### Summary

Movement’s trend model invests in diversified stock index funds and seeks to avoid the severe losses associated with buy-and-hold stock investing. The model is based on academic research by Gary Antonacci, AQR, and Meb Faber.

The core components of the trend model are:

- A
**relative momentum**step to select the top-performing equity region. - An
**absolute momentum**step to reduce the probability of a severe loss. - A
**rebalancing**step to ensure the model’s stance reflects recent data.

### Relative Momentum

Relative momentum compares the returns of different assets to each other. Think of relative momentum like a horse race – always investing in the top-performing asset. Movement’s trend model is applied to U.S. stocks and international stocks. Movement specifically uses Vanguard’s total market-cap VTI (for U.S.) and VXUS (for international) funds. This universe covers 100% of the global equity market and is extremely low cost, with an average fund expense ratio of 0.07%.

Relative momentum takes advantage of the fact that the performance of domestic and international stocks tends to ebb and flow in multi-year cycles. For example, if the line in the graph below is higher than 0%, it means that U.S. stocks have outperformed international stocks over the past three years.

The main input for the relative momentum step is the momentum calculation for each stock fund. The most common momentum time period is 12 months, meaning a fund’s performance is evaluated over the past year. For example, consider the following prices:

Date | VTI | VXUS |
---|---|---|

12/31/2017 | $134.68 | $55.18 |

12/31/2016 | $111.11 | $43.71 |

For this data, the 12 month momentum is calculated to be +21.2% for VTI and +26.2% for VXUS. International stocks had higher relative momentum than domestic stocks as of 12/31/2017.

Movement’s momentum calculation is an average of five different time periods: 3 months, 6 months, 9 months, 12 months, and 15 months. The momentum effect has been shown to persist in all of these time windows, but not over very short or very long periods. Movement doesn’t use an average momentum metric to try to outperform the standard 12-month period. Rather, we do so to diversify the model and not rely on a single time horizon when calculating momentum.

The chart below shows this average momentum measure for domestic and international stocks. You can see persistent trends in performance, from U.S. stocks outperforming in the late 1990s to international stocks in the mid-2000s.

Below is a simplified view of the above chart, only showing the fund with the top relative momentum. There are a few periods of back and forth when each fund’s momentum was similar, but the relative momentum step typically stays in one region for years at a time.

### Absolute Momentum

This step takes the stock fund with the highest relative momentum and makes sure that its momentum is positive, not negative. Negative momentum has historically led to a higher probability of a large future loss.

The main step in calculating absolute momentum is comparing the top relative momentum fund to a “hurdle” asset. The hurdle asset is a conservative security that represents a risk-free investment. The trend model uses SHV as the hurdle asset since it only owns short-term U.S. Treasury bills.

For example, the chart below calculates the average 12-month future return of domestic stocks since 1994 based on two different scenarios: one where the average momentum metric was positive and another where the average momentum metric was negative. You can see that periods of positive momentum were typically followed by stronger returns.

This behavior isn’t unique to U.S. stocks. Research has shown that negative momentum has historically been associated with lower returns (and higher volatility) in all major asset classes over the past century.

Referring to the above relative momentum example, international stocks were outperforming U.S. stocks as of 12/31/2017. The +26.2% average momentum of international stocks was also higher than the +1.5% average momentum of SHV (the hurdle asset), meaning international stocks had positive momentum. In this scenario, the trend model would thus be invested in international stocks.

The main goal of the absolute momentum step is to lower the probability of experiencing a large drawdown. Drawdowns measure the max peak-to-trough loss of an investment. Large drawdowns are both emotionally painful and capable of derailing retirement portfolios. The chart below shows historical drawdowns for U.S. and international stock funds since 1994:

When absolute momentum turns negative, the trend model rotates from a stock fund to a bond fund. The bond fund depends on an investor’s account type. If the account is tax deferred (like an IRA), the fund used is VGIT, an intermediate-term U.S. Treasury fund. On the other hand, if the account is taxable (like a brokerage account), the fund used is VTEB, an intermediate-term municipal bond fund.

Movement uses these funds, rather than a blended fund that tracks the popular Bloomberg Barclays Aggregate Bond index, to avoid taking credit risk when the trend model avoids stock exposure. Movement also uses intermediate-term funds (rather than short-term or long-term bond funds) to avoid taking an active stance on the future direction of interest rates. This is explained further on the passive model page.

### Rebalancing

The final step in the trend model is to rebalance the model to reflect recent data. Most active investors run monthly models, meaning the models are rebalanced based on data at the end of the month. Movement’s approach is different for two reasons: 1) monthly models implicitly bet on the last day of the month to be the best day to rebalance, and 2) monthly models tend to underestimate true volatility.

The first reason is called timing luck and represents the amount of potential over or underperformance of a strategy solely due to its rebalancing date. The second reason why Movement doesn’t rebalance monthly is because monthly observations don’t capture volatility that happens within a month. For example, the max drawdown of international stocks in October 2008 based on monthly data is -22%. The drawdown when calculated with daily data is -34%. Monthly models observe fewer data points and underestimate volatility.

Movement’s solution is to rebalance the trend model once a week but freeze the model’s stance for thirty days after a new position is initiated. This helps avoid wash sales in taxable accounts and also reduces back-and-forth trading.

The trend model is now complete. It measures relative momentum between domestic and international stocks, chooses the top performer, ensures that it has positive momentum, and then rebalances once a week.

It’s also important to understand another aspect of the trend model.

### Probabilities and Payoffs

Some momentum models have been incorrectly marketed as able to “earn the upside without the downside.” In practice, momentum models impose a very real cost for side-stepping most severe stock losses. The cost is paid through false-positive signals when absolute momentum dips slightly negative, but a larger correction doesn’t develop.

Imagine you know that a coin has a 25% probability of landing on heads. If you were offered a payoff of $0.50 per heads and $1 per tails, you should always bet on tails since it has a higher expected value than heads. The expected value of betting on tails is its probability of 75% multiplied by its payoff of $1, or $0.75 per coin toss. This is greater than the $0.125 expected value (25% * $0.50) of betting on heads.

Now let’s say the payoffs were skewed, still paying the same $1 for tails but now $5 for heads. The expected value of betting on heads changes from $0.125 (25% * $0.50) to $1.25 (25% * $5). This is greater than the $0.75 expected value of tails. In the long run, you’d make more money by betting on heads, regardless of its lower 25% probability.

The purpose of the coin flip example is to show that the payoff matters just as much as an event’s probability. To extend the coin flip example with market data, the table below shows every time over the past 25 years that absolute momentum has been negative for U.S. stocks.

The data below shows the same average momentum measure and rebalancing logic from the Movement trend model. The table shows how long absolute momentum was negative for U.S. stocks and their performance during that time window. The table also shows the dollar value of gains lost when stocks rose and the dollar value of losses avoided when stocks fell during the negative momentum window. Dollar values are for a hypothetical $1,000,000 position each time period. Observing only what happens between two points of time hides the volatility in the middle, so drawdown data is also included.

For example, from 7/1/1994 to 8/5/1994, U.S. stocks rose 2.6%. An absolute momentum model 100% in U.S. stocks would thus lose out on 2.6% in gains (or $26,150) since it would be out of the market. This is a false-positive momentum signal.

On the other hand, from 9/29/2000 to 6/13/2003, U.S. stocks fell -27.8%. The same momentum model avoided $278,303 in losses and a substantially large drawdown. This is a “correct” momentum signal since a larger correction materialized.

Returning to the coin flip example, the two graphs below summarize the probabilities and payoffs of the U.S. stock momentum data. The probability chart shows the percentage of correct and false-positive momentum signals. The payoffs chart shows the average gain lost and the average loss avoided.

A false-positive momentum signal should be an investor’s baseline expectation. The asymmetry between gains lost and losses avoided is partly why momentum has been coined the “single biggest embarrassment” to the efficient market theory. There’s an ample amount of evidence on the persistence of momentum over many decades and across many asset classes.

That being said, momentum strategies are not a cure-all that allow you to participate in 100% of stock market gains without any downside. They have historically allowed you to capture a majority of the upside, but at the cost of occasional false-positives. I personally consider this a price worth paying to have a high probability of avoiding large future losses.