Update: If you’re coming over to this article from Mr. French’s article over at RetirementResearcher, please note the last few paragraphs below where I shoot down his shockingly sloppy analysis.
Bonds diversify your equity portfolio risk. Everybody knows that, right? Well, how much diversification potential is there, really? Much less than we thought! (For full disclosure, though, bonds still serve a purpose, but it has nothing to do with diversification!)
Pop Quiz: Over the last 10 years, a portfolio of 80% stocks (U.S. Broad Equity Market) and 20% bonds (U.S. Aggregate Bond Market) had what correlation with the stock market?
A: 0.998
B: 0.857
C: 0.800
D: 0.683
The correct answer is A: the correlation was +0.998, so an 80/20 Stock/Bond portfolio would have been extremely highly correlated with the stock market. We might as well round it up all the way to 1.0 because from a statistical, financial and economic perspective that’s pretty much a perfect correlation. This correlation coefficient is for a broad U.S. stock market ETF (use Vanguard’s US Total Market VTI) vs. a portfolio made up of 80% Vanguard’s VTI and 20% Barclays Aggregate bond index (we used the iShares AGG total returns). Monthly returns are from 07/2006 to 07/2016.
Don’t believe the correlation is that high? Check out the scatter plot of monthly returns with the VTI ETF on the x-axis and the 80/20 portfolio on the y-axis:
Another unpleasant fact about bond diversification: during the worst five months of equity returns (all of them fell between June 2008 and February 2009) the bond index lost value as well. That’s due to the corporate bond exposure in the index and the spike in credit spreads during the Global Financial Crisis.
Ok, before we get too pessimistic about bonds, of course, the 80/20 portfolio did have a lower equity beta (=slope), pretty much exactly 0.8 and also a lower volatility (also about 0.8*the equity only volatility). But that is due to the lower equity weight and has very little to do with the 20% bond share. In fact, just holding 80% equities and 20% cash in a money market account would have generated a very similar result in terms of correlations and risk.
How far do we have to move out of stocks to reduce the correlation significantly? Let’s look at the return stats for portfolios with different equity shares. Specifically, we gradually reduce the equity weights in 10% increments, shifting them to either bonds (iShares AGG bond ETF) or simply into cash (earning the prevailing 3-month T-bill rate, Yahoo ticker ^IRX):
Even at 30% stocks and 70% bonds we still get a correlation of almost 0.9. To push the correlation below 0.5 we would need a 90% bond, 10% stock allocation. How crazy is that?
Also, the risk reduction in the portfolios with lower equity weights does not come from bonds. Plot the portfolio risk as a function of the Bond/Cash weight and we see that you could have achieved even more risk reduction by simply moving out of stocks and into an (essentially) free risk-free money market account, see figure below:
What causes the high correlations of the stock-bond portfolios with stocks?
If the broad bond index and equities have roughly a zero correlation (or about +0.05 as in our case), why is the correlation between the 80/20 portfolio and a 100% equity portfolio so high? Shouldn’t it be closer to 0.8? Skip this section if you don’t like math, but for math and finance geeks here’s the explanation, see figure below:
- Bonds had a tiny annualized standard deviation of only under 4%, while equities had a close to 16% annual standard deviation.
- Portfolio risk is not averaged via the standard deviations of the components, but rather you sum the weighted variances (=risk-squared) plus covariance (times two) to generate the portfolio variance. For the example here we ignore the covariance because the correlation between the assets is so low (only 0.05).
- The share of variance that’s coming from the equity portion (0.8*16%)^2, expressed as the blue square below is many times larger than the orange square for the variance contribution from bonds.That’s because 0.8*16% is already much greater than 0.2*4% and this difference is magnified by taking squares. The size of the green box is the total portfolio variance and because of the vast size difference between the blue and orange squares, the majority (>99%) of the portfolio variance is still coming from equities, despite their 80% weight.That high percentage translates into a high correlation. Who would have thought that Pythagoras ever becomes handy in personal finance!?
Does that mean that bonds are useless?
Of course, this is not to say that bonds were useless. Quite the contrary, as is evident from the table above, bonds had much higher average returns than cash. To visualize this better, let’s plot the average annualized return over the 10 years as a function of the Bond/Cash weight:
Because bonds had such an impressive run over the last 10 years, the opportunity cost of lowering equity weights was much lower: The aggregate US bond market (government plus investment-grade corporate bonds) beat the cash return by almost four full percentage points (4.91% in AGG ETF vs. 1.12% cash).
Side note: if you remember our post from a few weeks ago, you never raise cash to reduce risk, but rather walk along the efficient frontier, most likely by shifting out of equities and into bonds. So our result here is exactly consistent with our previous results: bonds offer a better risk vs. return tradeoff when trying to reduce portfolio risk.
Some additional comments:
- U.S. Government bonds did have a slightly negative correlation with equities, around -0.2 to -0.4. So, the diversification would look a bit better when using only safe government bonds while ignoring corporate bonds. But you also get a much lower yield, currently only 1.5% for the 10-Year Treasury bond. There’s no free lunch!
- With an unleveraged portfolio and only 20% bonds, there cannot be much diversification. It’s window dressing! Thus, in order for diversification through bonds to work, we’d need massive leverage in bonds, specifically leverage in government bonds with a negative correlation as we pointed out in a previous post (Lower risk through leverage) but that’s obviously not so easy to implement. It would require buying bonds and/or equities on leverage through futures. For example, 80% equities and 120% bonds (leveraged through Treasury futures) and not everybody has the appetite for that.
Summary:
- Part of this post was inspired by the recent guest contributions on Physician on FIRE (part 1 and part 2), where a financial planner wrote about why she doesn’t use bonds when investing for the long-term. My rationale is a bit different but with the same final conclusion. Contrary to popular belief, replacing U.S. stocks with a broad U.S. bond index creates very little diversification through bonds themselves. The risk reduction is entirely due to a lower equity weight, especially if the bond weight is in the 1-20% range. Unless the bond weight moves to a staggering 70% or more the “diversified” portfolio still maintains a correlation with stocks north of 0.90.
- Bonds merely serve as a return booster to cushion the opportunity cost of a lower equity weight. In the past, this worked extremely well because the Barclays U.S. Aggregate Bond index beat your short-term T-bill returns by almost 4% p.a.
- It is unlikely that bonds will maintain this strong outperformance over cash yields. The current yield in the Barclays Agg is just above 2% (2.29% yield over the last 12 months according to iShares, at the time of writing this). If interest rates were to move up too quickly, bonds could see painful short-term losses. Then bonds would go from non-diversifier plus return booster to non-diversifier plus return-detractor. The worst of both worlds!
- Moreover, the attractiveness of bonds will erode even further if we consider more attractive cash yields in some money market accounts that are closer to 1% if you shop around. That’s getting pretty darn close to the 1.5% for the 10-year government bond!
- Bonds have the additional problem that over longer horizons (say 10, 20, 30 or more years) they can have long stretches of bad returns (80+ years of zero real return!), see our analysis here on 145 years of bond return history.
PS: The Retirement Researcher article
If you are coming over from Retirement Researcher, please note this: Nothing the author, Bob French, writes on his page negates anything I say here. In fact, quite the opposite, he repeats exactly the argument I use to prove that there can’t be much diversification: “The volatility of the stock market monstrously swamps the volatility of the bond market” – a nice summary of my central argument, see the Pythagoras picture above. I have seen my fair share of people disagreeing with me, but it’s the first time I see anybody try to disprove me, using the exact same arguments that I provided.
Three more notes:
- I never make the “suggestion that you buy bonds on margin” and I actually say that this is something hard to implement and only appropriate for sophisticated investors with the appetite for this unconventional method. Mr. French seems to lack some basic reading comprehension.
- Mr. French graciously admits that in the five worst months for equities, the Barclays Agg Index was down as well. Thanks. It doesn’t matter that bonds were down less than equities as Mr. French quite correctly claims. A cash allocation of 20% would have been up. Case closed: The “diversification” is mostly due to the lower equity weight, not the 20% bond weight!
- My article from last year is actually not the most recent one on this topic. Recently, I published Have bonds lost their diversification potential? and I show that going forward, even a slight expected increase in bond yields would move the entire Stock-Bond efficient frontier below the x% cash, 100-x% Stock line. I wonder if Mr. French wants to “disprove” that article too. Who knows, maybe he inadvertently comes up with some new arguments in favor of my claim again!
How large is your bond share? Have you calculated the correlation of your portfolio with the equity-only share lately?