Where’s My Lunch?

Fuzzy Definitions

It's easy to see this can't be true in general. Just adding arbitrary extra investments — say, sports bets - with zero or negative expected returns can't possibly help your portfolio. So, perhaps we should refine the definition, replacing "the most discrete investments" with "the most separate sources of return." But as we'll see, this doesn't fare much better.

To see why, consider whether the equal-weight S&P 500 portfolio is better than the market-cap-weighted version. Each stock is a source of return, and the equal-weight portfolio is more evenly spread across them, so by our updated definition, it is more diversified. But is it better?

Choosing to hold each stock in equal proportion rather than at its market-cap weight is itself an active bet — a collection of overweights in smaller companies and underweights in larger ones. This is stock picking, and by simple math, every overweight must be exactly offset by someone else's underweight. So you should only expect the equal-weight portfolio to be better than the market-cap portfolio if you expect the people on the other side of your bets to be unwittingly providing you with a good trade.

That's possible, but one thing we know about competitive markets is that this is not a safe assumption.

Our updated definition of diversification hasn't failed quite as completely as the first cut, but we can see that it doesn't reliably lead to better portfolios either. We're left with the conclusion that simply maximizing diversification just doesn't seem to be the right objective.

Balancing Risk and Return

The core problem is that an overly narrow focus on diversification can lead us to lose track of expected return. A natural way of incorporating the return qualities of a portfolio, along with the diversification qualities, is to maximize the ratio of portfolio return to risk. Commonly called the Sharpe ratio, this is a move in the right direction, but it doesn't go the distance.

For one thing, it can be misleading in cases where returns aren't normally distributed. More fundamentally, Sharpe ratio measures the quality of a return stream, but says nothing about how much of it you should own. As a result, you can't fully determine your portfolio just by maximizing Sharpe ratio.

Rather than trying to maximize incomplete metrics like diversification or Sharpe ratio, the full-credit solution is to maximize the expected risk-adjusted return of your overall portfolio. We discuss the philosophy and mechanics behind risk-adjusted return in The Missing Billionaires and elsewhere. Using it requires a bit more work, and some introspection about your personal risk preferences, but it's a doable task well worth undertaking.

Beyond Public Markets

Perhaps the biggest diversification question on investors' minds today is whether they should go beyond public market stocks and bonds — easily accessed through low-cost, tax-efficient index funds — to also invest in alternative investments, from private equity to hedge funds and everything in between. Investing in alternatives will increase the diversification of your portfolio, but as we've seen, more diversification doesn't necessarily mean a more attractive portfolio.

It will come down to whether these investments increase the expected risk-adjusted return of your portfolio, which in turn depends on your assessment of their after-fee, after-tax returns, their risk, and their relationship to the public-market portfolio you already hold. Even if inclusion of some of these assets does increase your risk-adjusted return, if you're starting with a well-diversified portfolio to begin with, the incremental improvement is likely to be very modest. For many investors, the practical conclusion will still be "just buy the indexes" — and that's a perfectly good answer.

Our argument here isn't against diversification. It's against treating diversification as the destination rather than one ingredient in a broader optimization. Diversification is a valuable quality in a portfolio — and whenever you can reduce risk without reducing expected return you should do it — but it isn't the only quality that makes a portfolio good. The real objective is maximizing expected risk-adjusted return — and pursuing that goal is what turns a free lunch into a hearty meal.

Endnote

¹Sharpe’s “arithmetic of active management” makes the more general point that the positions of all stock-pickers taken together equals the market portfolio and so they must earn the market return before fees and frictions. The Risk Matters Hypothesis extends this logic to the dimension of risk: showing that the average risk across all active portfolios must exceed the risk of the market portfolio. So even before fees, the average stock-picker faces a worse return-to-risk tradeoff than an index investor. See Sharpe, “The Arithmetic of Active Management” (1991) and Haghani, Ragulin, Rosenbluth and White, “The Risk Matters Hypothesis” (2024).

Victor Haghani is founder & CIO of Elm Wealth, a Philadelphia-based asset manager. James White is Elm Wealth’s CEO.

This is not an offer or solicitation of investment services or financial advice. It reflects the views of the authors, subject to change, and not necessarily the views of Elm Wealth, where the authors work. Although this article discusses taxation, the authors are not tax experts and nothing herein should be construed as tax advice. Past returns are not indicative of future performance.

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