In our inaugural Algo Bootcamp, we teamed up with our super-active community of traders and developed a long-only, always-in-the-market strategy for harvesting risk premia. It holds a number of different ETFs, varying their relative weighting on a monthly basis. We’re happy with it. However, the perennial question remains: can we do better?
As you might expect, we found evidence suggesting that risk premia are time-varying. If we could somehow predict this variation, we could use that prediction to adjust the weightings of our portfolio and quite probably improve the strategy’s performance.
This might sound simple enough, but we actually found compelling evidence both for and against our ability to time risk premia returns.
We’re always telling our Bootcamp participants that developing trading and investment strategies requires the considered balancing of evidence in the face of uncertainty. In this case, we decided that there was enough evidence to suggest that we could weakly predict time-varying risk premia returns, at least to the extent that slight weight adjustments in accordance with these predictions might provide value.
The strategy was already decent enough, so we were loath to add additional complexity that could bite us later. There was compelling evidence that our predictions could add value. But there was also a troubling deterioration in the quality of these predictions over time. In the end, we added only a very slight weight adjustment on the basis of these predictions.
Why am I telling you all this?
Well, I am really curious as to whether you would have made the same decision as we did. In this post, I’ll provide a bunch of our findings and let you make up your own mind. The best decision for us at the time was to only incorporate a very small timing aspect in our risk premia strategy and move on to something else. But I don’t think everyone would agree. This stuff is always context-dependent, and we all have a different context, but still, I’d love to hear what you would have done in the comments.
Our Baseline Strategy
As I mentioned above, our strategy was already looking quite decent before we started exploring ways to time the market. Here’s a long-term backtest, before costs (many of our ETFs weren’t around for the entirety of this backtest, so we had to create synthetic asset data from indexes, mutual funds, and other relevant sources):
The strategy had a backtested Sharpe ratio of 1.22 and a Compound Annual Growth Rate (CAGR) of 6.6%. If we could lever it up 2x costlessly (which of course we can’t) we can bump up the CAGR to over 12%:
Over the same period, the S&P500 delivered a CAGR of around 8.3% at a Sharpe of approximately 0.6.
How To Time The Market
Two anomalies seem to pop up over and over again in the markets: momentum and value. The AQR paper Value and Momentum Everywhere is a good summary for the uninitiated. Essentially, the authors demonstrate a momentum and value effect within every asset class they look at, as well as across asset classes. This suggests that we might be able to use relative momentum and value rankings across the assets in our risk premia universe as a simple prediction of future returns.
The Momentum Effect
We ended up ignoring the value effect for now (we ran out of time, and the strategy was good enough to get into the market at the end of the Bootcamp, but we’ll likely revisit this in the future), and instead focused on the momentum effect across our risk premia universe.
The thing with momentum is that we don’t really know exactly what it is or how to calculate it. So we deferred to the simplest approach we could think of to estimate it: the rate of change of price over some formation period.
Momentum Factor Plots
We performed a classic rank-based factor analysis by:
- Calculating our momentum estimate.
- Ranking each of our assets according to this estimate.
- Looking at subsequent returns over some holding period for each rank.
So our momentum analysis is really subject to two parameters: the formation period used in the momentum estimate, and the holding period used to assess the momentum factor’s relationship with future returns.
We looked at all combinations of 1, 3, 6, 9 and 12 month formation periods and 1, 3, 6, 9 and 12 month hold periods. We found a clear and persistent momentum effect, at least on average over the whole sample.
Here’s a selection of factor rank bar plots showing the mean future return by momentum rank (1 representing the highest momentum, 8 the lowest):
We actually saw some sort of momentum effect in every combination of formation and holding period that we looked at.
Next, we tried to quantify the strength of this cross-sectional momentum effect. We did that by looking at the difference in annualised returns between the top and bottom n assets by momentum rank (again, for a combination of formation and holding periods).
Here are some plots that show the difference in annualised returns between the top and the bottom n assets by momentum rank. The formation period (in months) is on the x-axis. The holding period (in months) is on the y-axis. The colour represents the magnitude of outperformance of the top-ranked asset.
First, for n = 2:
And for n = 4:
We see that pretty much across the board, assets with higher recent momentum tend to outperform those with lower recent momentum, again on average over the whole sample of our data.
We can also see that the effect is greater the shorter the holding period. This is unsurprising, but from a strategy development point of view is somewhat disappointing, because the shorter the holding period, the more frequently we’d need to adjust our positions to capitalise on the effect and the higher our cost of trading. Nothing comes for free, apparently.
All Aboard the Momentum Train!
To summarise our findings to this point, we see a strong momentum effect for formation periods of 3 to 12 months. And the effect is stronger for shorter holding periods.
You might, therefore, be convinced (and indeed many of our Bootcamp participants were) that we should only hold the assets in our risk premia universe with the highest 3-12 month momentum.
But so far we’ve only looked at the mean momentum outperformance over the entire 20-year data set. Markets are dynamic and noisy, and looking at summary statistics like the mean can hide important information.
Therefore, before we made any decisions, we looked at the consistency of momentum outperformance over time.
Here are some plots of 3-month and 6-month momentum outperformance over time for formation periods 3 to 12.
The dots represent mean outperformance of top-ranked assets over the holding period annualised over the given year. The lines are LOESS curves.
These plots suggest that the momentum train has been running out of steam for a number of years now. That is, we see a clear decline in the cross-sectional momentum effect over the sample period.
The momentum effect over the whole sample is significant. But the decaying performance suggests caution in trading the effect aggressively.
Momentum Backtest 1: Asset Rotation
At this point, many of our Bootcamp participants were wondering why we’d still bother looking at momentum given the clear decaying performance in the previous charts.
But at this point, we were still taking it seriously because it has worked exceptionally well for as long as we have history available. But there is a real question to whether the increased turnover and potential reduction in diversification as we rotate into high-momentum assets is justified given the decaying performance.
Here’s a backtest for a strategy which, every month:
- ranks each asset according to its trailing six-month returns
- selects the top four assets and weights each in inverse proportion to its volatility over the previous three months
This backtest has a before-cost CAGR of 8.9% at a Sharpe ratio of 1.14. This is a higher return than our baseline strategy at a similar, though slightly lower, Sharpe ratio – probably due to a reduction in diversification.
We can get some insight into what this strategy is doing by looking at its asset weights over time:
Compare this to the asset weights of our baseline strategy:
Chalk and cheese. The momentum strategy has higher returns and better drawdown control. It’s lower Sharpe comes by way of increased concentration (reduced diversification), and it turns out that it has over 5x the turnover.
We weren’t overly impressed by this trade-off. Specifically, we weren’t sold on the idea that there’s enough evidence to convince us to run a momentum strategy at the expense of diversification (what do you think? Let us know in the comments). However, despite its decay over the last decade or two, the historic momentum outperformance is remarkable. You won’t see a much bigger anomaly than that. We could therefore certainly entertain overweighting assets with high relative momentum and underweighting those with low relative momentum, based on the evidence we’ve seen to date.
Momentum Backtest 2: Weight Adjustment
Intuitively, we prefer a more subtle way to incorporate the momentum effect, one that adjusts portfolio weights slightly based on our estimate of relative (cross-sectional) momentum. That way, we’re always holding some of each asset in our universe, but we might be underweight when an asset class has been underperforming relative to the others.
It’s possible to get super-complicated with this (Black-Litterman, Bootstrapping, etc.). Knowing that any improvement is likely to be marginal above our already-decent strategy, we decided not to try anything too complicated here. We simply adjusted our baseline asset weights slightly depending on the relative momentum factor.
Here’s how that backtests:
This gives a CAGR of 7.4% at a Sharpe of 1.3. Here are the asset weights:
The portfolio is consistently well diversified and we’ve increased returns and Sharpe ratio over the baseline strategy. However, it turns over about 2x more than the baseline strategy. We feel that this is a much more attractive trade-off. Do you?
Weighing the Evidence
In our recent Bootcamp, we took a deep dive on the momentum effect and tried to make a sensible decision about incorporating it into our risk premia strategy. The evidence for the momentum effect includes:
- A wealth of empirical evidence in favour of momentum over many years
- On average, a clear and persistent momentum effect (noting that when looking at averages much detail is hidden)
- On average, clear outperformance of top-ranked assets over bottom
The evidence against includes:
- Outperformance is more pronounced for shorter hold periods, which implies more frequent rebalancing and higher costs
- Recent deterioration across the board
How can we weigh up this evidence in the context of our risk premia strategy? Here’s a summary of our thought process:
- We are confident that exposure to risk premia is a good idea that is rewarded over the long term.
- Every time we are not in the market we are giving up exposure to that risk premia.
- So we need to be pretty confident in our timing ability to get out of the market.
- We are not that confident.
- We can see an obvious and clear momentum effect (at least in the past).
- This effect has deteriorated in the past decade or two.
- We give up quite a lot to access the momentum effect if we make binary decisions to get in or out of an asset. Specifically, we give up exposures to certain risk premia at certain times, and we give up diversification benefit on our portfolio variances.
- We also increase turnover significantly.
- We can, to an extent, have our cake and eat it too by adjusting baseline asset weights based on the cross-sectional momentum factor, rather than making binary in-out decisions.
- Using this approach, we give up some of the momentum effect, but we retain the benefits of diversification as well as constant exposure to the risk premia.
That thought process seems to logically suggest that the momentum adjustment approach makes the most sense in the context of our risk premia strategy. This also implies that we need to give some thought to how we implement these adjustments.
In the end, we decided that a simple adjustment to the baseline weights based on our estimate of the momentum factor is sufficient – it affords us simple and easy access to the momentum effect without compromising our exposure to risk premia or the benefits of diversification. Previously, we alluded to some more complex approaches for adjusting these weights, such as Black-Litterman, which would probably allow us to squeeze out a couple more drops of performance.
But that’s not the best use of our time given the bigger picture of our broader trading operation. First and foremost, we’re not building a risk premia strategy – we’re helping our members and Bootcamp participants build out their trading capability. At the early stages, we stand to gain a lot from adding additional edges to our portfolio. We would probably gain something from a more complex momentum tilt on our risk premia strategy, but it’s going to be nowhere near as beneficial as diversifying across strategies. So we opted for a simple approach that gets us into the market and hot on the trail of active alpha strategies to add to the portfolio.
This bigger picture will change. When our portfolio is more mature, it will likely make a lot of sense to revisit the risk premia strategy and try to squeeze a little more out. There might well come a time when this is our biggest or most sensible opportunity. But that time isn’t now.
- Our strategy is based on exposure to risk premia for the long term.
- We think we might be able to gain some benefit from trying to time our risk premia exposures.
- Momentum has been a remarkable anomaly for a long time.
- Its performance has deteriorated for a decade or two.
- Strategy design is all about weighing evidence in the face of uncertainty.
- Context matters both at the strategy level and the bigger picture trading operation level.
- For our specific context, we found a way to incorporate momentum timing into our risk premia strategy with sensible trade-offs.
One of the most fun things about independent trading is not only weighing the strategy-level evidence that you collect yourself, but deciding what it actually means for your specific situation. No one can tell you what the right answer is – partly because it doesn’t exist, and partly because everyone’s context is different. You have to make a decision at some point and take action based on your best judgment. It’s the ultimate exercise in backing yourself and taking responsibility for your own decisions. That’s also why I think trading isn’t for everyone – not everyone is comfortable taking on that level of responsibility. But if you do, then trading is the best game in town.
The tricky part about weighing evidence and making smart trading decisions in the face of uncertainty is that it takes experience to do it well. You get that experience by getting kicked around in the markets for a few years – which isn’t particularly enjoyable or financially rewarding. In our Bootcamp program, we pass on the experience and intuition that we fought hard for over many years, minus the battle scars that we picked up along the way.
If that sounds like something you could benefit from, join the waiting list for our next Bootcamp program.