returns, volatility of returns, correlation of returns

If all investment occurred via a single product, with a single pattern of returns, and no choice, and if this happened over a sufficiently long period that the short term swings of volatility become secondary when measured against the timeline of a typical investor's expected life, then the only one fact you can survive with is the (long term) expected return of that product.  I refer to it as a product and not an asset because I imagine it to be the offering of a company or set of companies which may have the freedom to manufacture this product.  

But reality isn't like that.  And as soon as a second product emerges as a choice (or even if you examine how the company manufactures this product), then correlation and (therefore volatility) enter into the frame.  

In the history of major assets, cash was invented first.  (Of course, loans existed before all that, and were a huge part of early human culture - the loans being loans of non-cash valuables for non-cash rewards e.g. slaves, food; these goods, like cash, may also have been understood to be fungible and tradeable).  Not surprisingly, the place which brought us writing also brought us the first bond.  The city state of Nippur in Sumeria offered one.  Italian city states pioneered state bonds as far back as the twelfth century, quite a while before the official story that Amsterdam and then the Bank of England invented them.  Certainly they set the modern pattern.   Shares were known certainly in Roman times, as was property, which had deep underpinnings as the earliest Greek and Roman religions were domestic hearth ancestor religions.  This simultaneously raised the cultural value of property but also introduced a whole bunch of restrictions, rules, taboos around selling property.  As the Roman republic evolved, and as class war between patricians and plebs loosened the grip of the old domestic gods, property as an asset class began to evolve too.

Inflation, of course, is not an asset.  But it is the force which makes cash experience volatility in real terms.  So these are the primary financial assets:  Cash (and loans), Property, Equities, Bonds.  And inflationary pressures contribute to the volatility of all four of these assets.  The primordial question is to work out how much each one will return to you, and how uncertain that return could be, and finally, to design of set of weightings which might exploit their time-evolving correlations.

By the time Markowitz came to develop the standard maths of modern portfolio theory, he addressed just two assets, equities and bonds.  Why?

crescet and titubit

The speed with which one's wealth grows, and its absolute level, are tied to one's life style (one's consumption of one's income).  A useful simplification is to assume one's income derives largely from one's wealth.  Economically, this is almost completely unreasonable, since it applies only to a vanishingly small fraction of humanity.  One then needs to spend to live from this wealth.  There are however minimal quality of life spends which may imply several modalities in the relation between the wealth growth process and the spend process.  I assume for simplicity that wealth is sufficiently large that the income spent can be made in a way which still leaves wealth growing.  Put another way, there is an assumption that the wealth process grows faster than both inflation and the daily consumption of your lifestyle.   A second critical threshold is for now also ignored - as with the case where the lifestyle spend significantly impacts the wealth process, transaction costs also can incur a third hurdle to overcome.  These assumptions clear away much of the thrust of the Darst book on asset allocation.

Next, an implicit starting assumption is that wealth at time $t$ may be considered as residing in one or more currency (short term fixed income) buckets.  One then imagines that the mean value theorem can be applied to the act of taking financial risk above this risk free (globalist) position.  That is to say, in equilibrium, the entirety of the job of strategy allocation and capital deployment can be waved away as solved for now, and modelled as a single 'bet' over an appropriate time frame, whose outcome can be a win or a loss.  One then determines the ideal bet size, per unit of time, based on the mathematics of Gambler's Ruin.  That is to say, that the average bet size can be no bigger than some fraction $\delta$ of wealth at point $t$ if volatility (and long term, ruin) is to be avoided.

Of course, in reality, the complete opposite applies with titubit.  Bet sizing is often ignored and instead one's lifestyle generates the major driving constraint to investment returns variance tolerance.  In short, our lack of funds makes us bet too big - this together with transaction costs, destroys our wealth.

Strategy allocation: a wealth process (crescet), a volatility constraint (titubit) and an expected life (fugit) and a cycle (circuit)

In chapter 2, Darst tries to carve up the space of approaches to 'asset allocation' through dimensions of style, then how strategic the approach is, and finally how quantitative the approach is.  As I mentioned in the last post, I think the 'style' dimension is bogus.  This in the limit can be replaced by owning the market of available strategies in toto), in their market weights, and then by implementing risk appetite purely through levering the in toto portfolio.  Next his seemingly clear quantitative versus qualitative  distinction breaks down too - for an ideal strategy allocation algorithm, the parameterisations are empirically calibrated and the discovery of new strategies are qualitative, whereas ideally the implementation, given a broad parameter set, ought to be quite algorithmic and computationally tractable.  Again ideally, the re-allocation decision might in theory be near-real time.

Finally, the dimension of 'strategic' v 'tactical' is the difference between Kant and Machiavelli. 

I think you want the algorithm to be as autonomous as possible, and to make a call on the strategic/tactical dimension based on the following inputs: where you are on your own expected wealth process and your expected lifespan.  Your spend process ought to follow from these two, and shouldn't count as an input.  Likewise this set of input parameters can be used in the determination of how much leverage to use (how long do we think it will take us to get there).  Your expected spend (and the lumpiness thereof) is really a (time-dependent) constraint on the volatility you desire on your wealth process.

The starting point (the long term equilibrium point) would be based on the maximum likelihood weightings, based on as much data as there is available for the strategies.  If one then subsequently had a model of strategy cycles, then that would be burned in too, to a degree proportional to one's confidence in the cycles model.  The mean value theorem guarantees that your long term equilibrium parameters are a good starting point, in the face of no certainty about cycles at all.

Crescet, titubit and fugit are facts about you.  Curcuit and the long term equilibrium weightings are parameters of the strategies.

leverage and the universe of strategies (the strategy market)

In just the same way that prior to Markowitz investment advisers performed this charade of matching the riskiness of a set of single names with the risk appetite of the customer, safe stocks to widows, racy high growth stocks to adventurous greedy investors with long time horizons, so to does Darst expect his potential customers to be willing to accept this cumbersome and sub-optimal selection process to satisfy.  It doesn't.  Just as with CAPM, one can satisfy the customer's risk profile simply by leveraging up (or down) on the market portfolio, likewise one ought to be able to sample strategies in the same way - having the full universe and weighting them with leverage according to their risk/return profile.  This is indeed what the population of managers of 'fund of funds' do.  They take investor capital, then, depending on how risk hungry they are, they avail themselves of more or less PB leverage on their collection of strategies, and reap a hedge fund average return.  Strategies, like companies, can be born, can run to exhaustion, can be merged, delist, go bust.  And like stocks, the space of strategies can be partitioned into its own sector or industry - just as GICS partitions the universe of stocks.  And occasionally new 'strategy sectors' can be born (just as, eg real estate can become a new GICS sector).  

How would this index of all strategies arrive at weightings?  Probably by capital invested in the strategy.  If this drove your allocation sizing, then you'd always get 'the market'. And just like with ETF providers who model the whole market by targeting a subset only of representative stocks, accepting a degree of tracking error, so too in theory with strategies.  You could select representative institutions or canonical implementations of the main strategies, and this would serve you, to a sufficient degree of error, as a proxy for the market of strategies.  These days, factor models allow you to get a handle on the factor exposure, so I think it ought to be possible to apply the same technology, given the right data, to the issue of constructing a portfolio of names which, in toto, sufficiently closely tracks the full investible market. 

By sheer AUM allocated (the equivalent of market capital), I would suspect that long equities and long credit would simply dominate the weightings.  Also each strategy has its own internal (eg asset based) leverage, so the concept of a singular leverage value which can be tweaked up and down needs to be revised.  Some strategies are inherently more capital intensive, some less, and the meaning of 'increase leverage to get more risk' needs to be transformed into a series of leverage adjustments for each of the strategies.  A further point is that one can also have in the equity world the concept of an equal weighted index, which typically gives you more risk and more return.

In practical terms, find the set of n ETFs which best represent the universe of all strategies.  Find the weightings by invested market capital.  Buy the basket.  Lever up or down, depending on your risk profile.  Re-balance on a very slow timescale.  Unless of course you have a cycle based model for investment weightings.  Perhaps cyclicity would be one of the 'factors' in a strategy factor analysis.  What else might take the place of, say, fundamental factors?  

I wouldn't put the strategy equivalent of market cap in there, since this is expressed in the weightings.  Perhaps sensitivity to volatility, to equity, to credit, and to interest rates.  Perhaps asset class exposure, country exposure, sector exposure and inherent leverage of strategy (gross exposure over capital allocated) and liquidity.  These would be the areas I'd be looking to get strategy factor models out of.  They also provide more or less well known hooks into modelling cycles (credit conditions predict economic contractions,  the debt/equity relationship of corporates could see itself recapitulated in the relative allocation weights for debt and equity.

The anti-FOMO movement

There are n strategies, each with returns $r_i$.  Ranked top to bottom, so $r_1$ is the strategy with the highest return (long term).  Why not just put your wealth all in strategy 1?  Putting only a fraction of it in 1 and fractions in 2,3,...n leaves one with a feeling of missing out.  I suspect if you live to be 640, then this would be the effective result of the ideal allocation strategy.  Indeed if you have a 60 year perspective, this might also be the case.  But history doesn't always repeat itself.  So you can never be sure the future will continue sufficiently to be like the past.  Hence you'll want to diversify.  For example if you are Russian, living at the turn of the twentieth century and happened to note in 1901 that the St Petersburg stock exchange was your $r_1$, and decided to put all your wealth in there, then you'd be in for a shock when the Russian revolution came and wiped your wealth to zero.  If you were an ultra risk-adverse German post WW1 and thought you'd keep your money in nice liquid deutsche-marks, then the hyper-inflation would have likewise wiped you to effectively zero.

The degree to which you trust the institutions which underpin the strategy returns you feel you have access to is the degree to which larger and larger fractions of your wealth will go into strategies 1, 2 etc. rather than into tail end strategies.  Conversely, the degree to which you are uncertain of the future of those enabling institutions (and this, to be sure, is an uncertain act of political tea-leaf-reading) determines how distributed your wealth will be.  Your degree of confidence in strategies 1, 2 also grow to the extent that your future wealth-investment time horizon is long.

Besides the above unknown unknown, is the idea of correlation.  If all strategies 1,...,n are fully correlated with each other, then each of n is as good, in this one respect, as all the others.  But the degree to which any two (or more) strategies are uncorrelated or lowly correlated, opens the possibility that there was a combination of these strategies which was ideal, in some wider, as yet to be defined sense.  

So a world with a lot of serious unknown unknowns presents a difficult environment for the ideal strategy allocation algorithm, as does a world with cross strategy high correlation.  Thankfully so far the world we live in is somewhat known, somewhat predictable .  And this is the space that the theory of the ideal strategy allocation algorithm can work within, where the past can tell us something about the future, and where strategies have less than perfect correlation.

Floor entropy and ceiling noose

The whole space of strategy allocation is shaped by two massively important risks - inflation risk and gambler's ruin.  The first bites your wealth from below, when your allocation strategy overall is too focused on principal protection, where the return can be below the inflation rate, and the second bites your wealth from above, when your allocation strategy overall is focused on principal growth and your 'bet on green' at the roulette table of life stops you out and you go home early.  Each fate is ugly, you either dying in dog food penury or dying young in a bloody accident.  It ought to be the goal of an ideal strategy allocation approach to avoid both outcomes and instead enjoy healthy lunches - free and paid for - over as long a stretch of your life as you can.

This blog post is in general a post for everyone, but of course poor people first need to arrive somehow at a pool of investable capital (separate from their day to day living costs and the capital they have for investing in their business).  I think it is a fair statement, at this early stage, to suggest that younger folks with capital can afford to be closer to gambler's ruin than older folks, since they can trade their labour, brain, body, time for paying their today costs, whereas post-retirement oldies have less flexibility and hence have a big income draw-down demand.

How close a young investor gets, of course, to gambler's ruin, is a cultural question as well as an economic one.  Their appetite for risk ought to be higher, insofar as making the tilt for wealth growth over wealth protection is paid for by their greater expected lifespan. I've heard it said that private equity / startup investors like to hear from a founder that they failed once or twice in the past.  Secondly, bankruptcy law is all about buying back in gamblers who have reached ruin with their firm.  Our culture of long term GDP growth has some of this risk taking burnt in.  There's a sense that the fable of Icarus is seen not only as a warning but also as admirable somehow.  Back through human history, we have moved forwards in time by combining our prudence with our spirit of adventure.

And vigour, life, vitality, novelty, creativity, growth, these are all inter-connected concepts culturally.  As opposed to self-sustainability, entropy, predictability, familiarity, maintenance.  But the ideal strategy allocation algorithm must partake in all of those concepts.   Unfortunately, all too often, both of these existentially definitive risks are under-emphasised on behalf of investors.  But wealth generation is in the limit a lifetime activity (longer, for companies, or for aristocrats or for anyone who plans to leave an inheritance for their loved ones).  It is a common fate for us collectively to understand the importance of long term planning only as we get to be old.