### Asset Allocation is Not for the Faint of Heart (Long Live Diversification)

I’m starting to feel like a rancorous curmudgeon, but I am frustrated by some of the misguided commentary on asset allocation and how diversification is a myth. We have posted a lot of research on fairly complex asset allocation topics, but I think many readers would be surprised to learn that I am actually highly skeptical about historical market statistics. I don’t think that we can draw any meaningfully precise conclusions about long-term returns or asset relationships from examining historical data. I think the maximum extent to which we can quantify risk premia is with a 0 or a 1. Either the premium exists based on a sufficient set of broad criteria, or it doesn’t. Trying to quantify the absolute or relative value of premia is a fool’s errand, which makes strategic asset allocation based on even the most robust mean-variance optimization equally foolish.

The question then becomes: “**How would you invest if you could not draw strong conclusions from historical data**?”

There are a couple of no-brainer answers to this question, which we have described at great length in several articles and presentations. Inexperienced investors might hold all liquid assets in equal weight. This is exactly what we observe with DC pensions plans – most planholders, when given the option of which funds they would like to invest in, and without any other guidance, choose to hold all funds in equal weight. Of course, most plans offer vastly more equity funds than bond funds, so investors end up being extremely equity-centric.

Slightly more thoughtful investors may look to what everyone else does to inform their investment decisions. This often leads to herding toward popular asset allocation methods like the so-called ‘Endowment Model’. However, when taken to its logical conclusion, this method would lead to the global market-capitalization weighted portfolio (GMP). Sharpe offered proof that, under the assumption of perfect macro-consistency and efficiency, this portfolio is mean-variance optimal. So it’s actually a perfectly reasonable choice for many investors. Of course, you can’t perfectly mimic the GMP, but you can get close enough with currently available ETFs. Again, we presented this option in great detail in our first webinar this summer:

Webinar 1: Exposing the Active Risks of Passive Portfolios

Critically, **the equal weight method and the GMP are the only parameter-free, utility-maximizing methods of asset allocation. Every other utility maximizing approach requires parameterization*.** That said, in practice most investors have preferences which deviate from the implied risk/reward balance of the GMP, so investors must either estimate covariances to back out implied *relative* returns from this portfolio using the Black-Litterman method, and then perform a mean-variance optimization to hit investor preferences or; they must estimate the expected return and risk of the underlying portfolio, and scale exposure to the portfolio up or down the Capital Market Line. So in fact these solutions are only parameter-free if an investor expresses preferences that are directly aligned with the average investor.

It turns out that there are other ways for investors to express a belief in market efficiency, though these methods also require certain parameter estimates. For example, one might assert that markets are efficient if participants have priced assets to produce the same return for equal risk. This would preserve the Fundamental Theorem of Asset Pricing, where arbitrage capital would be expected to flow toward assets that are expected to produce higher return with less risk, and away from assets with lower expected return and/or higher risk. Risk parity approaches reflect this definition of efficiency, as they assume major diversified asset categories should produce similar long-term returns for similar risk, i.e. similar Sharpe ratios.

Webinar 2: The Art and Science of Portfolio Optimization

Risk parity methods require some estimate of risk, and perhaps correlation, but no estimates of relative or absolute expected returns. This is because the strategies assume excess returns are proportional to risk. Some managers (like Bridgewater) estimate risks according to the fundamental nature of each asset, i.e. duration, fixed maturity, etc., and how each asset should theoretically respond to certain economic regimes. While they may examine historical correlations to help inform their model, their model is not based on historical estimates. Other risk parity implementations use near-term dynamic estimates of risk and correlation, or some combination of short and long-term estimates, to engineer diversified portfolios. In each case however, the strategies reflect the assumption that, under reasonable definitions of efficient markets, diversified asset classes should have similar Sharpe ratios.

Webinar 3: Risk Parity – The Antidote for Unbalanced Portfolios

Once you move on from risk parity type approaches, there is no escaping active bets on returns. Moreoever, optimizations become highly sensitive to errors in estimated returns. There are ways to minimize this sensitivity which are beyond the scope of this article, but the fact is things get messy fast. For those (like me) who have little faith in long-term average returns, or econometric estimates of expected risk premia, strategic portfolios engineered in this way hold little appeal. However, I do believe certain factors can provide useful estimates of *relative* asset class returns at short horizons (momentum) or perhaps intermediate horizons (value).

Webinar 4: Adaptive Asset Allocation: A Dynamic Strategy for Good Times and Bad

NOW…what does all this mean for distribution strategies. First off, I would assert that you can’t have an intelligent discussion about distribution strategies without a very strong understanding of all the foundational material I described above. After all, the single most important parameter in most planning exercises is the return estimate, followed by the standard error of the estimate. Traditional mean-variance optimization requires you to estimate means for all of the assets in the portfolio, and their correlated random standard errors. In contrast, risk parity strategies only require that you estimate the diversification ratio, and the slope of the capital market line. While there is considerable scope for error in the latter formula, it is much more parsimonious than the former. Furthermore, if you use estimated means for optimization, and the same means for planning, you run the risk of compounding errors in asset class mean estimates by first using those mean estimates to find the optimal portfolio, and then using the same means to estimate returns for planning purposes. Yuck.

You see, asset allocation is pretty complicated, and not for the faint of heart. For my money, investors have the greatest chance of hitting long-term financial goals by investing in the most diversified portfolio possible (choose your definition), and saving as much as they reasonably can. Any precision beyond this level is a triumph of hope over uncertainty. Deal with it.

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Footnote

*****There is one exception (that I know of), which is not strictly utility maximizing, but is an asset allocation approach that does not require parameterization: the safety first method. This approach advocates an annual allocation to long-term TIPs in the amount of the minimum real income the investor wishes to receive 30 years in the future. Any excess is placed into a diversified cap-weighted equity index. As a result, the investor will receive a guaranteed real income each year as the TIPs mature to meet minimum income requirements, and would presumably expect to subsidize their minimum guaranteed income through income and withdrawals from their equity portfolio.

There are several challenges with this approach, but the most obvious one is that it is not utility maximizing. For savers whose minimum required income is very close to their current income, they will be required to invest an absurdly large proportion of current income in one of the world’s lowest returning asset classes. For savers whose minimum required income is small relative to current income, they will be investing a majority of their assets in stocks, with almost no diversification.

In both cases, investors would be ex ante better off in a diversified portfolio of risky assets than in the safety first portfolio in terms of utility maximization. The only exceptions are if the low income investor is almost infinitely risk averse, or if the high income investor is infinitely risk tolerant. Assuming more typical risk aversion preferences, clients would benefit from substantial exposure to a diversified basket of risk premia.

Find more research from ReSolve at investresolve.com.