The Great Bond Diversification Myth

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:

ScatterPlot Equities vs 8020
Scatterplot: Equities vs. 80/20 portfolio: Almost a perfect correlation! (Note: R^2=0.996 implies correlation = 0.998)

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):

Equities vs EqBo PFs - ReturnStatsTable
Return Stats for Different Equity/Bond/Cash weights

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:

Equities vs EqBo PFs - Risk
Portfolio risk reduction had nothing to do with bonds and had everything to do with lower equity weight

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!?
8020 Portfolio Variance Composition
Pythagoras meets Modern Portfolio Theory: Variance decomposition of 80/20 portfolio

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:

Equities vs EqBo PFs - Return
Shifting to bonds alleviates the return deterioration!

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:

  1. 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.
  2. Bonds merely serve as a return booster to cushion the opportunity cost from 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.
  3. 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!
  4. 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!
  5. 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 expcted 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?

 

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85 thoughts on “The Great Bond Diversification Myth

  1. Interesting and very helpful insights. As always, super detailed so I will have to read it 2 or 3 times. Please take that as a compliment.!!

    Regarding point #3, isn’t this sort of prediction a bit like saying what the markets are going to do when in reality nobody has a clue what it is going to do.?

    We currently have a decent sized bond exposure at 23%. Unlike some of the voters in our country, we are open to changing our mind on that approach based on acquiring new information.

    Your posts in general have got us thinking more on many fronts actually.

    Liked by 1 person

    • Thanks Mr. PIE!
      You’re right, #3 includes a prediction of sorts. Everything depends on the path of future interest rates and we have to decide how likely the 3 scenarios are:
      1: interest rates stay where they are now, i.e., assume status quo = the most naive forecast, but likely the most accurate and reasonable assumption. Then return=yield and we’re in a world where bonds still outperform cash, but by much less than in the last 10 years. Bonds are still useful in the portfolio but the opportunity cost of moving out of stocks and into bonds is no longer cushioned by 5% bond returns, but 2.3%
      2: interest rates rise. That means bonds give back some of their recent gains. If interest rates rise fast enough we could push the bond return below the cash return. Has happened many times before.
      3: interest rates go down even more. We’re in a Japanese scenario. Bonds will continue their outperformance of cash and can potentially still return much more than their yield

      In scenarios 1 and 2 bonds will be less attractive than they have been in the last ten years. To just keep up with their past performance we’d have to assume a pretty aggressive path (down) for interest rates.

      Like

  2. Thanks for this great insight. Your posts never cease to amaze me with the extensive financial knowledge that they contain. This is something that I have never considered but it makes a lot of sense. Since I began investing (not long ago) I haven’t seen a need for bond investments since the returns are so low. I have to admit, the treasury futures idea sounds great to me but is a little over my head at this point and I don’t even know where to start with trying to invest in something like that. It’s something I’ll be looking into in the future though for sure.

    Liked by 1 person

  3. Nice post! I’m 100% equities, no bonds because bonds don’t offer diversification like they used you and their return profile is sub par. I also liked the PoF posts. You both have offered great points, thanks!

    Liked by 2 people

    • I notice corporate bonds do not provide much diversification benefits, but government bonds do a better job. Over the past 5-6 years, the rolling 12-month correlation between the S&P 500 and the 10-year Treasury oscillates between +0.50 and -0.50; right now, at around -0.37.

      Liked by 1 person

      • Good point. I personally look at longer Windows than 12m and I put the S/B correlation at -.25 to -0.3 as my working assumption looking forward. The advantage with using 10Y treasury bonds is the negative correlation. The disadvantage is the very low yield right now.

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  4. Outstanding post ERN! You have vindicated my choice of 100% dividend paying equities. Well, this gentleman doesn’t prefer bonds! I have commented on the POF guest post as well complimenting her on recommending against bonds despite coming from mainstream finance. Your point 3 of the Summary is also right on, the biggest bull market is actually in bonds, and not in stocks. Imagine giving money for no return to the German government for 10 years just for the privilege of them holding our money (near-zero bund rates), no thank you! Treasuries are only marginally better than bunds. Both on a forward-return basis and on a risk reduction basis as you elegantly demonstrated here, Bonds are actually not worth any allocation in today’s environment in my view.

    Liked by 1 person

    • Thanks 10!,
      Good to know that we’re not the only ones with essentially 100% stocks. True, stocks seem expensive as well, but saving for an ambitious target like your $10! =3.6 million, it’s hard to accomplish that with 0% yield in Germany, below zero in Switzerland or even 1.5% in the U.S.
      Cheers!
      ERN

      Like

    • Investing in dividend-paying stocks pays off better when either the stocks trend up or when they trend down at a lesser amount than your dividend payout.

      With dividend stocks, like any other market, you assume price risk. Without a plan to limit your downside (e.g. using protective stop loss orders) in case the trends turn down, your dividends may not offset your losses.

      Liked by 1 person

  5. Great article! What are your thoughts on allocating a portion of your portfolio to TIPS? I do see the danger in the current bond market and I have been moving my previous allocation of bonds to TIPS (as well as the TSP G fund) to provide some level of diversification in my portfolio.

    Liked by 1 person

    • Thanks for that question. Great comment!
      TIPS (inflation protected US Government Bonds) would have some of the same issues as nominal bonds: essentially zero correlation, very low standard deviation in TIPS, so the overall portfolio risk level is very much dominated by equities. Same result.
      TIPS would obviously be one very brilliant diversifier against an inflation shock. If we had a 1970s style episode again over the next decade, TIPs would do really well and diversify.
      But there is no free lunch: if inflation drops again worldwide, and we enter a Japanese style decade (or century???) then TIPS underperform and nominal bonds will shine.
      Not an easy task putting together the right portfolio together these days! 🙂

      Like

    • Instead of picking a market to act as protection ahead of time, you may consider going with the trends. If TIPS don’t go up, then don’t buy them. If nominal bonds continue trending higher, stick with them. I believe reacting works better than predicting.

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  6. 0 bonds for us too. I don’t like that bonds just can’t add value like companies can.

    Bonds have been really helped with lowering interest rates since the 80s, and going forwards..well they can’t really go any lower. Interest rates are just going to go up again..and bonds will decrease, theoretically. This is a crazy world and central banks have created a monster that will be hard to put back in the box again. So many institutions are happy to accept an extremely mediocre return with these current bond rates. It can only be fixed with a big correction/interest rise – which wouldn’t be pretty 🙂

    Tristan

    Liked by 1 person

  7. This is a great post and I agree with your insights for what is being discussed here (the math doesn’t lie). However, I believe the scope of this post is too narrow to disregard bonds as a diversification tool, even if using a broad based bond index (as you alluded to the higher diversification of government bonds). I believe two other variables need to be considered (possibly a future post?). Primarily, reinvestment of income from both the equities and the bonds will show increased advantage to including bonds as a diversification tool. Secondarily (and of more importance as time horizon changes), rebalancing the portfolio (lets say semi-annually or annually) also increases the diversification benefit. If neither of these things is considered then the weight of the equities combined with the wide variability in equities will overcome most diversification benefits from a more stable investment such as bonds, especially when they are relegated to a smaller portion of the portfolio. However, if these factors are considered the portfolio will prove to be more stable and provide better risk adjusted returns over time. I believe it is William Bernstein that addresses this (as well as the government bond vs. broad bond index difference in diversification) in detail in “The Intelligent Asset Allocator” (this could be the wrong reference but I believe that is where I saw it). But it is something we can also find for ourselves by applying the same concepts and formulas you show here but adjusting for the named variables. Over the long term, an 100% equity portfolio is likely going to beat a equity/bond split every time. However, this doesn’t detract from the diversification advantage that bonds can provide if someone is seeking said diversification. Thanks again for the great post. If you have time I think your readers would benefit from a broader explanation including these concepts as well.

    Liked by 1 person

    • Thanks for this very thoughtful and detailed post. In fact, what you proposed is already what I did in my calculations:
      1: interest and dividends are reinvested
      2: the portfolio is rebalanced every month back to the X%, 100-X% ratio
      The reason for this procedure is that without the rebalancing the return of, say, an 80/20 portfolio during July 2016 would depend on when you started it. If you started it on 6/30/2016 then it’s 0.8 times equity return plus 0.2 times bond return. If you started it in 1999 it might have become an 85/15 portfolio by then. To prevent this kind of “can or worms” it’s safest to assume the portfolio rebalances every month.

      So, with reinvestments and with rebalancing, bonds still don’t offer much of diversification!

      Cheers,
      ERN

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    • To improve the diversification benefits of bonds when including them into a stocks-only portfolio, you may consider looking into setting your allocation amount based on recent volatility. This way, you normalize your position sizes based on the behavior of each market rather than coming up with some fixed allocation that you hope will work well in the future. Also, with vol-adjusted position sizing and periodic re-balancing, the better performing and higher volatility markets do not dominate your portfolio.

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      • That sounds like Risk Parity. That has obviously worked really well recently but mostly because bonds did really well. Risk parity is like portfolio optimization without knowing expected returns. If I do have views on expected returns I’d rather use them than ignore them.
        But I agree: risk parity will bring you probably close to the tangency portfolio. Take that, scale it up and you got much more diversification. See here
        https://earlyretirementnow.com/2016/07/20/lower-risk-through-leverage/

        But I’d rather arrive at the optimal allocation via mean variance optimization than simple risk parity.

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        • I don’t like Risk Parity in the way that Bridgewater or some other firms explain it and execute it.

          I also don’t like or feel comfortable with fixed allocations without considering if the trend is moving in your favor or against you.

          I believe in taking Risk Parity a step further and allocating to markets only when the trend moves in your favor. So, if you have a long-only bias, you only allocate capital when the trend is up and you set your position size based on what percentage of capital you want to allocate divided by the recent volatility.

          Does that make sense?

          Liked by 1 person

          • I think I know where you’re coming from. You are running a CTA (Commodity Trading Adviser) fund. It’s trend following. I would probably not dedicate a whole lot of my portfolio into a strategy like that. The bulk of my portfolio is to pick up a risk premium. I’m mostly a valuation guy, so momentum and trend is a bit foreign to me. But 5% in a CTA in the alternative bucket wouldn’t be so bad, I give you that.

            So my question: where do you see big opportunities to short? What is trending down right now? Bonds may soon see a down trend if the FOMC tightens. Maybe. But we might also go the Japanese route. Commodities seem to bounce around, so do equities. Where are your shorts right now, if you don’t mind sharing?

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            • Yes, I do run a trend following strategy.

              When you follow trends, you pick up the momentum risk premium. Why this risk premium occurs has to do with human nature and our desire to herd and chase and our fear of missing out. I wonder how you come up with your 5% allocation.

              Also, when you do not consider the trend, but instead elect to continue buying low as valuations get “cheaper”, I wonder how you manage risk against a persistent and/or sharp downtrend. My preference for following trends and having an exit plan for each investment stems from my desire to survive and my belief that I don’t know if the investment will rebound.

              Due to regulations, I cannot disclose my feelings about my positions in an open forum. If you’d like to talk about this privately, please shoot me an email at mike.melissinos@gmail.com.

              Liked by 1 person

              • The reason I would never dedicate more than a few % to a CTA is that the Barclay CTA index shows pretty measly returns for the last five years, not even beating CPI inflation. 10 years window was not much better.
                Now, I don’t know if this is just a temporary dry spell or something more fundamentally flawed with the CTA model. Cliff Asness, of course, would argue that the 5 year rolling return is the WORST return metric to look at. Something that performed poorly for that stretch of time is bound to come back (and vice versa). Let’s all appreciate the irony in this: the one reason to not lose hope in the CTA model is, of all things, a mean-reversion argument. Who would have thought?
                But I do think that there is something flawed: as more people are jumping on the momentum bandwagon the expected returns get smaller. It’s that simple. In the 80s and 90s, CTA returns were awesome. That trend line going straight up has suffered a pretty significant kink since.
                But I certainly wish you all the best with your fund!

                Like

                • CTAs go through dry spells just like buy-and-hold and fundamental strategies – sometimes for 5-10 years at a time depending on the manager. Equities, bonds, gold, etc experience similar ups and downs over the years. I notice many investors view the drawdowns of traditional asset classes as buying opportunities and as only temporary setbacks, but with CTAs they declare the strategy as broken forever. It’s weird to me.

                  I notice the upward trend line in the Barclay CTA Index you speak of remains in tact. I do not know how you define a “kink”. I wonder if you see any kinks in the S&P 500s chart. Barclay CTA chart and track record here – http://www.barclayhedge.com/research/indices/cta/sub/cta.html

                  Also, I notice the Barclay CTA Index produces a much smoother return than the S&P 500 and other stock indexes. Since 1980, the CTA index produces a MAR of ~0.63; the S&P 500 MAR comes in at ~0.15. Sure, there are years and short blocks of time where the S&P 500 can outperform (like the last 5-7 years) but I believe making decisions only based on the last 5-10 years may not be enough data to make the best decision or get the full story.

                  I may add that the Barclay Systematic Traders does a better job at tracking trend following performance. The broader CTA index includes sector-specialists, discretionary and fundamentalist strategies that do not correlate with strict price-only trend followers.

                  Basing your CTA allocation level on the previous five year performance may not produce as effective results going forward. Instead, you may consider looking at the CTAs volatility (you can allocate less to higher vol programs; more to lower vol programs) and other things like the manager’s process, track record length, MAR and Sortino vs his/her peers, etc.

                  Thank you for the kind words.

                  Liked by 1 person

                • The kink appears if you plot the cumulative return on a log scale to distinguish different growth rates across different periods.
                  I don’t care if the CTA returns are smooth. I’m not investing in a CTA as a total return strategy. If CTAs have negative correlation/crisis alpha I actually want them to be volatile to give me the maximum diversification for the least amount of principal invested.
                  But the whole momentum issue has definitely sparked my interest. If you can get this much excess returns during a downturn it’s something to consider in the overall portfolio context.

                  Liked by 1 person

  8. Great article! I love it when I get to actually review data sheets and graphs! It just pulls me right back into my research days! Fantastic job and excellent clarity!
    Bonds and their true value are always a tricky thing for me. I tend to have an aversion to them only because I prefer to have my money more actively working then passively playing it safe. Especially at my relatively young age, I feel that the higher risk options are more attractive long term. However, your perspective of using bonds to cushion the opportunity cost makes them a lot more appealing to me! I will have to reconsider my approach again.

    Like

  9. I’m joining the green swan here, I have 100% of retirement and non-retirement investments in index funds with 0% allocated to bonds. I’m in my early 30’s and I probably won’t use a bond until I near retirement.

    Liked by 2 people

      • 100% equities will give you terrible drawdowns in the next bear market. you need to add a 7-10% gold position plus a 10-13% REIT and/or commodity position to mitigate downside risk. An 80% equity / 10% gold /10% REIT portfolio will have MUCH less risk than a 100% equity portfolio. The risk-adjusted returns will be better also.

        Liked by 1 person

        • For folks who don’t plan to retire anytime soon, they shouldn’t worry about the potential drawdown in the next 3 years. I would be afraid of having a return drag from Gold (long-term return = 0-1% real).
          I agree with real estate investments but prefer direct investments (private equity funds) over REITs. REITs look still too expensive.

          Like

    • I worry when I see young people go all in on one investment, especially without an exit plan if/when the trend turns down.

      Depending on your goals, bonds, like other non-stock markets can help smooth the returns of your portfolio over time. Having a portfolio of many different markets and strategies reduces the need to pick the right one and it allows you to perform well even if half of your investments don’t work out (provided you cut the losses quickly). Removing non-stock markets from your portfolio indicates curve-fitting and prediction, both of which can lead to poor performance.

      Stocks do not have to go up in the future. No law of the markets exists to make this true. Sometimes they can go down by a lot and stay down for a long time. This has occurred most recently in Greece, but more prominently in Japan where stocks haven’t made new highs in 30 years.

      My point is to be open to all opportunities. Closing yourself off to bonds, or any other market, eliminates your ability to profit from their trends.

      Liked by 1 person

  10. Wow, this is a very detailed post, thanks for putting this together!
    Well, maybe I’m the only here but I do have 70% stocks / 30% bonds. I’m not going to say that I have a bullet proof explanation for this. It’s my impression that 100% is too risky for what I can stomach in the event of a crash like 2000 or 2007. After reading your article, I’m not sure my decision actually makes any sense if there’s no diversification benefit?
    An additional question for you : if we had to go into a market crash, considering that both stocks and bonds are expensive right now, how would the downside compare between a 100% bond portfolio and a 100% stock portfolio?
    I love the detailed analysis, looking forward to reading more of these articles!

    Liked by 1 person

    • Thanks for stopping by!
      Again, the lower equity weight creates lower volatility, so if you’re uncomfortable with 100% equity style vol (~15% annualized on average, though much lower right now) you should be in bonds to reduce the risk.
      Regarding your question: It depends on the type of the crash. The last few recessions saw a drop in stocks but a rally in bonds. So there was diversification through that (though as the last 10 years show, the bulk of the cushion came from a lower stock weight, not the bond diversification).
      The one scenario where even the bonds will not help is a 1970s style inflation shock (bad for bonds and stocks). That would be a disaster for all the bond holders.
      Cheers,
      ERN

      Like

  11. I had no idea that stocks and bonds had such a high correlation, I learned something today! My investments are just by what Warren Buffett said he will do for his investments after he passes away, 90% in s&p and 10% in bonds. I invested my 401k based on this and will be blaming him if it doesn’t work out! (just kidding, I am confident that it will beat hedge fund returns though).

    Liked by 1 person

    • Hi, Thanks a lot!
      Again, it’s not that S/B are very correlated (the correlation was about 0.05 over the last 5 years), it’s that 80% Stocks +20% bonds are still highly correlated with stocks.
      Yeah, Warren Buffett is correct on Hedge Funds. They have a hard time beating the equity market over long periods.
      Cheers,
      ERN

      Like

  12. Thanks for the great analysis. I didn’t know the correlation was that high. In our investment portfolio, we have about 80% equities and 20% bonds. The main reason I have 20% in bond is because I want to have some purchasing power when the stock markets crash. We didn’t have much money to invest during the last market crash and I want to have some powder in the keg next time.

    Liked by 1 person

    • Hi, thanks for stopping by and your comment!
      Well 80/20 is not bad if you want to reduce volatility. It’s a higher expected return than 80% stocks and 20% cash.
      In terms of keeping powder dry for the next drawdown, that’s also a great idea in theory, but how does it work in practice? Recall that in the stock/bond simulations I already made the assumption that the portfolio rebalances every month back to 80/20, so after a large stock drop you take money from bonds and shift to stocks. At what point, though, do I believe stocks are so cheap that I move to 90/10 or 100/0? Was Feb 11 this year cheap enough when the S&P500 went down to a little over 1800 intra-day? I might have been too scared to “catch the falling knife” when everybody thought the world will end. Or post-Brexit? Even harder to time the bottom because the drop lasted two trading days and then the index marched straight up after that. And once I am 90/10 or 100/0, when do I move back to 80/20 again? It’s just too much of a can of worms. My 100% equity portfolio takes away all those headaches, though at the cost of higher volatility. 🙂
      Cheers,
      ERN

      Like

        • That’s a great plan. Thanks for sharing! So, it looks like even the drop in February this year didn’t even come close to the 20% threshold. That would have been closer to 1700 points in the S&P at the time, while the S&P dropped to 1810 or so intra-day on Feb 11.
          I for myself are at 100% equities and it’s hard to find the way out again. Especially with bond yields to low, haha.
          Cheers,
          ERN

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  13. The “flight to safety” has been interesting the past year. Just when people thought bond yields couldn’t get lower, they did! haha So if you’re looking for diversification by negatively correlated assets, US treasuries are the way to go (like you pointed out).

    Personally bonds are meh for me, given the super low yields and implied returns. They are mostly for principal protection/peace of mind these days, if you ask me–not necessarily for diversification in the negative correlation sense.

    It’s got to be nerve wracking trying to retire in this environment. Seeing so many people starved for yield branch out to risky junk bonds and bidding up defensive stock sectors so even utilities have low yields!

    Liked by 1 person

    • Thanks!
      Yes, bonds are “meh” at best. Probably better than cash to reduce risk, due to higher yield. But why do I need to lower risk? Equity volatility has been low. Even with the recent disasters (August last year, Jan-Feb this year) volatility has been pretty muted. I see no urgent need to lower my portfolio vol.
      Cheers!
      ERN

      Like

  14. Wow, ERN! Some serious math up in aqui… I love it!

    Like you, I’m no fan of gummint bonds. Which I think might be the riskiest of asset classes in today’s economic environment.

    But hmm… I’m not sure if I entirely agree with the suggestion that bonds don’t provide valuable diversification benefits to an equity-based portfolio. Maybe bonds aren’t the best diversifier out there, but they seem to (usually) do what they’re supposed to.

    If I look at your chart that tabulates the returns and risk for various equity/bond portfolio mixes, I think I see valuable diversification in action. For instance, the overall return for the 100% equity portfolio was 7.97%, and that portfolio’s “risk” was 15.78%.

    Changing the mix to 70/30 equities/bonds reduces the return by around 0.6% to 7.34%, but reduces the “risk” from 15.78% all the way to 11.16%. Which, I think is what the idea of beneficial diversification is all about: A valuable forgiveness of some fraction of gains in exchange for a larger reduction in volatility.

    Quantifying this kind of thing can be done with approaches like the Sharpe Ratio (even with its theoretical shortcomings).

    There’s no question that, over the long run, equities outperform all other asset classes. But to obtain that equity premium, you have to “pay” for it with relatively high, stomach-churning volatility.

    So my view on asset class diversification tends to be that, over the long term, it’s almost unambiguously bad for maximum wealth accumulation: 100% (or 200%) in equities all the way, baby. But with shorter-term horizons, lots of volatility can be a killer, and so there’s a place for lower-returning and less-volatile vehicles like bonds in these situations.

    I don’t discount the possibility that I’m missing something here, and I offer these thoughts in the spirit of valuable discussion. But I don’t think the fact that two equity-heavy portfolios exhibit similar total returns arcs means that bonds do not provide diversification benefits to equity-based portfolios.

    Liked by 1 person

    • Thanks for stopping by. Very good comment. And should emphasize that you and I are 100% on the same page.
      All I’m saying is that the risk reduction comes entirely from the lower equity weight: 70% stocks, 30% money market had a lower risk than 70% stocks, 30% bonds (11.04% vs. 11.16%). But with bonds you had the great benefit of much higher return. Hence, the higher Sharpe Ratio when using bonds. If that is what people mean by diversification, so be it. But I’m trained to think of diversification as something inherently related to second moments (variance, covariance, correlation).
      That said: I don’t know many people (or any?) who believe that bonds with a current yield of 2.3 (Barclays Agg) will again return 4.91% p.a. over the next ten years. So in terms of outperformance of bonds over cash, we all should get used to leaner returns going forward. Much leaner!!!
      But again: we don’t want to trash bonds or anything. In fact we have written about how equity+bonds and no cash is much better than equity only plus a cash emergency fund:
      https://earlyretirementnow.com/2016/07/27/emergency-fund-bad-idea-one-chart/
      And we have written about how to do better than the efficient frontier by levering up the tangency portfolio (Max Sharpe):
      https://earlyretirementnow.com/2016/07/20/lower-risk-through-leverage/

      Cheers!
      ERN

      Liked by 1 person

  15. I have to disagree with the message of this post. First I would suggest that the time horizon of 2006-2016 is not indicative of historical asset correlations. The government intervention in the money supply has increased correlation of all asset classes by enabling free money. That being said my view of bond allocations is still borne out from your analysis. I.e. The lower risk of bonds provides diversification of risk at the extremes. Bonds are not protection against market volatility like we have had since 2010, but rather a protection of some set of funds given a Japanese stock market type scenario or a 2008 scenario. Even when moving in tandem if both portfolio sets move to 3 Stdev below norm you have .7*48 and .12*.3 then you have a 12 percent reduction in loss for a 30% allocation in bonds. Rebalancing would then allow the purchase of additional stock near the bottom.

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    • “First I would suggest that the time horizon of 2006-2016 is not indicative of historical asset correlations.”
      True.

      “The government intervention in the money supply has increased correlation of all asset classes by enabling free money.”
      Definitely false for Stocks vs. Bonds. The extraordinary monetary policy has created a noticeable shift to lower correlations between Stocks and bonds. If we were to ever go back to “normal” conditions, the diversification benefit of bonds would be diminished even more.

      Like

      • It depends on if your talking about the movement of bond yields/ coupons or the capital gains on existing bonds. Existing bond prices have been following stock prices in a more tight correlation in the last 10 years or so, really only moving in the up direction like the stock market. Yield being the inverse of price has gone the opposite direction. The increase in money supply has largely flown into the stock and bond markets

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        • Ie One can argue the flight to safety never ended after the last crash. Studies have shown a larger amount of cash on the sidelines the last 6-7 years or so. In a normal bull market it’s when people forget a crash could happen any moment that the correlation is at its lowest. I’d argue we have yet to see that point in 7 years. In buffet terms most people are still fearful not greedy. Correlation will change if when the yield curve inverts.

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        • “It depends on if your talking about the movement of bond yields/ coupons or the capital gains on existing bonds.”

          The only SENSIBLE object to look at in the S/B correlation is the correlation between stock and bond RETURNS because that’s what impacts my portfolio. And that correlation has been -0.25 to -0.30 over the last 15 years. That correlation has been +0.2 to +0.4 over the 1970-2000 time span.
          So going back to the original issue: where have you seen an increase in S/B return correlations going up recently? I don’t see it in S&P500 vs. 10Y Treasury benchmark bonds, but maybe I’m missing something.

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            • Yes, yes, yes. It seems we’re on the same page. The S/B correlation changes. It has been very negative recently (and even then diversification wasn’t that great).
              You bring one reason after another to further support my initial post titled “The Great Bond Diversification Myth” but why do you start with the phrase “I have to disagree with the message of this post”???

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              • It comes down to the conclusion, or at least the conclusion some are drawing. There’s more to a bond allocation then higher average returns and going with no bond or bond like allocation in your portfolio is a bad idea regardless of the overall impact to your portfolio risk. The biggest concern is one of risk tolerance. It’s easy to go all in stocks now at the top of a 8 year bull market. Without going through a pull back you don’t know how you personally will react. As a secondary concern you have the 3rd level sigma risks I mentioned in my first post. Bonds and bond like allocations are not about smoothing normal risks. There about protecting you when the market drops 40-50 percent in a year. I fear investors as a whole are becoming too complacent that this type of drop can’t happen. Ie I fear we’re starting to see that shift towards greed. The performance of people in my work life asking me if I bought on the dip, and even then sheer number of early retirement blogs are a sign of it. Some have great plans. Others are blinded by the bull.

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  16. Great article. I have never understand the point of bonds because their performance above their stated yield has all come from rates dropping. It appears you wrote this article last summer, and now it seems your “prediction” of higher rates is coming true. For me personally, ~50% equities, and ~50% fixed income which includes FDIC-insured CDs, rental income and high-yielding “hard money loans.”

    Liked by 1 person

    • Haha, yes thanks for pointing that out. That long bond rally is definitely stopped for now. Do you have a blog? Did you write anything about the hard money lending business? That might be something I like to learn more about.
      Thanks!
      Cheers,
      ERN

      Like

  17. One note I’d add and I don’t want to get political but if the Republicans pass their corporate tax reform and the corporate tax rate is lowered from ~35% to say ~20%. Equities in theory should take off the next few years and with interest rates only going to go up the gap between Bond and Equity returns could widen even further.

    Liked by 1 person

    • That’s what I predict, too. Equities might perform well, despite slightly rich valuations. Not so sure about bonds. The best you can hope for is the measly yield, and you might even lose a bit on duration is yields go up more. Not a pretty picture.
      Cheers & thanks for stopping by.

      Like

  18. > 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…replacing U.S. stocks with a broad U.S. bond index creates very little diversification through bonds themselves

    Diversification comes from having low correlation between assets WITHIN a portfolio. Stocks and bonds have low correlation with each other.

    I find it very weird that you are looking at how a Stock100% portfolio is correlated with a Stock80%+Bond20% portfolio. That doesn’t seem a useful way to look at things, and I’ll try to explain why I think that.

    Imagine a hypothetical asset class: relionds, which have an expected return just below stocks and no variance in returns at all. Thus, relionds are perfectly uncorrelated with all other asset classes.

    Since relionds have no variance in returns at all, the correlation between a Stock100% portfolio and even a Stock1%+Reliond99% will be 1. By your post’s logic, relionds do not help with diversification, but I hope you will agree that relionds are great for diversifying a portfolio.

    On the flipside, imagine volatonds, which have expected return same as relionds, have a variance in returns 1000 times the variance in stock returns, and have a 0.5 correlation with stocks. The correlation between a Stock100% portfolio and a Stock99%+Volatond1% portfolio will be 0.5. By your post’s logic, volatonds are wonderful for diversification, but that’s simply because they are high variance.

    Your post’s logic penalizes relionds because they are low variance and rewards volatonds because they are high variance. We should not penalize an asset class for being low variance.

    The only reason we care about diversification is because we want our portfolio to have the most return for the least risk. Looking at how two possible portfolios correlate with each other does not help in this endeavor.

    Liked by 1 person

    • I completely agree: diversification is about having low correlation assets within a portfolio. Never claimed otherwise. The reason I wrote this post is to point out that an 80% Stock, 20% Bond portfolio would have roughly the same volatility as (or even slightly higher than) an 80% Stock, 20% Cash portfolio. None of the volatility reduction came from diversification and all of it came from the lower equity weight. But I do state that the appeal of bonds came from the higher than cash returns. Though that may not last forever. Bonds got hammered since November, remember? So, believe me, I am familiar with the concept of getting the most expected return per unit of risk. I apply it every day in my job ad my personal portfolio.
      In the example you gave, I would have never picked the “volatonds” over the “reliatonds” portfolio. In fact, quite the opposite: Introduce another asset: Boringtonds with zero volatility and the same return as cash (much lower than the Relionds). Otherwise known as cash. I would argue that with interest rates on the rise in the medium-term, a portfolio with 80% stocks, 20% cash/boringtonds probably looks more attractive than 80% stocks, 20% (10Y-Treasury) bonds. If I could get my hands on one of those Relionds it would be an even easier choice, of course.

      Like

      • Thanks for your reply and the many interesting and informative posts on your blog.

        >diversification is about having low correlation assets within a portfolio

        So, having bonds can help diversify a portfolio?

        >The reason I wrote this post is to point out that an 80% Stock, 20% Bond portfolio would have roughly the same volatility as (or even slightly higher than) an 80% Stock, 20% Cash portfolio.

        Then I don’t understand why your post makes a big deal of the correlation between a Stock100% portfolio and a Stock80%+Bond20% portfolio.

        Your post also says: “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?”

        Why are you focusing on that sort of comparison? How does that help a person make decisions? I’m really not understanding the purpose of looking at correlations across portfolios.

        >In the example you gave, I would have never picked the “volatonds” over the “reliatonds” portfolio.

        That was the point of the example, to show how both of us would pick relionds over volatonds, because neither of us care about correlation of a 100% stock portfolio to a mixed portfolio. Also, the example shows how relionds are great for diversifying a portfolio despite a Stock1%+Reliond99% portfolio being perfectly correlated with a Stock100% portfolio. You talk about the extremes with bonds to “push the correlation below 0.5” but apparently neither of us care about that correlation.

        Liked by 1 person

        • In an 80/20 portfolio, bonds don’t offer diversification. The reduction in volatility is entirely due to de-risking equities. You could have done that with 80% stocks, 20% cash. The case for bonds came entirely from their higher realized return vis-a-vis cash over the last decade. But it’s not clear that will always be the case.
          The correlation between a 100/0 and 80/20 portfolio is used to show why that 80/20 portfolio doesn’t succeed in lowering the volatility beyond a 0.8 beta portfolio (80% stocks, 20% cash). You do know the link between beta and correlation and standard deviations, right?

          Like

          • Thanks for your response and efforts to help me understand your post.

            > In an 80/20 portfolio, bonds don’t offer diversification.

            I would think this is a prime example of diversification. Bonds offer returns that aren’t perfectly correlated with the other assets in the portfolio (stocks). As Wikipedia says: “In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets. If asset prices do not change in perfect synchrony, a diversified portfolio will have less variance than the weighted average variance of its constituent assets, and often less volatility than the least volatile of its constituents.”

            > The reduction in volatility is entirely due to de-risking equities.

            Okay, but I don’t see how it matters where the decrease in volatility comes from. Going from a Stock100% portfolio to a Stock80%+Bond20% portfolio is “allocating capital in a way that reduces the exposure to any one particular asset or risk”. Diversification is happening, by definition. It’s okay if you don’t want to give diversification “credit” for lowering volatility compared to a Stock100% portfolio. I’m not trying to argue about “the real cause” of decreases in volatility from portfolio changes.

            > You could have done that with 80% stocks, 20% cash.

            That would be yet another example of diversification, very similar to the example with 20% bonds.

            > The case for bonds came entirely from their higher realized return vis-a-vis cash over the last decade.

            Okay. Not all ways of diversifying are equally good. There are plenty of ways to diversify that are even bad. Making a portfolio more diversified does not necessarily improve the portfolio or even decrease its volatility.

            Perhaps we have a disagreement over what the term “diversification” means? I thought maybe we agreed when you said that diversification comes from having assets within a portfolio that are not perfectly correlated with each other. I also thought we agreed that stocks and bonds are not perfectly correlated. But then you say stuff like “in an 80/20 portfolio, bonds don’t offer diversification” over a 100% stocks portfolio. That confuses me. I must be missing something in your conception of diversification.

            Could you offer a definition of diversification? It’d be great to know where we start to differ.

            Like

            • Going from 100% equities to 80% equities/20% cash is not diversification. It’s called derisking. And do you know what the difference is? Imagine you have a job in finance and someone asks you for suggestions on how to diversify a portfolio. If you answer “scale by a factor of 0.8 and mix in 20% cash for diversification” you will be laughed out of the room. And if you protest “But I read that on wikipedia” everybody will get an even bigger laugh and you will get fired on the spot.

              But you know what: Our positions are not even that far apart:

              Jacob Egner: A portfolio with 80% equities and 20% bonds offers about the same diversification as 80% equities and 20% cash

              ERN: A portfolio with 80% equities and 20% bonds offers about the same “diversification” as 80% equities and 20% cash

              So we seem to agree on the fact that that the 20% bond allocation isn’t really doing much in terms of diversification, right?

              Like

  19. >Going from 100% equities to 80% equities/20% cash is not diversification. It’s called derisking.

    It certainly fits the definitions of diversification I’ve seen people use, including your statement “diversification is about having low correlation assets within a portfolio”. That action reduces the overall correlation between invested dollars in your portfolio. It reduces your exposure to some particular risks. The action might be very suboptimal compared to other diversification possibilities, but that alone doesn’t disqualify it from being diversification.

    I’ve read several articles where people talk about diversifying into cash. Usually they include other asset classes to diversify into, but they do include cash as one of the asset classes to diversify into.

    It’s possible for an action to be correctly described by two different words. For instance, it might be unusual to point to a square and call it a quadrilateral or a rhombus, but it would still be a quadrilateral and a rhombus.

    Perhaps it would be unusual for you to call that action diversification, but I haven’t seen anything definition-wise to disqualify it. Could you elaborate on why going from Stock100% to Stock80%+Cash20% does not fit your definition of diversification?

    >And do you know what the difference is?

    I previously asked you to provide your definition of diversification since we seemed to have different definitions, and I’d like to repeat that request now. We could talk about diversification vs derisking, but that might not be very productive if we’re still using different definitions of diversification.

    >So we seem to agree on the fact that that the 20% bond allocation isn’t really doing much in terms of diversification, right?

    We do not agree. Hopefully once you tell me more about what you mean by diversification (or just link me to something you think is suitable), we can effectively get to why we disagree.

    Like

    • I’m not saying that the wikipedia definition is wrong. That would be my definition as well. I’m just saying that you apparently misunderstand it. In a 100% stock portfolio, all risk in your portfolio comes from stocks (duh!). In an 80% stock, 20% cash portfolio the total risk is lower but all of the risk still comes from equities. That’s not diversification. That’s derisking. I provided the distinction between diversification and derisking: Diversification is one one that doesn’t get you laughed out of the room.

      In an 80% stock, 20% bond portfolio the overwhelming majority of the risk contribution is from stocks: See the Pythagoras triangle: 0.016384/0.016448=0.996, i.e., 99.6% of portfolio variance still comes from equities, 0.4% from bonds. Very little diversification. All using the wikipedia definition.

      What you read on the internet about people shifting into cash and calling that “diversification” – I’m sorry but I can’t compete with a line of reasoning a la “if it’s written on the internet it’s gotta be true” so I will end this discussion here now.

      Like

  20. I use portfolio visualizer to look at efficient frontier.

    https://www.portfoliovisualizer.com/efficient-frontier

    The tangent portfolio is the portfolio that has best Return v Risk vs a 1 month T-Bill. The tangent stock bond portfolio shows 17% US stock and 83% Total US Bond. The remainder of the frontier is a straight line of reward v risk meaning a 1:1 correlation. So I agree with your conclusion but the reason is not because of failure of diversity.

    In fact any 2 asset like portfolio even if it 3 or 4 “assets” (like Bogelhead 3 or Bogelhead 4) still resolves to a tangent portfolio (best reward v risk) in the 15:85 range AA of stocks and bonds.. Add gold and tips to the mix and look at this portfolio v the 2 asset portfolio (4 assets v 2 assets) Very different picture. So I think the problem is the 2 asset portfolio essentially has no diversity past the tangent portfolio precisely because Stock volatility wins past heat point. A better diversified portfolio like stocks bonds gold tips moves the efficient frontier much farther right and therefore is more efficient

    You can graph these 2 asset v 4 asset portfolios on the same plane, using “dual efficient frontier” and ticking the assets you want included in each frontier’s graph.

    Liked by 1 person

    • Good point. I like that site. I still prefer to run the Efficient Frontier calculations myself because I want to be able to apply my own expected returns, additional constraints, etc.
      But you’re right: the max Sharpe Ratio portfolio is very bond-heavy.

      Like

  21. PS I’m NOT recommending gold. I read your gold rant. Warren buys companies and I buy decreased volatility. I do own a little, like 5% gld to leverage fear and add diversity. The VIX is too expensive to own and the ETN’s don’t track the VIX well enough and also are too expensive to own. To leverage Warren I own BRK.B. I merely wanted to point out what I see as the issue in a 2 asset portfolio. It’s not really diversified part the tangent.

    Liked by 1 person

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