Comments on the Floor Leverage Rule

I was sent a link to a paper from the Stanford Institute for Economic Policy Research by a friend the other day. 

SIEPR Discussion Paper No.13-013
The Floor-Leverage Rule for Retirement
By Jason S. Scott and John G. Watson
Stanford Institute for Economic Policy Research
2013

The abstract is thus:

The Floor-Leverage Rule is a spending and investment strategy designed for retirees that can tolerate investment risk, but insist on sustainable spending. The rule calls for purchasing a spending guarantee with 85% of wealth and investing the remaining 15% in equities with 3x leverage. Surprisingly, this leverage is a tool for managing risk. We compare our rule to some popular strategies, illustrate it for a variety of retiree preferences, and evaluate its historical performance.

The following is neither comprehensive nor exhaustive, just a riff based on some thoughts as I read my friends email.

Some Correspondence To a Friend

Here is my response to my friend's prompt:

"Didn’t read whole thing end to end but I see what they’re doing. Some thoughts  

• classic floor and upside. When income is floored typically the remaining risk allocation goes to 100%, i.e., up to the end of the EF. Here, they’re just removing a "no leverage constraint." They’ve extended the EF to the right. Makes sense.
• this kind of approach, but for the floor, seems like it would be a sequence-risk hell esp in 2020 after a 12 year bull market. Sequence risk doesn’t need spending to manifest but spending can make it worse.
• expense ratio for SPXL is 1.02%. Just to mention that.
• the risk portion of the portfolio begs for geometric mean analysis. We’ve seen that going outward on the EF in "multi period geo mode" there can maybe be a critical point where u start to shoot ur self in foot by taking more risk. Even Markowitz admitted that. Maybe 2x lvg is better than 3; or maybe a 4x if it existed would be better. No idea. 
• their utility functions look, at a glance, like they avoid random life weightings which, if true, would be a bit of a hole... for me.
• in general I’m not opposed to the floor-leverage idea and can see why it’d work under certain conditions. I just wouldn’t bite it off whole in 2020 when the probabilities for suppressed returns for a while looks higher than not. "

Testing allocation and spend choice with and without income in a Utility model to see where the allocation to risk will go. 

This won't be apples to apples since I am borrowing these next two figures from a past post I didn't publish.  My point is to show that adding life income will nudge spend rates up and also allow a portfolio to take on more risk with the remainder portfolio. This is more illustrative than analytical then. In essence I am just looking for where "the grey box" (the range of optimal allocations for a given scenario spend rates) goes when changing from figure 1 to figure 2.  

This evaluation comes from testing different spend rates and allocations for a 60yo male using a lifetime consumption utility simulator where the consumption utility is time preference discounted and probability weighted for survival, conditional on being 60. [1]

1. Scenario 1: no income floor. The lines are lifetime utility "scores" for different asset allocations (x axis going from 0% risk to 100% in 11 steps - for 3 different spend rates (each color). I didn't run it under 3.5% so a lower spend might have been better but no idea now. 

Figure 1

2. Scenario 2: add a modest income floor.[2]. Note that I have not attempted to match everything apples to apples, since this is old work of mine. The author's use a "convert 85% of wealth" approach; I use "convert 3/10 of W;" Authors (I think) are not longevity weighting U; I longevity weight.... You get the basic idea. 

Figure 2

The only take away here -- other than the lines are pretty flat after 50-60% allocation to risk -- is that as one adds life income or a structured floor to spending, the ability to take risk goes up (we see that in the rightward move of the grey box in figure2), especially if one wants to suboptimally spend more (see bottom red line in figure2).  

My guess is that if the floor were to created from 85 % of wealth we probably would most likely end up with a final allocation of very high/100% risk -- all else equal and given a no leverage constraint.  The other related take-away implicit in this is that we are walking up the efficient frontier in terms of consumption-utility optimized portfolios and that we stop at the upper right of the EF when we have hit the end of our allocation journey. 

Now Let's Add Some Leverage, Say the Authors Above

The "boundary" of 100% equity on the EF is arbitrary and can be breached if someone does not have a serious leverage constraint. The authors point out that 2X and 3X levered ETFs and funds now exist to make the execution of that idea a little easier for a retail investor.  Examples in the real world are funds like SPUU and SPXL, 2X and 3X S&P respectively.  

I have to admit that I did not read every last sentence here so I probably missed important things.  My general read, though, was that the authors concluded that, compared to other methods or baselines, that spending 85% of wealth on life income and then levering the residual W up 3x is best.  

My only thought on that conclusion was that it might look a little different if we made some suspiciously convenient assumptions for ourselves and then looked at something like geometric mean analysis to see where it goes. I went this direction because it seems like the high vol of the 3X leverage might actually come back to bite us if we are not careful. We know that the long-horizon geometric (realized) return for a high vol instrument can be lower than one with lower return and lower vol. But we are rarely sure unless we look.  Let's see what I mean.  

Steps:

1. Find available funds that could plausibly construct a "pseudo" frontier.  I used Morningstar data to profile return and risk for the following. I'll assume, maybe boldly, that returns are presented as arithmetic. I should check that:

Fund	risk wt	r(15)	r(5)	sd(?)
VASIX	0.20	0.0475	0.0463	0.0287
VSCGX	0.40	0.0556	0.058	0.0458
VSMGX	0.60	0.0637	0.0691	0.0681
SPY	1.00	0.0927	0.1218	0.1231
SPUU	2.00		0.2098	0.2428
SPXL	3.00		0.2816	0.367

Only the first 4 had 15Y return data, the last 2 were limited to 5 years. Standard dev we took at face value but it looks like Morningstar, like Yahoo, has a impoverished lookback. 12% std deviation is not the really the long term expectation depending on your horizon. Whatever.  

2. Create an efficient frontier with the fund data without asking too much about the data and my methods. This would be the blue line in figure 4.

3. Re-conceive the return in figure 4 (blue) as a geometric mean return (red) for a very very long horizon. The horizon I have in mind is longer, at infinity, than we really need for retirement but it makes a point here. I am using the sometimes debated estimator of  r[g] = r - V/2 where r is the expected arithmetic return V is vol = sd^2. For each SD along the EF we then use the estimator to re-calculate the long horizon geometric return.  The resulting line is the red one. Red and Blue are constructed using the 5 year returns here. 

4. Imagine the possibility that 15 year returns are different than the 5 year look-back for the funds that do not have the 15y data but also different in some use-ably predictable way. This requires some speculation and creativity since no one really knows the answer. To imagine this kind of thing I took the percent difference between the 5Y return and the 15Y return for the first 4 funds and then extrapolated for the last 2. This is a pretty suspect thing to do but if one can hold one's nose it might look like this:

Figure 3

5. Re render "r" again using the new "speculatively adjusted" returns and then proceed to use the same geometric mean estimation we did in #3. Now present the resulting doubly-adjusted frontier in "grey."

The result of the steps above would look like this in Figure 4

Figure 4. 

Discussion  

• 3x leverage worked in the Author's paper. But it looks sub-optimal here using some sketchy new assumptions that are probably not all that unreasonable. There seems to be a critical point somewhere between 100% equity and 3X leverage if my 15Y adjustment trick was not too corrupt. Here, the critical point happens to be at ~2X leverage.  

• I am using a different utility model where, for example, I am weighting and discounting lifetime consumption utility with a conditional survival probability.  That weights early life a bit more than if you don't.  Could account for some of the differences. 

• In a decent simulator, the effects of the multi period geometric means that are realized in the process will flow out in the time-steps of the simulation.  If that's the case then as Richard Michaud demonstrated in one of his papers, geometric mean analysis can stand in for and is the implicit engine behind simulation and can also be used for its calibration. It is also simpler and more transparent sometimes. Let's at least call it "triangulating the question" in order to see what several voices say about our portfolio choice.  The second voice, geo mean analysis, says to me: watch out for excessive risk (e.g., leverage in this case) because you might not get what you were expecting over the long haul.   

• In this faked-up example 2X "won" on the lower grey line but: a) we don't really have enough data to make that judgement, b) even if we did we'd have no ability to say if that data is stably projectable into an unknown future, and c) Since there is a critical point on grey, that means there are both diminishing returns going from 100% equity to 2X and then declining returns thereafter. That means that adding leverage into that diminishing and inflected return curve may be a little like riding a bike in first gear: a lot of heat and motion for not much forward progress and a lot more risk.  

• Also, in 2020, I am not personally betting with my own money, with coronavirus on the ridgeline above and a decade of a world class bull market behind us, that we'll easily see the "good side" of 2 or 3X leverage...at least for a while.  Academics can lever; I'm retired with a thin safety net and so I think I'll hold off for a bit.  

------------ [ notes ] --------------------------------

[1] the other major assumptions without getting in the weeds are: 1M of wealth, age 60, risk aversion coeff = 2, stylized EFF based on commonly used risk premia for equities and fixed income, 10000 iterations.  You might have to also buy into utility theory which is sometimes a big buy. 

[2] spend 300k of initial wealth to get an income stream forever; priced at immediateannuities.com.