Adding a Third Asset Class (Systematic Alt Risk) to the Utility of Simulated Terminal Wealth

 In several prior posts (here here here) I looked at the utility of terminal wealth in a basic simulation context. In those posts I created a simple world with a 2-asset-class model, 25 periods and several spend rates ranging from 3 to 5%.  The assumptions were generic [1]. The conclusion, such that it was, based on a CRRA utility function, for spending in the 3-4% range with moderate risk aversion, was to perhaps allocate conservatively to risk somewhere in the 40-70% range to based only on the results in that fake-sim-world. [1a]

Now, I wanted to ask: "given the same general assumptions, if I were to be allocated right now to a 50/50 mix of stocks and bonds and I also had access to a strategy (this is basic alternative asset allocation so it's not that dramatic, I just wanted to look at a special type of strategy) that had highly efficient characteristics -- like my own "bench strategy" given that I'm stupidly willing to assume that those characteristics would extend into the indefinite future -- how much should I allocate to the new strategy at the expense of the other two if I kept the proportions of the first two constant?" 

I know the efficiencies of low vol and high return strategies have advantages in a retirement-consumption setting when it is extended over long/mutiple periods.  Articles on sequence-risk and most muti-period geometric math will tell you that before you even get to thinking about simulation.  I even tried to do the Kelly math for "Edge/odds" but I got jumbled up on the math. I thought I came up with a negative expected value with respect to the baseline. That usually means "don't take the bet." That was counterintuitive so I retreated to some simple geometric mean approximations like G[r] ~ (E - V/2).  Using linear return and standard deviation assumptions of .076 / .097 for the 50/50 portfolio[3] and .075 / .04 for systematic-alt-risk I get .071 and .074 for the strategy returns, respectively.  That's not much difference and probably not too meaningful at that level but it gives a slight edge to the alt-risk strategy.  The question was, assuming an edge, how far might I take it.

To answer this question I decided a simulator might help. That meant, though, that I'd have to recode my simulator from a two-asset model to three. A pain but at least it is now a hybrid sim: stock and bonds have historical returns while the third asset class comes from a synthetic distribution using some R code.  All of this can be blended into one portfolio return for more sim flexibility than I ever had before. [2]

Note that for stocks and bonds I am using 88 years of some Stern School data. Bonds are total return and the bond allocation is blended internally to 70/30 bonds/bills.  Stocks returns are capped to match modern era max returns.  For the new alt-strategy to be added I am going to use an assertive (re future expectations I mean) 7.5% mean return with 4% standard deviation. There is a slight up-skew of .06 when annualized at 1/sqrt(12). This distribution just happens to match the last 3.3 years of my systematic alt risk strategy but I would not be so dumb as to assume that that means anything for the future. I just wanted to play "what if?" This is partly because I have been curious lately about how much I could or would scale my own strategy if it's recent performance were to last forever and I had no fear of scaling or the efforts related to long term self-management. The generic sim assumptions don't really match my personal situation but we'll roll with all of this anyway.

Using these odd expectations for "history will repeat" and "my alt strategy will look perfect forever" and "I'll really run this strategy until I'm 90,"  none of which will ever come to pass, I turned on the simulator for a 25 period excursion and ran 11 scenarios, moving from 0% alt-risk to 100% alt-risk while taking the other two assets down from 50-50 to 45-45 to 40-40 etc.  When I do this, this is what we see, keeping in mind that a 0% allocation to alt-risk is really the base-case from the prior post with 4% spending and a 50/50 allocation.

Here is one chart with fail rates and fail duration which might be considered standard sim output:

Here is another chart with two lines: 1) my retirement omega calc from logic described in a prior post using a threshold of zero wealth and allowing, against better judgement, simulator negative-wealth to be both acceptable and meaningful, and 2) a CRRA utility function of terminal sim-wealth using a coefficient for risk aversion of "4" and the same assumptions for negative wealth as in the other line but here making U(Wt) = -(1/(gamma-1)) for wealth values <= $1.00 and = W^(1-gamma)/(1-gamma) for wealth values > $1.00.

Conclusions?

Well, if one were to be able to fight through the various weaknesses and absurdities of the assumptions while ignoring common sense at the same time then I guess one would want to allocate as fast as one can to the alt-risk strategy…up to about 90% of the total portfolio.  Me? I'm not going to do that. Why? First of all, we are not using my own data. Then, I'd also want to check all the other combinations of the three assets but there are 66 total for a three asset portfolio (If I have my combinatorics right) so 55 left to go.  I won't do that; too much work.  Also I know that there is no way I can project into the future the alt-risk return distribution in any way in it's current form.[4]  Then there is the age thing.  There is not a chance I would self-manage a strategy like I have done so far all the way to age 90...I'm not even sure I can do it to 59.  And we have not even gotten to tax efficiency yet where I know intuitively (intuitive because I don't really know) that it is bad.  I'm sure there are other reasons.  On the other hand I guess a big conclusion for me personally, if not for the universe at large, is that I don't really have to be shy about scaling my own strategy a little bit further for a little while. Or at least I shouldn't scale it back for now.  I'm curious now what this would look like using my real data... 

notes ---------------------------------------------------------

[1] ($1M endowment, age 65, no spending variance or shocks, some simple tax effects, random inflation based on history, no spending deflections, no return suppression, no SS, no spending trends, etc.)

[1a] this is not advice, this is just reportage from fake-and-flawed-sim-world.

[2] using rsnorm().  This is handy because that third can represent any third asset or combo of assets I wish if I know the shape of the asset or "subportfolio" distribution up to the first three moments.  It can also be the only asset for other research. 

[3] I think in that data, without checking, the capped SnP mean returns were something like 11% and Stdev of .19.  

[4] This points out a problem that I think is shared with mean variance optimization. This and MV are pretty sensitive to the inputs in a way that can defy common sense and they can choke "out of sample" which in normal-speak here means future real life.