Risk targeting and dynamic asset allocation: absolute or relative momentum?
Quite a few of my recent blog pieces have been picked up by the lovely folk atallocate smartly. So I thought I'd write an asset allocation piece, as the readers of my second book "Smart Portfolios" probably feel neglected with the lack of articles on investment rather than trading.
Absolute or relative momentum?
The motivation for this comes from a desk in my 2d e-book, which exposes an thrilling problem. Here is the desk (really a barely modified version of it, so that you won't understand the proper numbers), and I'll explain what it way and what the trouble is:
Arithmetic mean Geometric mean Std. Deviation Sharpe Ratio
Fixed weight 8.37% 8.04% 8.14% 1.03
Relative momentum 9.26% 8.89% 8.62% 1.07
Absolute momentum 8.93% 8.61% 7.96% 1.12
Fixed weight: This is a portfolio with 75:25 risk weightings in US equities and US bonds (using the last 12 months of monthly returns to calculate the appropriate volatility for risk weighting; this works out to roughly 60:40 cash weightings on average).
Relative momentum: This portfolio tactically rebalances the strategic fixed weights using the relative 12 month total risk adjusted return of equities and bonds. The rebalancing is a 'tilt' to account for forecasting uncertainty; the maximum tilt is to 148% of the original portfolio weight, and the minimum is 60% of the original. The relative momentum portfolio is always fully invested.
Absolute momentum: This portfolio tactically rebalances the strategic fixed weights according to the absolute 12 month total risk adjusted return of equities and bonds, again using a 'tilt'. The absolute momentum portfolio may not be fully invested if momentum is relatively weak in one or both assets. The minimum investment is 60% (which is not unusual), and the average is 93%.
All portfolios are rebalanced month-to-month, the use of information from January 1954 to March 2016 (I could replace this, however I wanted to apply the same statistics as within the book, and it would not have an effect on the consequences a whole lot). Returns proven are excess returns, net of the threat free price.
Let's do some basic analysis of these results. Using absolute momentum results in a slightly higher risk than for fixed weights, because equities have spent more time going up in a risk adjusted sense. I call this the historical volatility boost. That more than compensates for the fact we aren't always fully invested, which drags down risk. The average cash weight to equities is 67% versus the 61% under fixed weights. But the extra risk is well rewarded with a higher arithmetic and geometric return, and a higher Sharpe Ratio.
Absolute momentum is a exquisite popular asset allocation technique, because human beings just like the 'drawback protection' of being partially in cash when markets are promoting off.
Relative momentum has even higher threat; again it has a scientific bias in the direction of equities and a historical volatility enhance, however because we're constantly absolutely invested that all hits the 'backside line' inside the shape of higher hazard. The average cash weight to equities is 70%. The more chance is rewarded with a higher arithmetic and geometric imply return, however the Sharpe Ratio is truly decrease than for absolute momentum (though still better than constant weights).
Relative momentum is much less popular among the general public, as it appears tough to justify a large allocation to bonds just due to the fact they aren't falling quite as speedy as equities. It also has a worse Sharpe Ratio, so 'theoretically' it's inferior (in case you're an investor who can use leverage).
In my e book I rather blandly concluded that relative momentum changed into higher because of the higher geometric suggest.
However, we're not comparing like with like. Strictly speaking we should probably compare relative momentum with an absolute version that has a higher strategic allocation to equities, so that their risk levels are comparable. To put it another way: is it better* to use relative momentum, or to use absolute momentum and crank up your strategic risk target to compensate for the reduction in risk?
Already we will see that this is a variation of the classic quandary that traders with out get right of entry to to leverage and excessive risk tolerance have: should I choose the best Sharpe Ratio, or for something with better danger (and go back) but a lower Sharpe Ratio? However this story is more complicated, due to the fact we've transferring components: the unique hazard weights, and the choice of rebalancing strategy (fixed weights, absolute, or relative). The interplay of those will produce portfolios with unique go back and threat profiles.
* The dilemma would be the equal** for any form of forecast, but momentum is a famous and properly understood rule to establish conditional returns.
** Strictly talking the idea of an 'absolute' forecast calls for some kind of equilibrium cost at which we have a 0 function. So dividend yield as a forecast wouldn't be beneficial for absolute weighting, however some thing like (divided yield - hobby charges)*** would make sense.
*** the 'Fed model'
The experiment
The general question we want to answer is:For a given risk tolerance, what is the best choice of strategic risk weights and rebalancing strategy?
My criteria will be to judge a particular outcome by looking at the geometric mean (my reasons for choosing that are documented here), and the standard deviation of returns.
The variety of strategic risk weights I will take into account are from 10% equities 90% bonds, up to ninety% equities 10% bonds. All strategic threat weight portfolios may be fully invested. Note that humans with actually low danger appetites could be exceptional served through the maximum Sharpe Ratio portfolio plus a cash allocation; but I may not don't forget that option here. After all the trouble we're exploring is maximum acute for investors with better chance appetites.
To make the consequences starker, I'm going to permit the 2 tactical portfolios to 'tilt' all the manner from 10% to two hundred% of the authentic strategic weight. Obviously this won't have an effect on the constant weights. For much less aggressive tilts the relative outcomes may be the identical, however the numbers could be nearer together.
First permit's examine the Sharpe Ratios:
The black line is what you'll expect; the maximum SR portfolio is roughly 50:50 in equities and bonds. Absolute momentum is in the main not so good as the alternative options besides for extraordinarily excessive allocations to equities. Relative momentum suggests declining overall performance as we boom the risk weight.
However these differences in SR won't be significant (I'll speak this later inside the post), but more importantly 'we can not eat Sharpe Ratios' if we're not leveraged buyers, so permit's alternatively cognizance on the geometric method and general deviations.
Each line shows a classic 'green frontier', with one line for fixed weights, one for relative weights, and one for absolute weights. Each pass is a exclusive strategic allocation, in 10% steps. So the first black go on the lowest cease of the constant weights line is 10% danger weight in equities, the subsequent move is 20% in equities, and so on as much as ninety% at the pinnacle right give up of the road.
We can safely forget about all the portfolios with lower danger than 30% equities; for these we might be higher off blending the maximum Sharpe Ratio portfolio with coins.
It's clear from this graph that the out performance of relative momentum is pretty consistent. For a given risk target relative momentum is better than fixed weights or absolute momentum. It also looks like there is no benefit from using a risk target of greater than 80% in equities.
Which strategic portfolio weights should we use?
There is an crucial query that isn't always effortlessly responded via the graphs above: how an awful lot have to I adjust my strategic weights to atone for the effect of applying a relative or absolute momentum tactical weight?
So, as an example, if you want a general deviation of eight% you could use:
- a fixed risk weight of ~75% to equities
- tactical absolute weighting with a strategic risk weight of ~68% to equities
- tactical relative weighting with a strategic risk weight of ~40% to equities
That is some extensive distinction!
How sturdy are those effects?
First let's consider the differences in geometric manner. I'm extremely confident that 12 month momentum is a sturdy effect that has existed in the beyond, although we can argue about whether it will retain within the destiny. So I'd count on both kinds of momentum to overcome constant weights.
What about the out performance of relative momentum? Cross sectional momentum across asset training is a much less popular idea (even though incredible popular within asset instructions e.G. Throughout shares), however it would be unexpected if there has been a big difference among the two forms of forecast.
However in a long most effective portfolio absolute momentum is operating with one hand tied in the back of it is lower back, as it can't pass quick. This might provide an explanation for the fantastically poor overall performance of absolute momentum. Even when it has a barely higher Sharpe Ratio (for incredibly excessive fairness weightings), the discount in volatility method that absolute momentum can't compete on a geometrical mean basis.
What about the differences in standard deviations? By construction the standard deviation for absolute momentum will always be lower than that for relative momentum.
The motives for the growth in widespread deviation whilst using relative momentum is much less strong (threat also rises for absolute momentum, except for extremely low or very excessive fairness allocations). In idea, if each equities and bonds had the equal average forecast going ahead, then the usual deviation will be the equal for relative momentum as it's far for constant weights.
Radically reducing your strategic weight to equities to compensate for the expected 'volatility boost' from your tactical overlay might not be wise. The existence of a risk boost is probably the least robust finding here - I wouldn't be 100% sure it will exist in the future.
Conclusion
I'm reasonably happy that my superficial analysis in "Smart Portfolios" was correct when put through a more thorough test: relative momentum gives a higher geometric mean than absolute momentum, except for investors with low tolerance to risk. Therefore for most investors it's preferable.
In terms of more unique recommendation, the graphs above suggest the most effective portfolios are:
- If you can use leverage, the highest Sharpe Ratio comes from using relative momentum tactical weighting with a risk weight to equities of somewhere between 30% (15:85 equity/bonds in cash weights based on current vols) and 50% (30:70 equity/bonds in cash weights). Within that range I'd err towards a higher weight in equities in case the 'risk boosting' that occurred in the past is absent. Recommend: Strategic risk weights 50% equity 50% bond, cash weights 30% equity 70% bonds, relative momentum tactical weighting.
- If you can't use leverage and have a high risk tolerance, the highest geometric mean comes from using relative momentum tactical weighting with a risk weight to equities of somewhere between 60% (40:60 in cash weights based on current vols) and 90% (80:20 in cash weights). Within that range I'd err towards a higher weight in equities in case the 'risk boosting' that occurred in the past is absent. Recommend: Strategic risk weights 90% equity 10% bond, cash weights 80% equity 20% bonds, relative momentum tactical weighting.
- If you can't use leverage and have a modest risk tolerance (but higher than 8% standard deviation a year): I'd use relative momentum but with a lower risk weight. If you don't buy the 'risk boosting' story then you will need between 60% and 90% risk weighting in equities; if you do buy the story and believe history will repeat itself, between 30% and 60% risk in equities.Recommend: Strategic risk weights 60% equity 40% bond, cash weights 40% equity 60% bonds, relative momentum tactical weighting.
- If you can't use leverage and have a low risk tolerance (lower than 8% standard deviation a year): I'd invest in the maximum Sharpe Ratio portfolio (see above), and blend it with cash.
