0.33 | 0.196 |

### The full sample does not rescue the idea (Sharpe difference vs buy-and-hold)

Sharpe difference per variant in the evaluation window (2024-06 onward) and over the full sample (2020-01 to 2026-10). The sign flips for several variants and the values stay between -0.204 and +0.157; the full-sample figures have no interval and are descriptive only.

|   | Evaluation window | Full sample |
| --- | --- | --- |
| BTC 10d, 1x cap | -0.024 | -0.043 |
| BTC 10d, 2x cap | -0.158 | 0.037 |
| BTC 20d, 1x cap | -0.031 | -0.103 |
| BTC 20d, 2x cap | -0.204 | -0.121 |
| BTC 60d, 1x cap | -0.005 | -0.14 |
| BTC 60d, 2x cap | -0.129 | -0.089 |
| ETH 10d, 1x cap | 0.014 | 0.038 |
| ETH 10d, 2x cap | 0.045 | 0.157 |
| ETH 20d, 1x cap | -0.036 | -0.028 |
| ETH 20d, 2x cap | -0.164 | 0.045 |
| ETH 60d, 1x cap | -0.022 | -0.121 |
| ETH 60d, 2x cap | -0.062 | -0.094 |

### Sizing did not consistently change the 1x drawdown and deepened it at 2x (maximum drawdown, % of peak)

Depth of the worst peak-to-trough fall in the evaluation window, managed against buy-and-hold. At the 1x cap the gap is -3.9 to +0.7 points with no consistent direction; at the 2x cap the managed position falls 6.1 to 21.4 points deeper in every variant.

|   | Managed | Buy-and-hold |
| --- | --- | --- |
| BTC 10d, 1x cap | 52.8 | 53.0 |
| BTC 10d, 2x cap | 66.3 | 53.0 |
| BTC 20d, 1x cap | 53.7 | 53.0 |
| BTC 20d, 2x cap | 68.8 | 53.0 |
| BTC 60d, 1x cap | 52.8 | 53.0 |
| BTC 60d, 2x cap | 74.4 | 53.0 |
| ETH 10d, 1x cap | 63.6 | 67.6 |
| ETH 10d, 2x cap | 73.7 | 67.6 |
| ETH 20d, 1x cap | 66.5 | 67.6 |
| ETH 20d, 2x cap | 81.6 | 67.6 |
| ETH 60d, 1x cap | 67.4 | 67.6 |
| ETH 60d, 2x cap | 80.9 | 67.6 |

## Interpretation

**Why it failed (interpretation, not established):** Interpretation, not established: a one-day-lagged volatility estimate gave no usable warning here. One possible reason is that volatility spikes coincide with drawdowns that arrive too fast, and that lagged volatility does not predict downside volatility well enough, The wide intervals mean the test also could not rule out small gains or small losses.

**Lesson:** In this test the worst drawdown moved by -3.9 to +0.7 points at the 1x cap with no consistent direction, and the 2x cap deepened it by 6.1 to 21.4 points. A Sharpe comparison over a short window is also a weak test: the evaluation-window half-widths of 0.03 to 0.37 could not separate small differences from zero.

**Scope:** Covers Bitcoin and Ether perpetual futures, daily rebalancing, trailing volatility of 10, 20 and 60 days, caps of 1x and 2x, long-only weights, 7 bp per unit of turnover, an evaluation window from 2024-06 to 2026-10 and a full sample from 2020-01. It does not cover other assets, and funding payments are not modelled.

## Reproducibility

**Steps:** 1) Download hourly closes of the Bitcoin and Ether USDT-margined perpetuals for 2020-01 to 2026-10 and take the last close of each UTC day; compute simple daily returns r. 2) For L in {10, 20, 60}, sigma(t) = standard deviation of r over the previous L days, lagged by one day. Raw weight = 1 / sigma. 3) Scale c(t) = expanding standard deviation of r divided by the expanding standard deviation of (raw weight x r), both lagged one day. Weight w(t) = min(cap, c(t) x raw weight), cap in {1, 2}, set to 0 where undefined. 4) Daily P&L = w x r - 0.0007 x |change in w| (the first day pays on w). 5) Sharpe = mean / standard deviation x square root of 365, for the managed series and for r over the same days, from 2024-06 and over the full sample. 6) Moving-block bootstrap of the Sharpe difference on the evaluation window: block length 10 days, 3,000 resamples, 2.5th and 97.5th percentiles.

**Grade:** COMPLETE

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AI-generated research, checked but not peer-reviewed. Historical, experimental research, not investment advice. Dataset Terms of Use: https://alphanotfound.eu/terms