Projection vs Convolution_1
Real work done by Herb Haynes ?
As noted in Part 3 of this series of posts, the LRPC system builds on the foundations of the original Kipling ROC system in that it ranks assets based on momentum (and volatility) in exactly the same way. However, the new system adds Projection and Convolution parameters to trigger buy/sell signals.
These new parameters require the choice of look-back periods to calculate values used in the system. In this post we take a look at the effect of changing these look-back periods on seven individual performance metrics that an investor might choose to consider in order to evaluate overall system performance. Remember that we are keeping ranking parameters the same – short-term momentum look-back period = 60 days (50% weighting), long-term momentum look-back period = 100 days (30% weighting) and volatility = 10-day SD (20% weighting).
In these tests we vary the Projection look-back period (L1) from 20 days to 200 days and the Convolution look-back period (C1) also from 20 days to 200 days. Each of these parameters (P1 and C1) has another parameter associated with it – the L1 slope is projected forward a chosen period of days (P1) [see Part 2 for reminder] and, for these studies, we keep this fixed at P1=20 days (i.e. the projected value approximately one month in the future). The C1 slope is re-traced back a chosen number of days (the “Offset” period) – and this will be the focus of a future post in this series – but, for the current tests the Offset period (O1) is set fixed at -50 days.
Also, as a logical step from the original Kipling ROC momentum model, we retain the SHY filter i.e., an asset must be ranked higher than SHY to be included in the portfolio. We also allow a maximum of 10 assets to be included in the portfolio (MF=10) i.e., since the Rutherford Portfolio only offers 10 assets for possible selection there is no restriction on the number of securities that can be included in the portfolio (provided that they rank higher than SHY).
All tests are run from 12/31/2007 to 11/30/2017 (almost 10 years). We recognize that this is a predominantly bullish period for the markets – and the implications of that on back-testing – but it’s all the data we have for these ETFs.
With all the parameters set let’s look first at the total returns:
The above figure shows a heat map (HM) of the value of total returns as a function of the two variable parameters (L1 and C1). We should not be focused specifically on absolute values, since we try to avoid “optimization”, so the color coding is based on a percentile ranking rather than absolute values. We are looking for “robustness” or generous “sweet spot” areas where, even if our parameters might not be “optimal”, performance is “acceptable”. Therefore, we are looking for parameters amidst the “green” areas. For purposes of focus, as we move forward, I’ve highlighted 2 cells – one at L1=150, C1=110 and the other at L1=100, C1=90. Although I have stated that we should not be focused, obsessively, on maximum/optimal values it is logical that we are likely to migrate to these cells unless we have a system that is not robust and is characterized by a number of random “outliers”. The above map looks pretty smooth in terms of tolerance to “lack of optimization”.
Let’s convert the above returns to corresponding Compound Annual Growth Rates (CAGR’s):
Not surprisingly, the HM looks essentially the same as for the total returns with CAGRs (over 10 years) ~11% in the top percentile cells. In both of the above HMs our focus is towards the lower half and to the right of the map and away from the top left corner.
Now, let’s take a look at portfolio volatility:
Here, we see that the highlighted cells do not fall in the most preferred (green – low volatility) areas – although neither are they in an obvious “bad” (red – high volatility) area.
Note that an investor that was strongly volatility/risk averse might prefer to focus on low volatility (top left corner of volatility HM) but that this would come at the expense of returns. [Probably not an issue in this example because of the relatively small volatility differences – but the correlation persists/is enhanced at wider differences.]
One way to balance these metrics is to look at the “Risk-Adjusted Return” as measured by the Sharpe Ratio. Strictly speaking, this ratio measures the annual return in excess of the return that could be generated by holding a risk-free asset (usually assumed to be a short-term treasury bond) relative to volatility. In this study, since interest rates (and hence risk-free returns) have been low over the past few years, we have ignored the correction and simply used CAGR/Volatility to calculate the “Sharpe” ratio.
Here’s what the Sharpe Ratio looks like:
Our highlighted cells are showing very reasonable ratios of 0.97 and 0.84 and these look reasonably “robust” compared to values around them. However, note that 0.97 is not the maximum/optimal ratio (0.98) that can be found at L1=200, C1=80. The “low volatility” areas are only generating a Sharpe Ratio of ~0.5.
Many investors may be more concerned about draw-down (DD), or the difference between a maximum portfolio value “top” and the value of the portfolio at a subsequent “trough” before recovering to make a new “top”.
Here’s what the maximum draw-downs look like for the Rutherford portfolio in these tests:
The maximum DD values in our highlighted cells are very reasonable if an investor is comfortable accepting this level of risk. Remember that these results assume 100% investment in qualified assets and do not use stops of any form – therefore, if an investor is uncomfortable with a 15% DD, they might have to consider a superimposed method of risk management such as using stops – perhaps as suggested in the Position Size sheet of the LRPC workbook. Note that DDs using other combinations of L1 and C1 result in much more worrying DDs in the high 20’s% range – although this is still well below the 50+% DD of a buy-and-hold strategy through the 2008 financial crisis.
One way to balance returns against DD is to look at the MAR ratio (CAGR/Max DD):
Again, our highlighted cells show a favorable ratio – and note that, unlike the Sharpe, the MAR at L1=200, C1=80 is not optimal.
Finally, something that might influence some investors – although is probably less important than other factors unless everything is very close – is the trade frequency. The following HM shows the calculated number of trades in the above tests:
The number of trades identified here might be frightening – 480 trades represents 4 trades per month – but this is deceiving in a practical sense – many of the “adjustment trades” would be ignored by the practitioner (see e.g., my post at https://itawealth.com/rutherford-portfolio-review-tranche-1-19-january-2018/ where 4 “adjustment trades” are suggested but all are ignored). Use this map as a comparison chart – maybe divide by 4 for a more realistic practical estimate of trade frequency.
A downloadable copy of this post is available at https://www.dropbox.com/sh/ix9tocyjyf4ycl3/AACoRWSYilTa4Eu6sUi60GI3a?dl=0
In the next post in this series we will take a look at the impact of ignoring the SHY filter.
Herb and David