# Probabilistic Absolute Momentum (PAM)

In the last post on Probabilistic Momentum we introduced a simple method to transform a standard momentum strategy to a probability distribution to create confidence thresholds for trading. The spreadsheet used to replicate this method can be found here. This framework is intellectually superior to a binary comparison between two assets because the tracking error of choosing one versus the other is not symmetric across momentum opportunities. The opportunity cost of choosing one asset versus another is embedded in this framework, and using a confidence threshold that is greater than 50% will help to standardize the risk of momentum decisions across diffferent pairings (for example using momentum with stocks and bonds is more risky than with say the S&P500 and the Nasdaq).

The same concept can be used for creating an absolute momentum methodology–this concept was introduced by Gary Antonacci of Optimal Momentum in a paper here. The general idea for those that are not familiar, is that you can use the relative momentum between a target asset-say equities- and some low-risk asset such as t-bills or short-term treasurys (cash) to generate switching decisions between the target and cash. This can be used instead of applying a simple moving average strategy to the underlying asset. In this case we can apply the same approach with Probabilistic Momentum with a short-term treasury ETF such as SHY with some target asset to create a Probabilistic Absolute Momentum strategy (PAM). In this case, I created an example with the Nasdaq (QQQ) and 1-3 year treasurys (SHY) and used the maximum period of time when both had history available (roughly 2800 bars). I chose 60% as the confidence threshold to switch between QQQ and SHY. The momentum lookback window chosen was 120-days. We did not assume any trading costs in this case–but that would favor PAM even more. Here is a chart of the historical transitions of using the probabilistic approach (PAM) versus a simple absolute momentum approach:

Here is the performance breakdown of applying this strategy:

Here we see that Probabilistic Absolute Momentum reduces the number of trades by over 80% from 121 to 23. The raw performance is improved by almost 2%, and the sharpe ratio is improved by roughly 15%. More importantly, from a psychological standpoint using PAM is much easier to use and stick with as a discretionary trader or even as a quantitative portfolio manager. It eliminates a lot of the costly whipsaws that result from trying to switch between being invested and being in cash. It also makes it easier to overlay an absolute momentum strategy on a standard momentum strategy since there is less interference from the cash decision.

David, very long time no chat! It’s been 4 years probably! One way to reduce round-trips is to vary the sell rank, no? So for example with 20 assets one can buy the top 5 and sell only if one goes below say rank 8. Perhaps I’m jumping ahead, since we’re just looking at 2 asset portfolios. I wonder how that methodology would compare with Probabilistic momentum. Cheers!

hi Alex, good to hear from you. Indeed it has been a long time. The method you are describing is reasonable with multiple assets, but it still doesn’t capture the relative tracking error into a probability. As a consequence the rank-based method will have to be optimized as a function of the universe of assets chosen–and this obviously is a potentially noisy process. The rank method works well to reduce transactions but shows variable performance depending on the parameters across different universes and universe sizes. In contrast the probabilistic approach is more standardized and shows less variable performance. I hope that helps!

cheers

David,

Great post! I have tested your method as such: universe: S&P 500 Total Return Index(Equity), Barclay US Bond Aggregate Total Return index(Bond), Spot Gold(Gold), 3 month Libor(Cash);Data: monthly returns from 1977/12 till 2014/2; set look back window to 24 months and confidence level to 0.80; Run strategy to assets pairs: if A>B, 100% in A; if A<B, 100% in B; if not significant, 50% in A & 50% in B. Run back tests from 1979/1 to 2014/2,The results are as follows:

CAGR SHARP MAX DRAWDOWN

EquityBond: 0.1207 1.073 -0.1278

EquityGold: 0.11706 0.685

BondGold: 0.092 0.7358

EquityCash: 0.1056 1.064

GoldCash: 0.0705 0.567

Seems to me the strategy is quite robust. I wonder how it would perform in a long brutal bear market such as Japan.

Again thanks for sharing the great idea!

Bo

In your backtests how was your initial position determined? In other words, if the probability of one asset was greater than 50% but less than your threshold, how/when was an opening trade made? If you vary this opening trade decision, does it materially impact your backtest results?

The initial position is always 50-50. In case the probability is less than the threshold it goes back to 50-50.

David, for the multi-asset case would you construct a matrix (akin to a correlation matrix) where each entry is the PAM value between the two assets? You’d have to come up with some rules for selecting the set of assets… max n values from matrix, max average PAM per asset, or some other variant. Would appreciate your comments.

Thanks,

Victor

David, I came across this site that seems similar to your probabilistic momentum. I wonder if you’ve seen this research and would appreciate your opinion of it.

http://www.harlynresearch.co.uk/process/