For data, the mean-variance model for portfolio optimization uses asset returns to minimize portfolio risk (covariance matrix), which is asset returns volatility, and sometimes simultaneously maximizes portfolio expected return. Both objectives are based on asset returns data.

Is it possible to do asset allocation without any consideration to asset returns whatsoever? If so, what other data or techniques are there to use?

(please exclude price data and the well-known heuristic methods (equal-weight, market cap weight, inverse volatility, etc) from answer)

  • $\begingroup$ Hi: There are "factor models" but they are implicitly using returns ( because the factor models are based off of returns ) so you probably are including them in your list already. $\endgroup$ – mark leeds Jun 15 at 6:06

The "hedging theory of investment" (which I first heard about from R. C. Merton) says you should invest not for returns but to hedge your liabilities. LDI (Liability Driven Investment) is one name for it. So for example a pension fund should hedge pension liabilities. A university endowment should hedge the cost of producing education, which might entail investing in real estate in the local area, for example, or buying stocks involved in publishing. Wealthy people in the US often like to buy goods produced in Europe (cars, or holiday trips); the hedging theory says they should hold some EUR assets to hedge these future expenses, maybe buy shares in Mercedes Benz or BMW if they plan to buy such a car in the future.

However the hedging theory is not as well developed as other theories and not much practiced either as most people don't really know what to hedge and how. But it is an interesting idea.

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  • $\begingroup$ how does a zero-liability entity hedge? $\endgroup$ – develarist Jun 15 at 8:28
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    $\begingroup$ Not many entities are zero liability. Mutual funds can have money withdrawn at short notice, so can hedge funds. I consider that a form of liability which often gets exercised on drawdowns or underperformance vs benchmark. $\endgroup$ – dm63 Jun 15 at 11:00
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    $\begingroup$ Except for a miser who has millions but does not spend any money, most entities have some expenses, some use for their cash or some purpose for their existence and this is what should be hedged. (Sorry I did not see dm63's better and nearly simultaneous answer). $\endgroup$ – noob2 Jun 15 at 11:06
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    $\begingroup$ @noob2 Presumably even the miser has some motivation for accumulating money e.g. leaving behind a legacy to their children, in which case you can hedge their future liabilities to maximise what you leave behind. If the motivation is simply for the joy of seeing it accumulate, then you can still hedge the currency that you hold the money in. $\endgroup$ – JBentley Jun 15 at 14:21

For some clarification, what assets are you allocating and what is the objective? Does it include stocks, bonds, real estate, etc.? Do you care about returns, volatility, drawdown, etc?

Assuming the answers are yes and you are concerned with what is usually referred to as asset allocation, I would next ask why you want to completely ignore historical price data and presumably fundamental data which provide (relative) valuation metrics?

Drawing an analogy, would you feel comfortable gambling in a casino with absolutely no understanding of the odds and payoffs involved.

However, I think you really may be asking how to do asset allocation with no assumption about return distributions or estimation of the usual statistics. This is actually not a bad question.

It seems you are ruling out risk parity which at least avoids the problematic estimation of expected returns. It is basically mean-variance optimization assuming equal Sharpe ratios and potentially using leverage. Of course, expected volatility and correlation are inputs.

Without much else to go on, I would at a minimum consider the observed long-term risk premia of assets. I would forget about bonds even without considering the dismal prospects with the current US 10-year yield below 1%.

Then I would listen to Warren Buffet and invest 90% in S&P 500 and 10% in T-bills and rebalance annually or when the equity allocation fell to 80%. As a possibly better alternative I would invest almost all my capital in the S&P 500 and spend a small amount on an equity tail-risk hedge.

Maximizing compound annual growth rate and, hence, terminal wealth is what matters to most investors. Avoiding over-diversification, mitigating drawdown, and systematically rebalancing in a smart way have, historically, made big contributions to that objective.

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  • $\begingroup$ How would you define "overdiversification" ? $\endgroup$ – noob2 Jun 15 at 6:37
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    $\begingroup$ I'm waiting for the OP to clarify before I go too far afield. The question is poorly framed and I am giving some benefit of the doubt in answering in this way. I have unconventional views on this but in my opinion it is overallocation to bonds -- which most pension funds have done by following the conventional wisdom in estimating CMAs and running mean-variance optimization. The average funding ratio as of Feb 2020 (peak) was 72% among the major state plans -- after the longest economic expansion ever. The 60/40 paradigm has not worked well since before 2008. $\endgroup$ – RRL Jun 15 at 6:49
  • $\begingroup$ That was in the past -- and now the diversifying power of bonds looks even worse. $\endgroup$ – RRL Jun 15 at 6:51
  • $\begingroup$ Not knowing true return distributions, and given that return means and volatilities cannot be reliably estimated, are yes the reason why I am looking for something else instead of asset returns to construct portfolios. To start, lets keep the allocation to stocks only $\endgroup$ – develarist Jun 15 at 7:48

I can think of two.

First up is the naive Bayesian porfolio, ie run equal weights in the absence of any priors about any of returns, their volatility, correlations, or return-persistence. But then think ahead to the next step in the game. What do you do in 1,3,12 months time after the weights have evolved in line with realised performance?

You could let the portfolio run without rebalancing. Then it morphs into a momentum portfolio, implicitly suggesting that you do believe in return-persistence.

Else you rebalance back to naive/equal. But then you are effectively saying that your priors remain unchanged in the face of new evidence. Which might be correct. But to be correct thus, two conditions must hold. First, returns must be random (and thus independent; and thus realised correlations represent spurious accidents). But returns must also be completely heteroskedastic, ie their volatility is also completely random. Absent the latter, your priors about volatility should change given new evidence. If your vol priors change and you stick with equal weightings, then you're effectively saying that you believe that asset returns are proportional to their variance.

So one way or another, a "naive" portfolio cannot actually stay naive for very long. Whatever you do (or elect not to do), that forces you to start to make some hard assumptions about asset returns!

The other is Cover's "Universal Portfolio". You run every combination of every possible portfolio (in tiny size), and rebalance all of them to a fixed weight all of the time. So in the classic two-asset A and B framework, one portfolio would always be 73%A and 27%B; another always 42:58; and so on. Variants that allow cash in the mix, leverage and/or short-selling will have even more micro-portfolios to manage! Although in reality, it's only the aggregate of these that has to change in the real composite portfolio.

Maybe not in your own lifetime, but asymptotically, it can be proven (with a couple of inevitable caveats) that this set of portfolios will outperform both A and B. Thus it is argued that the UP represents an efficient response to the actual joint distribution of asset returns. These being unobservable, and thus beyond reliable estimation.

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  • $\begingroup$ a presentation by Cover says that the universal portfolio does use historical asset returns like Markowitz. and the description of the Bayesian approach also suggests returns are used since it writes realised performance and volatility, which is computed from returns $\endgroup$ – develarist Aug 16 at 17:39
  • $\begingroup$ hmmm... Cover's original paper on UPs has lots of historical backtests (usually on very niche high-vol low-correl pairs); but the algo itself doesn't depend on historical returns. You could set up a Cover portfolio on any two (or more) securities today with any history of past returns! As it happens, doing a write-up on a Cover-vs-Markowitz question recently asked here; so watch this space.... all the best. $\endgroup$ – demully Aug 16 at 19:56

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