The 60/40 portfolio looks “efficient”—until we drop the no-leverage constraint.

Most long term asset allocators would agree that the 60/40 equity-bond portfolio is a useful, established reference point. On top of this, many would claim that the 60/40 portfolio is an “efficient portfolio.”

Efficient in what sense? First, it sits on the “efficient frontier.” That’s the curve you get when you plot all possible equity-bond mixes on a graph comparing return and volatility, and highlight those that achieve the highest return for each unit of volatility. Second, among the various portfolio mixes that sit on that efficient frontier, 60/40 has a volatility level that is acceptable to many investors.

It is often assumed that there is no equity-bond mix that can provide more return for the same level of volatility than the 60/40 mix. In finance terms, there is no additional alpha available.

Is this true? Is 60/40 the best we can get? We do not believe so. We believe there is a significant amount of asset allocation alpha that investors are leaving on the table because they assume they cannot find a better mix than 60/40.


We should qualify the statement above. We do think that 60/40 is the best mix if the status quo, default, implicit no-leverage constraint is binding and cannot be changed.

If leverage is allowed at the margin, however, we think 60/40 can be improved upon. The charts below show that there are model portfolios that have better expected returns than 60/40 despite exhibiting the same level of volatility as 60/40, once we include asset mixes with gross exposure greater than 100%. Clearly, adding leverage increases the volatility of the individual asset classes, but by increasing the proportion of bonds in the mix to which we then add leverage we can maintain stable volatility at the whole-portfolio level.

The Economic Value of Relaxing the Leverage Constraint in a Stock-Bond Portfolio

Changes in Risk and Notional Exposures vs. Gross Exposure

Additional Expected Return at 60/40 Risk vs. Gross Exposure

Source: Neuberger Berman.
Note: The volatility of all portfolios shown is equal to the volatility of the unlevered 60/40 portfolio. We have reverse-engineered the expected returns for stocks and bonds using the Black-Litterman asset allocation model. This model combines the market capitalization weights of different assets (here assumed to be equal to 60% for stocks and 40% for bonds) with the user’s own views concerning the covariance of those assets and the marginal excess return required for each marginal unit of risk (the risk aversion parameter) to arrive at implied excess equilibrium returns, or the expected excess returns that would clear the market. For our inputs, we set stock volatility at 12%, bond volatility at 6% and stock-bond correlation at -0.20, based on approximations of the historical performance of these assets. We set the risk aversion parameter at 6: we believe that this is a conservative assumption, which results in implied excess equilibrium returns of 1.1% for bonds and 2.3% for stocks. The Black-Litterman model was first described in a 1990 Goldman Sachs white paper, and further in detail in Fisher Black and Robert Litterman (1992) “Global Portfolio Optimization,” Financial Analysts Journal, September/October, pp.28-43.

The top chart shows the allocations that generated the highest possible expected return, given the constraint of the 60/40 portfolio’s level of volatility, at various levels of gross exposure.

So, at 100% gross exposure, or zero leverage, the best possible expected returns come from the 60/40 portfolio, as anticipated—the blue line starts at 60% and the gray line at 40%. However, move along to 110% gross exposure, or 10% leverage, and we find that the best expected returns were generated by a portfolio with 59% in stocks and 51% in bonds. Move all the way over to 40% leverage and 140% gross exposure and we find that the portfolio with the best expected returns is roughly a 47/93 portfolio—just 47% in stocks and 93% in bonds.

We started with a portfolio tilted towards stocks. As we add leverage, aiming for the highest possible expected return but keeping the volatility target stable, we move to a very different portfolio indeed, one dominated by bonds.

Now look at the last chart. This shows how much additional alpha we can generate by relaxing the leverage constraint, bit by bit. Here, by alpha we mean the difference in the expected return of a leveraged portfolio with 60/40 volatility, and the non-leveraged 60/40 portfolio itself.

Of course, if there is no budget for additional leverage then there is no additional alpha, and we get what 60/40 supplies. Move across to 110% gross exposure, or 10% leverage, and our 59/51 portfolio has added 10 basis points of excess return. Move to the 40%-leveraged, 47/93 portfolio, and for the same volatility as a 60/40 portfolio we get more than 30 basis points of extra return.

We can think of this 30 basis points per year as the cost of imposing leverage constraints on a 60/40 portfolio.


In our view, the economic benefit of relaxing the leverage constraint seems clear, then. But it is important to note that there may also be a risk-diversification benefit. Indeed, that diversification benefit is almost certainly what enables leveraged portfolios to generate higher returns without dragging up the level of volatility.

The middle chart set forth above shows this effect. Rather than showing the dollar exposure of each asset class, as the top chart does, this shows what percentage of the overall portfolio volatility each asset class contributes.

Over on the far left of this portion of the chart, we see that stocks contribute 95% of the overall volatility of a 60/40 portfolio, and bonds just 5%. The implication is that, despite being 40% of the portfolio, bonds barely play any role. That’s important: the benefits of diversification derive from the fact that stocks and bonds tend not to perform in the same way at the same time—but you don’t get that benefit if the presence of the bonds is not felt.

Now look at the far right of the same chart. The 47/93 portfolio, with 40% leverage, which generated an extra 30 basis points of return, gets half of its overall volatility from stocks and the other half from bonds. Neither asset class dominates the model portfolio’s losses or gains, on average, which means the investor gets the full benefit of any diversification that exists between them. In short, as the leverage constraint is gradually eased, the portfolios that offer the best returns for a 60/40 level of volatility look more and more like the equal risk-contribution portfolio.

Alpha on the Table?

Most of the excess return that leverage squeezes out from a given level of volatility appears to be a “free lunch”—because it is a benefit derived simply from using diversification more efficiently and thoroughly.

A small part of the excess return may be compensation for risk that is not reflected in volatility, however—risks associated with leverage itself.

But we find that few institutional investors have anything against relaxing the leverage constraint, per se. We see leverage everywhere in institutional portfolios: in private equity and debt strategies, hedge fund and securitized credit allocations, portable alpha solutions and portfolio overlays. Think about how much leverage a pension fund applies when it hedges its interest rate exposure with a swaps-based liability driven investment (LDI) program, for example. If an investor can live with leverage in these places, it makes sense to live with it in a core portfolio, where it can save 30 basis points per year.

There are numerous ways investors can justify a risk-balanced allocation. Here we offer just one: starting from a 60/40 portfolio and assuming it is efficient, we find potential for excess expected return simply by allowing leverage at the margin and moving towards a risk-balanced portfolio. In today’s world gaining this additional leverage is quite cheap. At the whole-portfolio level, or through cost-effective “risk parity” allocators, we believe that prudent leverage can be utilized to help increase odds of hitting investment goals.