It's no secret that reducing turnover is a big focus for us here at Newfound. Despite being tactical managers, we like to be tactical about being tactical; in other words, avoid trading and turnover at all costs because they have sunk, guaranteed costs that we have to trade-off versus potential gains.
In the past, we've written about an overlay methodology that utilized principal component analysis (see Being Strategic about Tactical Allocations parts I and II). The goal of the methodology was to utilize the market structure to filter out weight changes that did not represent a substantial departure in the effective bets we were currently making. For example, a 20% allocation change from SPY (U.S. large cap) to MDY (U.S. mid-cap) in a globally-diversified portfolio may not create a large enough change in our beta exposures to justify the cost.
So while our cost-ignorant model may dictate certain weights, we may stick to our old weights because the new weights aren't worth the trading cost. Using the PCA-based method, we found that we could reduce portfolio turnover relative to model turnover by 2/3rds; however tracking error was fairly high at nearly ~1.5% annually.
While the PCA method implicitly considered many of the same concepts measured by tracking error, it did not reference tracking error explicitly (though, it could be fairly trivially extended to do so). Tracking error, however, may be exactly what we want to explicitly reference in our methodology. After all, what we are really trying to say is: "only make a weight change when it introduces a significant enough tracking error to my old portfolio weights."
How do we do this? Consider the following pseudo-code:
let w be the model weights let p be the current portfolio weights let C be the covariance matrix of underlying securities let t be our tracking error threshold for each date: z = (w - p) if sqrt(z'Cz) > t: p = w
Effectively, when the difference of model weights to the current portfolio weights creates a tracking error in excess of our threshold, we rebalance.
To test this methodology, I randomly created 100 model portfolios with daily weights. I then created new allocations for these portfolios by running this tracking error filter over them with a threshold of 1.5%. On average, portfolio turnover was reduced by 37.4% and average annual tracking error to the model portfolio was 0.96%.
So how does this math play out?
Let's assume that a full 100% portfolio turnover costs 10bp (execution costs, market impact & bid-ask spread). If we take a conservative approach and assume that the tracking error always goes against us, we'd have to generate 96bp of value to make up for it. In other words, we need: 37.4% * (T x 10bp) > 96bp. Solving out, T = 2566% -- an egregiously high turnover number that would make almost any investor cringe.
The take away here? While the tracking error threshold method did a great job of reducing our turnover, it did so at the cost of tracking error. Depending on our assumptions of how this tracking error can affect our total return, it may require an unrealistically high initial annual turnover level to justify.