Market Compass is built around a set of models that bring together macroeconomic, valuation and trend-following inputs to give a perspective on the attractiveness of different asset classes around the world, from the perspective of a Canadian or U.S. dollar investor. The core models are updated weekly to reflect market action and economic data, although some inputs are only available monthly (sometimes with a lag) and some (such as earnings and other valuation measures) are only available quarterly.

The blog has published the model outputs weekly, and as might be expected, there has been a lot of minor fluctuation week-to-week, as trend-following, momentum and volatility measures react to fluctuations in market prices. This raises a question about how to interpret the model outputs - should an investor who updates their models weekly respond to these variations? What is the threshold of significance for changes?

There are many reasonable ways to approach this question. One would be to take a statistical approach, and to try to determine which changes have some level of statistical significance attached to them. Another would be to impose some set of rules that define when a portfolio change will be made - for example, rebalancing to the model's outputs on some set frequency (e.g., monthly or quarterly), or making a change whenever the difference between the portfolio and the model allocations exceeds a certain number of percentage points. A taxable investor could overlay a tax-loss harvesting strategy, or delay changes to defer gains. Each of these approaches has its pros and cons.

This week's post looks at a very simple approach - what happens if the model outputs are simply rounded to reduce the number of potential trades? We use a simple momentum- and volatility-based model and a subset of the Market Compass asset classes to assess how model performance is affected by a rounding of the outputs to the nearest 5%, 10% and 20%.

The short (and somewhat surprising) example is that rounding has very little impact on model outputs. In a nutshell, reducing the models' sensitivity to small market fluctuations - and in fact even reducing precision of the "fine tuning" applied to things like position sizing - has relatively little impact. The major value seems to come from being "generally correct and not specifically wrong".

We can see an illustration of this in the following chart, which shows the growth from a value of 100 of a simple momentum strategy. The portfolio uses 8 asset classes (U.S. equities through SPY, international equities (NYSEARCA:EFA), emerging markets (NYSEARCA:EEM), U.S. real estate (NYSEARCA:IYR), global real estate (NYSEARCA:RWX), high yield bonds (NYSEARCA:HYG) and commodities (NYSEARCA:DBC)). The model assigns a basic target exposure to each based on volatility, and then allocates a greater or less multiple of that base exposure (from 2x for the top asset class, to 0x for the bottom 4) based on ranking by 12 month momentum. If momentum goes negative for any of the top 4, the model shifts that allocation into short-term Treasuries (NYSEARCA:SHY).

The "rounding" effect is applied to the volatility-based position sizing, and to the final position sizing that applies the momentum-based factor. As we can see, model results vary relatively little with rounding:

*Figure 1. Model Outputs with Different Rounding Factors*

*Data source: Yahoo Finance*

The observation period only goes back to 2008, due to the availability of historical data, but the results support the idea that rounding does not have a major impact on performance. If we apply a Monte Carlo approach and sample different start and end dates, we can see that this result applies generally throughout the period and is not specific to the start- and end-dates shown in Figure 1:

*Figure 2. Model Results for Random Start- and End-Dates*

As we can see, there is not a major difference in performance between the different rounding intervals. There seems to be some tendency for 10% to deliver slightly higher performance with this particular model, and 20% seems to lower risk somewhat, but at this stage, it's hard to know whether there are general principles at work in those observations, or whether they are specific to the idiosyncrasies of this model and testing period. In keeping with the overall notion that these results broadly support the "rounding doesn't reduce performance" thesis, we will be rounding weekly results going forward, although at this point we will use 5% (the outputs of the separate monthly model have been rounded to the nearest 5% since inception). The model results are available as always in the Current Model Outputs section of the blog.

One final note: astute readers may notice a few changes to the "Representative ETFs" listed for the Canadian dollar models. BlackRock has introduced a Canadian family of "Core" iShares with significantly reduced fees, so they get some additional representation in our sample line-up.

**Disclosure**: No positions