Some Thoughts On the Trade-offs Of Strategy Switching or Aggressive Tactical Allocation and the Virtues of Sometimes Taking a Tax Hit

The small number of people that read this blog probably know that I have been mining, if not perseverating on, a paper by R. Michaud (A Practical Framework For Portfolio Choice, Robert Michaud, Journal of Investment Management, 2003).  In that article he has a great example on the pros and cons of selling a high volatility one-stock portfolio in exchange for a more diversified fund especially when it comes to thinking about the upfront tax hit that stops many people from doing the smart long-term thing.  His point is that many people misapprehend the issue because they mis-understand the concept of geometric returns and the effects of time and volatility.  As a way to help myself understand his point I wanted to see if I could recreate some of that analysis especially as it applies to the concept of flipping between high and low risk strategies based on systematic rules or some kind of adaptive optimization framework.  I was originally thinking about this late last  year when I ran through an exercise in backward induction (BI).  My amateur attempt and the results of the BI optimization told me at that time, right or wrong, that I might want to start with a conservative allocation (in a two asset world, let's say a 30/70 or 40/60 stock/bond allocation) and then switch between that and a riskier portfolio (let's say 70/30 to 100% risk allocation) based on age and scale of wealth in any given year.  The project was fun but the thought of selling assets at any scale to switch strategies back and forth gave me the tax willies.  Michaud's paper attacks this problem head-on. 

The basic concept, which you can read on your own, is that the multi period expectations for a high return, high vol single stock may actually be lower n-periods into the future than the n period return of the safer asset might be even with the tax hit factored in. And the "crossover," when it happens, may be sooner than people think.  He has a nifty chart that illustrates the concept.  I could not, for the life of me, figure out how he did it. Now I want to try to do it myself and also to think in terms of the concept of switching from generic strategy A (high risk) to generic strategy B (low risk) since I myself engage in systematic alternative risk strategies and also because I often like to tell myself I would aggressively switch my passive allocation on a dime as the need arises to something riskier and vice-versa, a proposition I know to not be true at all.

The baseline -- The only way I could think to recreate what he charted was to do a mini-simulation with two different assets with distinct statistical characteristics.  I have as a starter set two assets. One has a mean return of .07 and an initial standard deviation of .25.  The other has a mean return of .04 and a standard deviation of .07. I'll assume a tax hit of .15 in year 1 on the second asset. We'll otherwise ignore the shape and nature of the distributions which is secret code for implying they might be normal for this example but I would never say that in public.  First I'll generate 1000 random returns for each asset and for each of 20 periods in the future.  Then I'll calculate the cumulative geometric return of each thread of returns over the 20 periods creating 1000 different paths that the geometric return could take for each of the two assets over our time frame. Then, to keep it simple and be able to coherently chart it, I'll average the two paths, separately. 

The twist -- Next I will take the risky asset and make it riskier by changing the standard deviation by 5%.  For the low risk asset, I'll keep every thing the same but I'll change the tax hit from .15 to .05.

To see what happens, we go to the chart*.  

Ok, so what do we have.  Given the baseline assumptions for strategy A and B (the heavy solid blue and green lines) we would probably, all else equal, never switch from A to B although the mult-period view of A  tells us that it is not as great as we think it is.  Also, strategy B, although taking a hit in year one is probably better than we think it is.  We are ignoring that the taxes will come find us sooner or later no matter what.  

Now, the twist.  Follow the dotted lines.  For strategy A when I change the vol to be higher the multi period equilibrium return goes down.  For strategy B, I take a smaller hit on taxes (why? who knows) in this scenario.  The result of the twist is interesting. The implication is that the expectation for longer term outcomes (vs the single period outcome) is better for B than A after about 4 or 5 years. Something I would've never guessed based on my experience if I'd never read the article.  

So should one be afraid of switching strategies? Probably, yes. But there may be cases where there is a good case that it is ok (again all else being equal). This might be especially true when the current strategy is really really risky and where the tax hit is modest and where the second strategy has statistical characteristics that can lift it to a positive outcome in a short enough timeframe** to make it compelling.  As in real life, it all depends.

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* the chart, even as an average, is one of an infinite number of simulation scenarios.  Some look good, some don't.  If you need to know, I cherry picked the ones above to make my point.  Also, note that since one only has "one whack at the cat," the actual path, not as an average, in real life could be radically different.  This is my best guess at the what the simulation scenarios are supposed to look like...with the black line being the average:

** It strikes me that, given nothing other than what is in this post, flipping back and forth between strategies while ignoring taxes and doing so in time frames less than years is probably unwise.  I may be wrong.