40% bonds & 60% equity

There seem to be lots of reasonably-smart people out there that advocate a 40% bond / 60% equity asset allocation for every investor, regardless of age.

And if you run any kind of portfolio backtesting that includes the last 30 years, it seems like an unbeatable rule to follow.

But I wonder how much of this strategy is driven by a backwards-looking view that doesn’t consider the tailwind of declining interest rates that have boosted bond performance since 1982…

To be honest, I’m not even sure where the whole 60-40 allocation came from, but it doesn’t make much sense to me. Given an expected amount of risk you’re comfortable with going forward, you should choose the portfolio with the highest expected return. People less comfortable with risk should adopt more conservative portfolios. When market volatility increases, you should reduce your allocation to equities.

Further, the expected return on government bonds over the long-run will be hurt by interest rates having little room to fall going forward. The strong gains since the early 1980s cannot be repeated unless inflation rises then falls.

Another critique is the whole risk parity argument that a 60/40 allocation actually has like 90%+ of the risk coming from equities. However, a risk parity portfolio without consideration of the expected returns would over-allocate to the bond portfolios.

I remember reading the the L3 material a rule of thumb that said people should invest 100 - age in equities. For example, someone who is 30 should invest 70% in equities. That’s a simple rule I tell people who are not very literate in the markets and who are not risk averse.

In my case, in my retirement account, I invest 90% in equities for 3 reasons:

  1. Like mentioned above, bonds have been on a bull run the last 3 decades (and even outperformed equities from 1979-2009, the first 30 period of outperformance in history). I think the bond party will come to an end soon. Yields might not increase because we live in a deleveraging world, but I don’t think they will decrease that much at these levels either.

  2. I have at least 35 years until retirement

  3. A more shorter term reason, equities had the worst decade in 2000-09 since the 30s so I expect a strong decade.

I believe the 60/40 recommendation precedes the 30 year bond bull run. I seem to remember it being recommended by Graham and Dodd in “The Intelligent Investor.”

Its just a rule of thumb that wwill have a hard time being replaced until those advisors who grew up with it die off and more customers start hearing other allocations recommended by more recently educated peopel and start to get used to them. When a client starts saying “everyone tells me 60/40 is the way to go,” you have to decide whether they are the sort of client that can understand why you might not recommend that or perhaps you simply decide to give them the best options that exist within their pre-existing mental framework. I personally try to educate, but it doesn’t always work.

I did one research project that suggested that an allocation of something like 85% bonds and 15% stocks gives you the highest two asset sharpe ratio from 1975-2010 (dates chosen for data availability). That’s surprisingly little in equities, although, admittedly, there isn’t as much absolute growth if you can’t lever that portfolio.

If you can’t lever and need more expected yield (even if you have to take more risk to get it), then you might start to up your equity exposure and 60% might be defensible. At 60-40% I seem to recall that something like 90% of the portfolio’s volatility is attributable to equities, whereas only 60% of the return is.

I have also seen the 100-(your age) rule of thumb that Bogle recommends, and this makes more sense to me, it’s just a variation on the rule of thumb. But some institutions have very long lifetimes (pension plans, endowments, etc.), and so they might well have assumed that they live forever as if they are a 40 year old earner. Presumably, institutions have become more sophisticated in their asset allocation, but in the old days, 60/40 may have been a benchmark standard for them too.

In my work, I’m often asked to use 60/40 as a comparative benchmark to use with other products, and I suspect that that is mostly what it is these days: either a rule of thumb for lazy managers or a benchmark to demonstrate that not being lazy pays off.

+1. IIRC Graham advocated an allocation between 25% and 75% to equities and the rest to bonds, irrespective of the investor’s age, and only considering their risk tolerance (ability and willingness.)

That’s pretty much my point; if you use data from the 35-year period beginning in 1975, you’re including the greatest bond bull market that the world has ever experienced – a three-decade long period that’s unlikely to ever reoccur.

If, on the other hand, you use data from the 35-year period ENDING in 1975, I wouldn’t be surprised if the highest sharpe ratio portfolio had a NEGATIVE bond holding.

The thing that surprises me is that so many smart guys have given asset allocation a lot of thought, and have come up with a 40% allocation to bonds as a generic recommendation:


Admittedly, the majority of these guys specify SHORT-TERM bonds, which I suppose are relatively insensitive to interest rate changes.

This discussion is so fascinating. *runs away*

But Sharpe Ratio only works if you can borrow money at the “risk free” rate, or something close to that. This might not be a problem for institutional investors, but personal investors might not be able to do this. For personal investors, maybe it makes more sense to apply a “no leverage” constraint, and then try to maximize expected utility based on some sort of utility curve.

Not sure who the “smart guys” are that still recommend a balanced (60/40) portfolio. There are still advisors that will recommend a single fund solution to investors with

But the “smart guys” don’t deal with those investors. Nowadays you have to account for a couple things. First off, most big advisory practices are fee-based. Since there are no transaction costs, the advisor can be much more tactical. Staying 60/40 isn’t a great way to justify their wrap fee. Secondly, you have to include an allocation to “alternatives,” generally around 20%.

Not saying this is the more successful route. Just saying the 60/40 balanced portfolio is long dead in the advisory world.

I’ve spent a lot of time looking at the optimization problems and after a lot of thinking my opinion is that it is better to target an actual amount of risk than deal with the utility functions. I think this for a few reasons:

  1. More intuitive - Different optimizations may have different time horizons. When you target a certain amount of risk, you could annualize the standard deviation or whatever to get some number that is comparable across all time horizons. For a standard mean-variance optimization, the lambda risk aversion coefficient would have to change as well when you’re dealing with arithmetic returns since they don’t scale perfectly. However, it is much less intuitive in the way it changes.

  2. Time varying moments -

a) When the mean and covariance matrix are varying through time, then the utility-based approach has to consider the relative importance between both the expected return and expected risk. This allows two things to change. For instance, if the covariance matrix is unchanged, but the expected return on equities changes, than a utility optimization will see a substantial change in the portfolio allocation. If the risk you’re targeting is standard deviation, then your allocation wouldn’t change as much as the above (it wouldn’t change at all for two assets, but for three plus it would).

b) As a result, utility optimization weights can move around more than when you target a constant amount of risk. This can lead to more transaction costs.

I don’t think there is a way to perfectly determine utility functions anyway. So, might as well use rules of thumb, target specific amounts of risk, or other sorts of partly arbitrary methods.

I also think that utility is unobservable and so utility functions become effectively arbitrary. All we really can say about them is that they monotonically increase and they have diminishing marginal returns. So I would rather use maximum sharpe ratio given constraints, which may include a minimum expected return or a maximum risk.

Not to hijack the thread but I wonder if that is true. If you believe in loss aversion, then utility functions actually have a hysteresis - they are different going from left to right on the return/risk curve than they are going right to left.

Consider a portfolio of a broad stock index fund and a broad bond index fund and assume that according to CAPM/CML/SML framework, stocks have a higher return/risk. If the stocks have fallen recently and have an actual negative return; the investor will stay in them to recoup the losses rather than shift left to the lower return/risk bond fund. So at the start, while shifting right to more allocation for stocks, he was willing to tolerate rational risk/return; but he refuses to budge left and wants more return even for a slightly less risk (because to accept that smaller risk, he has to lock in his losses in stocks.)

I’m not sure I entirely follow your argument. Let’s suppose you have loss aversion, one way to represent this is on the expected CVaR of the portfolio. If you experience a loss in equities and the expected distribution in the future doesn’t change, then the optimal portfolio shouldn’t change either (excluding the impact of transaction costs). You should re-allocate to maintain the same weights. This implies that you shouldn’t just stay in, you should increase your allocation, all else being equal.

However, if he experiences a loss and suddenly realizes that his estimates of risk were too lenient and increases his forecast of volatility or tail risk, then he would move to a more conservative portfolio.

One case where you can see a sort of hysterisis effect is in a CPPI-like strategy. In the context of portfolio optimization, a CPPI-strategy would be like adjusting your risk aversion or target standard deviation in a way to reduce risk after you’ve had losses in the past. It is possile to reduce the allocation to risky assets enough so that you’ll never re-coup your losses.

Well, that’s an argument in more detail than I cared to post, but I can see where you are going with this: the utility curve looks different depending on what recent performance or drawdown has been. It is effectively time varying.

While I agree in principle that this is a possibility, it still doesn’t get around the problem that we have no way to specify a utility curve with the level of confidence that would make it clearly superior to the other optimization methods of maximum sharpe ratio given constraints.

One exception: When it comes to volatility, I think that utilities that value volatility in terms of having to at the very least make up for the effects of volatility drag might be worthwhile. IIRC, this is the formulation of utilities that is most common, with perhaps a risk-aversion coefficient to penalize volatility over and above it’s drag on long term returns.

Two points, 1) if you’re concerned about the confidence in your estimation, you can perform robust or Bayesian optimization in a utility or some other format. 2) When you include a risk-free asset, the efficient frontier in any sort of mean-variance optimization (utility based or otherwise) is a line with a slope equal to the Sharpe ratio. So we’re all sort of talking about the same thing to that extent (ie. if you maximize the Sharpe ratio subject to a return constraint, you’re just doing a more complicated optimization that should get you to the same place on the efficient frontier as if you minimized variance with a return constraint). The only difference is where on the curve you want to choose.

Well, jmh you were also talking about a non-leverage constraint, so you can work your way down the slope if the optimal portfolio has too much risk, but you may not be able to work your way up the slope if you can’t have margin accounts. But I think we see things the same way here. I was just saying that maybe people move up the curve to 60% equities because they just can’t get the returns that they want without either 1) leverage or 2) going up that high in equities. If they can’t lever, then they just increase equities (I haven’t done the research on pre-1975 as Wendy suggests, but I’d be interested in the results if we can find the bond return information).

In terms of utilities, we just don’t know how to measure utility, and so whether the estimation is robust or whatnot effectively doesn’t matter. We can’t even tell if one person’s utility curve is functionally similar to another person’s with any method other than to just go ahead and assume it. All of that mathematics is like saying this slice of bread is better because it was buttered with a diamond coated knife instead of a plastic one. The precision of the instrument isn’t really relevant because you effectively can’t measure utility in the first place.

I’m not ridiculing you, because your quant chops are obviously good, but sometimes I think the mathematics fools us into thinking we know more about this than we really do. My main point is that it’s probably best not to try to guess people’s utility curves and stick with something more observable like observed returns and volatility.

In that, we both agree.

For a passive investment portfolio, I prefer the 25/25/25/25 allocation of Equities, Gold, LT bonds, and Cash (or equivalents), rebalanced yearly. The compounded growth of this portfolio from 1970 to now is a little lower than the S&P500 but it’s fairly rare to see a losing year (1994 was the last time it was negative on the calendar year; it gained about 1% in 2008.)

This is how I run my own money… I don’t even leave much in a savings account anymore and just stash my wealth in this asset allocation.

Of course, past performance doesn’t guarantee future performance… but the fundamentally neutral and negative correlations between the 4 asset classes drastically smoothes out the volatility. Of course, if the financal system were to permanently collapse, this would perform poorly, but in that situation, you have bigger things to worry about.

The black line is the resulting portfolio’s performance since about 1969: