Part X · Edges, one by one · Chapter 10D

Trend following

Time-series momentum

Where we are

Chapters 10B and 10C took two foundation premia that both lose in crashes. Trend following, the third, earns a place for a different reason: its value lies less in its own Sharpe ratio than in when it pays. This chapter builds the trend signal, weighs the evidence and the vehicles, and shows why a low-Sharpe sleeve can add more to a portfolio than a high-Sharpe one.

What you need first

Momentum as a positive weight on past returns, in the AR(1) model (Chapter 3B).
Volatility, and annualizing it by the square root of time (Chapter 1A).
Correlation, tail correlation, and how correlation sets the gain from combining strategies (Chapter 1F).
Futures (Chapter 4B), leverage (Chapter 1E) and Section 1256 treatment (Chapter 2E).
Edges with several sources (Chapter 1G), and the rules for a foundation premium (Chapter 10A).

In plain terms

Across asset classes and across centuries, recent winners tend to keep winning over horizons of 1 to 12 months. The effect is most visible in trending periods, such as the commodity crash of 2008, the inflation move of 2022 and the oil collapse of 2014 to 2015. It is frustratingly absent in chop, when prices swing back and forth without direction. Its mechanism has several parts: investors under-react to news, hedgers pay to shed risk, and trend followers provide liquidity in stressed markets.

1 · A century and a half of evidence

The headline study is Hurst, Ooi and Pedersen (2017), which runs from 1880 to 2016 across 67 markets. Its average net Sharpe ratio is about 0.4 after fees of "2 and 20", a management fee of 2% of assets a year plus a performance fee of 20% of profits. The strategy was positive in every decade since 1880. Its best decade was 1973 to 1982, a decade of rising interest rates, which refutes the critique that trend's record merely rode a long bull market in bonds. The Edge Book adds a record that runs past the study's end: trend was positive in 8 of the 10 largest drawdowns of a 60/40 portfolio, including 2008 and 2022.

Fees of 2 and 20 are heavy. On a hypothetical gross return of 12%, the 2% management fee leaves 10%, and the performance fee takes a fifth of that, leaving 8%: a third of the gross return is gone. So a net Sharpe ratio of 0.4 stands for a noticeably higher one before fees, which is why the idealized models of Chapter 13A start from 0.8 to 1.2.

2 · The trend signal

Trend following, or time-series momentum (TSMOM), sizes each position in proportion to a recent trend signal. For asset $i$ at time $t$ , the Edge Book writes the weight as

w_{i,t} = \frac{\operatorname{sign}(R_{i,t-12,t})}{\sigma_{i,t}}

(10D.1)

Here $R_{i,t-12,t}$ is the asset's return over the past 12 months, and $\operatorname{sign}$ turns it into +1 if it is positive and −1 if it is negative. The divisor $\sigma_{i,t}$ is the asset's current volatility. So the strategy is long the winners and short the losers, each scaled by its volatility. This volatility scaling gives a calm asset a larger position than a wild one, so that each carries a similar risk. It runs diversified across equities, bonds, currencies (FX) and commodities, and in aggregate it has a positive expectation and a distinctive payoff in crashes.

Worked example: Three markets, one rule

Step 1: the signals. Suppose, hypothetically, an equity index has returned +15% over 12 months with a volatility of 16%. A bond future has returned −8% with a volatility of 6%, and oil +30% with a volatility of 32%. The signs are +1, −1 and +1.

Step 2: the sizes. Scale each position so that it carries 10% volatility, which is $10\%/\sigma$ of capital. The equity position is $10/16 = 62.5\%$ of capital long, the bond position $10/6 = 167\%$ short and the oil position $10/32 = 31\%$ long.

Step 3: what the sizes mean. Each position now carries the same risk, so oil's wild swings do not swamp the others. The positions add up to about 260% of capital, which only futures make practical, so a trend sleeve is leveraged by construction (Chapter 1E).

The same rule explains when trend pays and when it hurts. The signal flips only after the 12-month return has changed sign, so the speed of a fall decides everything.

Worked example: A slow fall and a fast one

Step 1: a slow fall. Suppose an index rose steadily from 100 to 110 over a year and then falls 5% a month for 8 months. After 2 months it stands at $110 \times 0.95^2 = 99.3$ , below the 101.7 it stood at 12 months earlier, so the signal turns short. For the remaining 6 months the short position gains about 5% a month, while the index loses $1 - 0.95^8 = 34\%$ from its peak.

Step 2: a fast fall. Now suppose the index falls 30% in one month, to 77, and recovers to 110 the next. The sleeve was long during the fall. At the end of the first month the 12-month return is negative, so the signal turns short at the bottom. The short then loses about 43% of its size in the rebound.

Step 3: the lesson. A slow drawdown gives the signal time to turn, and trend profits from the rest of the fall. A V-shaped reversal catches it wrong-footed twice. Volatility scaling softens the second loss, because the fall's high volatility shrinks the new short, but it does not remove it.

3 · The evidence

Moskowitz, Ooi and Pedersen (2012), in the Journal of Financial Economics (JFE), is the canonical paper on TSMOM, across 58 markets.
Hurst, Ooi and Pedersen (2017), in the Journal of Portfolio Management (JPM), extend the evidence to 140 years.
Asness, Moskowitz and Pedersen (2013), in the Journal of Finance (JF), "Value and Momentum Everywhere", document value and momentum across markets and asset classes.
Live indices of trend-following funds, the SG Trend Index and the BTOP50, show realized Sharpe ratios of 0.3 to 0.5 over 20 years.

4 · Why it exists

Trend following combines all four sources of Chapter 1G:

Risk premium: compensation for whipsaw risk, the losses taken when a trend reverses before it pays.
Behavioral: under-reaction to information that prices take in slowly.
Institutional: the hedging needs of commodity producers, who pay to lock in prices.
Microstructure: liquidity provision, the service of taking the other side when others must trade.

The breadth of mechanisms is itself evidence. The effect has several independent reasons, and all of them would have to fail at once for trend to disappear. Chapter 1G adds a caution about the parts: the behavioral part is the one exposed to decay.

5 · In practice

The vehicles are managed futures funds, which trade futures across asset classes and mostly follow trends. Their managers are called commodity trading advisors (CTAs), a regulatory term that covers far more than commodities. The main retail vehicles are not interchangeable:

Vehicle	What it is	Trade-off
DBMF, iMGP DBi Managed Futures	Replication-style: infers trend funds' positions from their recent returns	Lower fees, but a lag of 1 to 2 months
KMLM, KFA Mount Lucas	Trend rules applied to a fixed universe of markets	Transparent, but less diversified
RSST, Return Stacked US Stocks & Managed Futures	100% US equity and 100% trend in one wrapper	Capital-efficient, but levered
Self-managed	Your own futures and signals	Feasible, but operationally heavy

RSST's structure is return stacking: $10,000 invested buys $10,000 of equity exposure and $10,000 of trend exposure, $20,000 in all. That is leverage of 2 times (Chapter 1E), and it is why the fund is capital-efficient.

In practice

The haircut: an academic Sharpe ratio of 0.8 to 1.2 on paper, 0.3 to 0.5 for a live index of trend funds, 0.25 to 0.45 for a live ETF and 0.20 to 0.40 in your account (Chapter 13A).
Tax: vehicles that hold futures get Section 1256 contract treatment, 60% long-term and 40% short-term (Chapter 2E).
One vehicle: hold a single transparent vehicle rather than several stacked, so that you know what you own and can measure it against its benchmark.

6 · When it fails

When it fails

Long whipsaw periods. The years from 2011 to 2018 were the worst trend drought in modern history.
Rapid V-shaped reversals, in which the trend forms in the wrong direction, as in March 2020.
Manager dispersion, which is real: the wrong vehicle can underperform the SG Trend Index by 200 to 400 bps a year.

7 · A decision rule

Decision rule

Allocate 10% to 15% of the portfolio to a single transparent trend vehicle, DBMF or KMLM, not several stacked. Do not time entries: buy and hold across cycles. The kill criteria are three:

The vehicle's drawdown exceeds 25% peak to trough (PTP).
Its tracking error to the BTOP50 exceeds 4% annualized.
Three consecutive years of negative absolute returns: reassess, but do not exit automatically.

A 25% drawdown needs a gain of $0.25/0.75 = 33\%$ to repair (Chapter 1E). A tracking error of 4% a year is about $4\%/\sqrt{12} = 1.15\%$ a month. The third criterion asks for a review, not a sale, because droughts of several years are how trend's premium is paid for.

Chapter 13B scores a 15% allocation to DBMF and finds medium conviction, held back by the regime score while trend sits in a drought. It suggests building the position over time rather than in one purchase. That staging spreads the entry; it does not replace this chapter's advice against timing trend's cycles.

8 · Portfolio contribution, not standalone Sharpe

The most common mistake with trend is to judge it alone. Chapter 1F showed that correlation sets the gain from combining strategies of equal weight. A sharper question is whether adding a small amount of a new sleeve $B$ to an existing portfolio $P$ raises the portfolio's Sharpe ratio. The answer depends on the correlation $\rho$ between them:

\text{SR}_B > \rho\,\text{SR}_P

(10D.2)

A sleeve helps if its own Sharpe ratio clears the portfolio's Sharpe ratio scaled by their correlation. A sleeve uncorrelated with the portfolio helps whenever its Sharpe ratio is positive, while a highly correlated sleeve must nearly match the portfolio to help at all.

Where the hurdle comes from

Put a weight $w$ in sleeve $B$ and $1-w$ in portfolio $P$ , with expected excess returns $\mu_B$ , $\mu_P$ and volatilities $\sigma_B$ , $\sigma_P$ . The mix has expected excess return $\mu = (1-w)\mu_P + w\mu_B$ and variance

\begin{aligned} \sigma^2 &= (1-w)^2\sigma_P^2 + w^2\sigma_B^2 \\ &\quad + 2w(1-w)\rho\,\sigma_P\sigma_B \end{aligned}

(10D.3)

Ask how the Sharpe ratio $\mu/\sigma$ changes as $w$ rises from zero, its derivative (Chapter 3C). At $w = 0$ , $\mu$ changes at the rate $\mu_B - \mu_P$ . Differentiating $\sigma^2$ and dividing by $2\sigma_P$ shows that $\sigma$ changes at the rate $\rho\sigma_B - \sigma_P$ . By the quotient rule, the Sharpe ratio changes at the rate

\frac{\mu_B\,\sigma_P - \mu_P\,\rho\,\sigma_B}{\sigma_P^2}

(10D.4)

This is positive exactly when $\mu_B/\sigma_B > \rho\,\mu_P/\sigma_P$ , which is (10D.2).

Worked example: A 0.3 sleeve against a 0.5 sleeve

Step 1: the portfolio. Suppose, hypothetically, a portfolio with 15% volatility and an expected excess return of 6%, a Sharpe ratio of 0.40. You can move 20% of it into one of two sleeves, each with 15% volatility.

Step 2: a trend sleeve. The first has a Sharpe ratio of 0.3, an expected excess return of 4.5%, and zero correlation with the portfolio. The mix earns $0.8 \times 6 + 0.2 \times 4.5 = 5.7\%$ . Its variance is $0.64 \times 225 + 0.04 \times 225 = 153$ , in squared percent, so its volatility is 12.4% and its Sharpe ratio $5.7/12.4 = 0.46$ .

Step 3: a correlated sleeve. The second has a Sharpe ratio of 0.5, an expected excess return of 7.5%, and a correlation of 0.8 with the portfolio, like premium selling beside equities. The mix earns 6.3%. The correlation adds $2 \times 0.2 \times 0.8 \times 0.8 \times 225 = 57.6$ to the same 153, so the volatility is $\sqrt{210.6} = 14.5\%$ and the Sharpe ratio 0.43.

Step 4: the verdict. The weaker sleeve lifts the portfolio more. By (10D.2), the trend sleeve's hurdle is $0 \times 0.40 = 0$ , while the correlated sleeve's is $0.8 \times 0.40 = 0.32$ , which its 0.5 clears by far less.

Common mistake: "trend has a lower Sharpe ratio than the VRP, so it is worse"

Trend's value is not its standalone Sharpe ratio; it is its crash complementarity. Trend was positive in 8 of the 10 largest 60/40 drawdowns, while the VRP was negative in essentially all of them. In a portfolio, a trend sleeve with a Sharpe ratio of 0.3 adds more to the portfolio's Sharpe ratio than a sleeve with 0.5 that is correlated with everything else that sells premium. Allocate by contribution to the portfolio, not by standalone Sharpe ratio.

Familiar ground

Combination regimens are built on non-overlapping toxicity. A drug with modest single-agent activity can add more to a combination than a stronger drug whose toxicity overlaps with the backbone. It can be given at full dose without compounding the harm. Trend is the agent with modest activity and a different toxicity profile. Its bad years, the droughts, fall at different times from the crashes that hurt equities and the VRP.

The figure draws the whole curve behind the worked example's two numbers. Press each preset, then slide the correlation and watch the premium-selling sleeve's hurdle rise.

sleeve Sharpe 0.30

correlation ρ 0.00

weight 20%

preset

Sharpe at 20% = 0.46

hurdle ρ × 0.40 = 0.00

best in range: 0.50 at 43%

Clears the hurdle. The sleeve's 0.30 beats 0.00, so a first slice raises the portfolio's Sharpe ratio above 0.40.

A weaker sleeve can lift a portfolio further. A portfolio with a Sharpe ratio of 0.40 and 15% volatility moves a weight from 0% to 50% into a sleeve with 15% volatility and the Sharpe ratio and correlation you set. The solid curve is the mix's Sharpe ratio, and the dashed curves are the worked example's two sleeves: trend at 0.3, uncorrelated, and premium selling at 0.5, correlated at 0.8. A sleeve raises the portfolio when its Sharpe ratio clears the hurdle ρ × 0.40, and the trend curve runs above the stronger sleeve's at every weight shown.

What to carry forward

Trend following is long recent winners and short recent losers across many markets, each scaled by its volatility: (10D.1).
Hurst, Ooi and Pedersen (2017) find a net Sharpe ratio of about 0.4 from 1880 to 2016, positive in every decade. Trend was also positive in 8 of the 10 largest 60/40 drawdowns, and live indices show 0.3 to 0.5.
It pays in slow drawdowns, loses in V-shaped reversals and chop, and can go years without paying: 2011 to 2018 was the worst drought in modern history.
Hold 10% to 15% in one transparent vehicle, do not time entries, and reassess rather than exit after 3 negative years.
Judge it by its contribution to the portfolio: a sleeve helps when $\text{SR}_B > \rho\,\text{SR}_P$ , and trend's low correlation sets its hurdle near zero.

9 · Check yourself

Question 1

What is the canonical evidence for trend following?

Answer

Moskowitz, Ooi and Pedersen (2012) established time-series momentum across 58 markets. Hurst, Ooi and Pedersen (2017) extended it to 67 markets from 1880 to 2016, with a net Sharpe ratio of about 0.4 after fees and a positive record in every decade. Asness, Moskowitz and Pedersen (2013) documented value and momentum across markets and asset classes. Live indices, the SG Trend Index and the BTOP50, show realized Sharpe ratios of 0.3 to 0.5 over 20 years.

Question 2

Why is trend's contribution to a portfolio larger than its standalone Sharpe ratio suggests?

Answer

Trend is roughly uncorrelated with equities and pays in slow drawdowns, when the rest of the portfolio loses. By (10D.2), a sleeve raises a portfolio's Sharpe ratio when its own exceeds the correlation times the portfolio's. Trend's hurdle is near zero, while a premium-selling sleeve correlated at 0.8 with a 0.40 portfolio must clear 0.32. In the worked example, the 0.3 trend sleeve lifted the portfolio to 0.46 and the 0.5 sleeve only to 0.43.

Question 3

What is the difference between DBMF and KMLM?

Answer

DBMF replicates trend funds: it infers their positions from their recent returns, which keeps its fees lower but leaves it 1 to 2 months behind. KMLM trades a fixed universe of markets, which makes it transparent but less diversified. Both hold futures and get Section 1256 treatment, and the rule is to hold one of them, not both stacked.

Question 4

How long can a trend drought last, and what does that imply for how you hold the sleeve?

Answer

The worst in modern history ran from 2011 to 2018, so a sleeve can go nowhere for years before a 2008 or a 2022 pays for the wait. Do not time entries, measure the vehicle against the BTOP50, and after 3 consecutive negative years reassess rather than exit automatically. Selling in a drought keeps the cost of trend and gives up its payoff.