Tim Olson
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71 lines
4.1 KiB
Markdown
71 lines
4.1 KiB
Markdown
---
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description: "Builds a long-only trend-following portfolio across multiple asset classes using ETFs, allocating weights proportional to cumulative momentum and optionally risk-adjusted by historical volatility, with an optional MA filter."
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tags: [etfs, trend-following, multi-asset, momentum, long-only]
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---
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# Multi-Asset Trend Following
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**Section**: 4.6 | **Asset Class**: ETFs | **Type**: Trend-Following / Multi-Asset
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## Overview
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ETFs allow efficient diversification across sectors, countries, asset classes, and factors in a relatively small number of instruments. This strategy constructs a long-only trend-following portfolio across multiple ETFs (and thus multiple asset classes) by allocating weights based on cumulative momentum, optionally filtered by a moving average, and weighted by historical volatility to manage risk.
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## Construction / Signal
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**Step 1 — Compute cumulative returns** over a T-month formation period (T = 6–12 months):
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```
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R_i^cum = P_i(t) / P_i(t+T) - 1
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```
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**Step 2 — Filter**: Keep only ETFs with positive `R_i^cum` (positive momentum required for long-only).
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**Step 3 — Optional MA filter**: Additionally keep only ETFs whose last closing price P_i exceeds their moving average MA_i(T') (typically T' = 100–200 days):
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```
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P_i > MA_i(T')
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```
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**Step 4 — Assign weights** to all surviving ETFs (not just top decile, since the universe is small):
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Option A — proportional to cumulative return:
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```
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w_i = gamma_1 * R_i^cum (371)
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```
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Option B — momentum divided by volatility (Sharpe-like weighting):
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```
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w_i = gamma_2 * R_i^cum / sigma_i (372)
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```
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Option C — momentum divided by variance (Sharpe ratio optimization for diagonal covariance):
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```
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w_i = gamma_3 * R_i^cum / sigma_i^2 (373)
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```
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where `sigma_i` is historical ETF volatility and normalization coefficients `gamma_1`, `gamma_2`, `gamma_3` are computed to satisfy `sum_{i=1}^{N} w_i = 1` (N = number of ETFs with nonzero weights after filtering).
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Option C (Eq. 373) optimizes the Sharpe ratio of the ETF portfolio assuming a diagonal covariance matrix `C_ij = diag(sigma_i^2)` (ignoring cross-ETF correlations).
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## Entry / Exit Rules
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- **Entry**: At each rebalance, apply momentum and MA filters, compute weights, and enter long positions in all surviving ETFs.
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- **Exit**: Rebalance monthly (or per the formation period schedule); ETFs with negative cumulative momentum or below their MA are dropped (weight set to zero).
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- **Position cap**: Bounds `w_i <= w_i^max` can be imposed to prevent overweighting of any single volatile ETF.
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## Key Parameters
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- **Formation period T**: 6–12 months
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- **MA filter length T'**: 100–200 days (optional; aligns with sector momentum rotation MA filter)
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- **Weighting scheme**: Equal (Eq. 371), volatility-adjusted (Eq. 372), or variance-adjusted/Sharpe-optimal (Eq. 373)
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- **Position cap**: Maximum weight per ETF (optional; mitigates concentration risk)
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- **Holding period**: Monthly rebalancing typical
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## Variations
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- **No MA filter**: Use only positive cumulative return filter
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- **With position caps**: Add `w_i <= w_i^max` to prevent overweighting high-momentum volatile ETFs
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- **Sector rotation overlay**: Combine with sector momentum rotation (Section 4.1) by restricting the universe to top-ranked sectors
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## Notes
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- Eq. (371) is the simplest weighting; it overweights volatile ETFs since on average `R_i^cum ∝ sigma_i`.
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- Eq. (372) mitigates volatility overweighting by dividing by sigma_i.
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- Eq. (373) is the optimal Sharpe ratio solution under the assumption of uncorrelated (diagonal covariance) ETF returns.
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- The key advantage of ETFs for multi-asset trend following: a small number of instruments (tens of ETFs) can provide exposure to many asset classes, sectors, geographies, and factors simultaneously.
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- Long-only construction avoids shorting complexity; the MA filter prevents buying ETFs in absolute downtrends even if they have relative momentum.
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- For some literature on multi-asset portfolios, dynamic asset allocation, and related topics: Bekkers, Doeswijk and Lam (2009), Black and Litterman (1992), Faber (2015, 2016), Mladina (2014).
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