How to predict bond returns

Hello again, it’s been a while.

I won’t bore you with the details of why I’ve taken a few months off, but I’m now out of hibernation and ready to dive back into the world of investing.

During my time off, my inbox filled up with questions. Alongside the usual requests for sponsored posts, advertising networks, and offers for hair loss treatment, I received plenty of interesting investing questions – almost all of which I’ve now managed to reply to (apologies if I haven’t managed to reply to you yet).

Of those questions, a huge proportion related to bonds.

“Why should I own bonds with yields so low?”

“Should I buy inflation-linked bonds now inflation seems to be reappearing?”

“Which bond funds should I buy?”

As a relatively young investor, I’ve been fortunate in being able to ignore the question of how best to incorporate bonds into my own portfolio. But by popular demand, I’m coming back to life with a series on bonds, covering questions like:

• How to predict bond returns
• Will the stock/bond correlation stay negative?
• Why own bonds with yields so low
• Bonds vs bond funds
• Nominal bonds vs inflation-linked bonds
• Short-term vs intermediate-term vs long-term bonds
• All about duration matching

If you have any other questions/topics you’d like covered (bond-related or not), please leave a comment and I’ll add it to the list.

But for now, let’s turn to the first question of the series, and get stuck into the topic of this article – how bond investors can predict their returns.

How to predict bond returns:

• Why are bond returns predictable?
• How predictable are bond returns?
• What about bond funds?
• Bond funds and interest rate risk
• The “2x duration – 1” rule
• What the research says
• What that means for UK investors
• Was the bond bull market caused by falling interest rates?
• Conclusion

Why are bond returns predictable?

Bonds have a reputation in the investment world for being incredibly boring. And I think that’s probably fair for an instrument whose return is often measured in eighths of one percent.

But to their credit (pun intentional), one advantage of their boringness is it makes it much easier to predict their returns.

Unlike equities, bond returns are relatively stable. And that’s because their cashflows are much more certain. If you buy a 10-year bond at par with a 3% yield, then after 10 years you’ll receive your initial investment back – plus you’ll have received your income of 3% a year. Sure the bond price might go up and down in the meantime, but if you hold to maturity and the issuer doesn’t default, then your returns are predictable from the day you buy the bond.

Equities on the other hand, have no contractual cashflows. They’re not obligated to pay you a dividend. And even if they were, the dividend isn’t a source of return – it’s not an extra return on top of your original investment, as we’ve seen in this article on ‘Is Dividend Investing a Good Strategy?’ (spoiler alert: the answer is no). They also have no maturity, and again there’s no agreement for you to receive your initial investment back. There’s far less certainty around the cashflows from equity – which is why they’re riskier than bonds and why they tend to have a higher return.

For the purposes of this article we’ll be thinking about government bonds, and assuming government bonds have a zero default risk. It’s not a perfect assumption as there’s always the risk that the world’s governments collapse and aren’t able to repay their debts. But it’s a pretty remote risk, and if it does happen, we’ll have much bigger problems than our investment portfolio anyway.

How predictable are bond returns?

Let’s say you bought a 10-year bond with a 3% yield for £100.

In this case, you’re guaranteed to get your initial £100 back after 10 years, which means your return is going to be 3% a year from coupon payments. That’s pretty simple maths.

And for investors who invest directly into bonds, it really is as simple as that.

My first exposure to exactly how predictable bond returns were was after reading the legendary John Bogle’s book – ‘The Little Book of Common Sense Investing’, which unsurprisingly makes it into my list of the best investing books for beginners.

The graphs below plot the 10-year Treasury starting yield against subsequent 10-year return:

This is pretty straightforward and uncontroversial – if you hold your bond to maturity, you’ll earn the bond’s yield over the life of the bond. And contrary to what some may say, this doesn’t rely on the bond coupon being reinvested.

But this does assume you’re buying a bond directly, and holding until maturity. And this isn’t how most people hold bonds in their portfolio.

What about bond funds?

The reason there’s such high correlation between starting yields and returns is because the direct bond investor holds the bond to maturity – so changes in interest rates don’t matter. As you hold the bond, its price might go up, it might go down, but as long as you hold it to maturity, you know exactly how much you’re going to earn.

But most people don’t own individual bonds to maturity in their portfolio – instead, they invest in bond funds. And bond funds don’t have a maturity date, but rather have a target level of duration – for example a duration of 3-5 years.

Now, owning a 5-year direct bond until maturity is exactly the same as holding a bond fund portfolio with a 5-year duration, then shortening its duration by 1 year every year. This is known as duration matching, and I’ll be writing a full post on it later in this series. For those who’d like to dive in right away, there’s a good article by Northern Trust called ‘The Myth of Holding to Maturity: Bond Funds vs Individual Bonds’ which explains the basics.

But most people don’t adjust the duration of their bond fund allocation each year. Instead, we tend to buy and hold a target duration bond fund, thus keeping the duration of their bond allocation constant.

In which case, how predictive of future returns is the starting yield for buy-and-hold bond fund investors?

Bond funds and interest rate risk

When owning a direct bond, your return will equal your starting yield if you hold to maturity. If you buy a 5-year bond with a 3% yield and hold for 5 years, your return will equal 3% annualised.

So far, so good.

But this isn’t the case for bond funds, because bond funds are constantly having to buy and sell bonds within the fund in order to keep duration constant.

If a 5-year bond fund didn’t make any trades over the course of one year, all the bonds within the fund would tick one year closer to maturity, and the fund would become a 4-year bond fund at the end of the year. In order to prevent this from happening and to keep duration constant, the fund manager has to recycle the proceeds from matured bonds, or sell a lower-maturity bonds early, and buy longer-duration bonds for the portfolio’s duration to stay equal to 5 years.

And this process of having to reinvest by buying new bonds introduces interest rate risk.

When selling a bond early (or reinvesting proceeds from a matured bond) the fund manager will have to buy a new bond, whose yield will be determined by current interest rates. If interest rates fell during the time the manager held the old bond, the bond will be sold for a higher price, but the proceeds will be reinvested in a new bond at a lower rate. Conversely, if interest rates rose during the time the old bond was held, it will be sold for a lower price, but the proceeds will be reinvested into a newer bond with a higher yield.

It’s this second scenario which causes a problem for bond fund investors.

As an example, let’s say you buy a 3% yielding bond fund at 5-year duration, and rates rise every year during the 5 years you hold the fund. This means the fund will constantly be selling bonds early for lower prices, and replacing them with higher-yielding bonds.

Rising rates over your holding period introduces the risk you may end up not holding the newer higher-yielding bonds in your bond fund for long enough to offset the falls in price from the older bonds.

So how long will it take, in a worst-case scenario, for the yield from the newly bought higher-yielding bonds to offset the falls in price from the sold bonds, such that our returns will equal the fund’s yield at the point we bought it?

The “2x duration – 1” rule

It’s not a particularly catchy name for a rule, but it works.

In a worst-case scenario where rates rise constantly during the time you hold the fund, you’re likely to earn your starting yield if you hold your bond fund for a number of years equalling 2x the duration of the fund minus 1 year.

For example, using our 5-year duration bond fund with a 3% yield, in order for that bond fund’s return to equal 3% annualised in a worst-case scenario, we’d have to own it for 9 years (2 x 5 – 1).

It’s worth noting that you might earn the annualised yield more quickly (if interest rates fall during the period you’re holding the fund), but in a worst-case scenario of constantly rising rates, you’re likely to earn your initial yield if you hold for 2 x duration – 1 years.

NB: For longer maturity positions, the assumptions underlying the rule may not be as appropriate. Convexity can play a large role in returns, and it’s very unlikely that interest rates move in a linear fashion over the longer term. This rule isn’t iron-clad, and should be viewed as a rule-of-thumb, rather than an immutable law.

What the research says

The source of this duration rule is a paper by Lozada (2016) titled “Constant-Duration Bond Portfolios Initial (Rolling) Yield Forecasts Return Best at Twice Duration”. It builds on plenty of earlier studies into the relationship between initial yields and duration, and finds that the optimal horizon to use yield as a predictor of return in constant duration or constant-maturity bond funds is at twice the duration minus one year. This is the time horizon over which changes in price are offset by changes in income earned.

For a more readable explanation of the concepts explored in the paper, refer to this article, titled ‘How to Predict Bond ETF Returns‘ which walks through a nice simple example, and explains why the rule works in theory.

So that covers how long you’d need to hold your bond fund for in order to earn your starting yield.

But another interesting question is what happens if you simply buy and hold a bond fund forever? How much of your long-term future futures are likely to be determined by the starting yield?

The gurus over at Newfound Research did a deeper dive on bond fund starting yields as part of this fantastic article, titled ‘Did Declining Rates Actually Matter?’ on whether declining interest rates were really the cause of the bond bull market.

They looked at the returns from a 10-year US treasury index (a proxy for a 10-year duration bond fund), and decomposed those returns into three components:

• Coupon yield (“Coupon”)
• Roll return (“Roll”)
• Interest rate changes (“Shift”)

Their analysis involves buying 10-year Treasuries at the beginning of each year, holding them for a year, and selling them as 9-year Treasuries. The proceeds are then reinvested back into the new 10-year Treasuries. As this is a good proxy for how bond funds maintain a constant duration, it’s useful for analysing how much the initial yield affects a bond fund’s returns. The analysis takes place over a 30-year time span, so gives a good indication of how much each component of returns contributes over the long-term.

Their research shows the bond fund’s coupon accounts for 70-75% of the fund’s returns:

Source: Newfound Research

Because bond funds have to periodically rebalance their portfolio in order to maintain this constant level of duration, profit/loss from shifts in interest rates are booked along the way as positions are bought and sold. Which is why starting yield accounts for almost 100% of returns for direct bonds, compared to only 70-75% for bond funds.

What that means for UK investors

Given how much future returns are determined by initial yield, this paints a pretty bleak picture for bond investors today.

Investors able to buy UK gilts directly can expect to earn over 1% annualised only if they invest for over 10 years:

Source: The Financial Times

And as for bond fund investors, it’s equally grim.

In the face of continuously rising rates, which is the worst-case scenario using our “2 x duration – 1” rule, returns don’t look particularly appetizing:

I don’t know about you, but I’m not particularly enthused about the idea of 1.3% per year for the next 41 years…

It’s not surprising bond investors are looking for alternatives.

The returns on offer are paltry, and if you’re looking to the bond portion of your portfolio as a source of return, then you’re likely going to be disappointed.

But that brings up another question – what’s the purpose of bonds? Are bonds really there to generate uncorrelated returns? Or are they there to hedge equities in a crash? Or to hedge inflation? Or to provide income? Or some combination of all four?

Those looking to bonds as a source of uncorrelated returns aren’t going to be particularly happy with the current state of affairs in bond-world. But that’s a meaty topic for later on in this series.

For now, we have to accept that bonds aren’t returning anywhere near what they were in the past.

Was the bond bull market caused by falling interest rates?

A slight tangent here before we wrap up – just because I thought it was interesting.

Everyone’s heard about the rampant bond bull market which has been roaring since the 1980s. Everyone’s heard about record-low interest rates. Because we all know that falling rates means higher bond prices, it’s easy to connect the two and say, “The bond bull market has been caused by falling interest rates”. I personally hear that one all the time.

But it’s not really true.

If we hold a bond to maturity, a fall in interest rates raises the price of the bond in the short term, this much is true. But as the bond nears maturity the bond’s price will fall back to its par value (the “pull to par”). Similarly, if rates rise, the bond’s price falls in the short term, but will climb back up to par as it nears maturity. The pull to par effect occurs because as a bond nears maturity, there are fewer coupon payments to be received, and the investor knows they’re getting closer to only receiving the par value of the bond back.

So if we hold a bond to maturity, rate changes really don’t matter, as they only cause unrealised gains/losses in the bond’s price over the short term. In the long-run, it’s all about our starting yield-to-maturity.

From this, it follows that the bond bull market wasn’t caused by falling rates (which have no impact on bond returns, if held to maturity), but by the bonds’ starting high yields.

The chart below shows the yield on gilts was touching 17% in the late 70s/early 80s:

Source: World Economic Forum

As we’ve seen, those gigantic initial yields would’ve generated incredibly healthy returns for long-term bond investors – regardless of where interest rates moved.

So, no – the bond bull market wasn’t caused by falling rates. Bond investors since the 80s would’ve generated excellent returns even if interest rates had risen, because their returns came from their high starting yields.

Conclusion

Bonds’ returns are predictable because they’re boring. The contractual nature of their cashflows means their returns are much easier to forecast than equities.

For direct bonds and duration-matched bond fund portfolios, you’ll earn the bond’s starting yield if you hold to maturity.

The starting yield of a bond fund is still good indicator of the fund’s future returns – we’ve seen that coupons account for 70-75% of a bond fund’s return. But the time period over which your returns are likely to equal your starting yield may be different.

For buying-and-holding bond funds, in a worst-case scenario you’ll earn your YTM if you hold for a period of 2 x the fund’s duration – 1 year. Although it’s always possible you’ll earn your fund’s yield earlier if interest rates fall during your holding period.

So when it comes to bonds, your bond fund’s yield will be a much better predictor of returns than trying to forecast what’s going to happen to interest rates – which is a useless exercise anyway. An entire industry seems to have sprung up around trying to divine the path of interest rates – but these forecasts are a) rarely correct, and b) don’t matter that much anyway.

Because of the strong relationship between starting yield and future returns, it was the high initial yields in the early 1980s which caused bond investors’ returns to be so high – not the falling interest rates.

But investors today aren’t so lucky.

The current low interest rate environment means yields on bonds/bond funds are much lower than in the past. Given the strong relationship between initial yields and future returns, bond investors today are likely to be disappointed if they’re relying on their bond allocation as a source of returns.

In light of the low expected returns, investors should be reconsidering the role bonds play in their portfolio, and what that means for their overall portfolio’s return expectations going forwards.