Thread by @choffstein

1/ Why the bond bull market had almost nothing to do with declining interest rates

(and why you shouldn't 😴 on roll yield or leverage)

A (long) 🧵...

(I wrote about this back in 2017 too: blog.thinknewfound.com/2017/04/declin…)

2/ It's often repeated that declining interest rates over the last 40 years created a bull market in bonds that is unlikely to ever be repeated again.

I do not believe the facts actually support that narrative.

3/ Let's start with a very simple graph: the price return versus the total return of the Vanguard Total Bond Market Index Fund (VBMFX)

4/ What's the difference here?

Total Return assumes the reinvestment of all distributions.

Price Return excludes distributions.

We can see that over the 30+ year history of this fund, the price return is, largely, negligible.

5/ What does this mean? It means that almost all of our bond market returns actually came from distributions.

But where do those distributions come from?

6/ Let's back up a second and ask ourselves a simple question: why do we think declining yields actually served as a tailwind to bonds anyway?

The quick answer is because most of us know the relationship that

⬇️ Yield ⟹ ⬆️ Price
(and vice versa)

7/ This comes from a simple arbitrage argument.

If I buy a 10y US Treasury today for 1.5% and rates instantly jump to 2%, the only way someone would buy my bond is if the price fell enough such that the *total return* (yield + price appreciation) was equal to 2%.

8/ "Aha! So changes in rates DO matter!"

Yes, my bond went down in price. BUT if I just hold it to maturity, I'll still earn my original 1.5%.

So it mattered mark-to-market, but not in my eventual realized return...

9/ That's why I like to say that all changes in rates do is push and pull returns from the future.

Rates ⬆️: Prices fall as we pushing returns into the future (higher yields).

Rates ⬇️: Prices climb as we pull returns from the future (lower yields).

10/ So if we hold a bond to maturity, rate changes really don't matter: it's all about our starting yield-to-maturity.

But what if we don't hold our bond to maturity? What if we hold an intermediate-term U.S. Treasury fund that only holds 7-10y UST?

11/ The water gets a bit murkier here, but things sort of still work out "on average" over time.

If I buy a 10y UST today and yields fall (rise), I'll end selling it at a higher (lower) price and using the proceeds to buy a new 10y UST with a lower (higher) yield.

12/ In fact, Lozada (2016) shows that "2 x Duration - 1" is a close predictor of the time horizon over which changes in price are offset by changes in income earned.

content.csbs.utah.edu/~lozada/Resear…

13/ e.g. if you buy an intermediate-term U.S. Treasury fund today with a yield-to-maturity of 1.5% and a duration of 7, you can expect to earn 1.5% annualized over the next 13 (2 x 7 - 1) years.

14/ What this math tells us is that a secular decline in interest rates would create short-term increases in price, but that price increase would eventually be offset by a lower income rate.

15/ So why isn't the long-term price return of VBMFX zero? Well, turnover within the index (from additions, deletions / defaults, paydowns, and reinvestment) can crystalize price returns.

16/ Nevertheless, what's really driving returns over the long run is the carry we earn.

The "40 year bull market" wasn't caused by a decline in interest rates.

It was from the fact that nominal rates started at 15%.

17/ So for long-term investors in bond funds, what we should really care about is the carry we earn.

And that carry largely comes from two places:

1. Yield (to-Worst)
2. Roll Yield

18/ The former is, hopefully, obvious.

The latter arises from the fact that yield (and credit) curves are usually not flat, and the passage of time means that e.g. our once 10-year bond is now a 7-year, but 7-year bonds have a different going rate!

19/ So let's say we manage an intermediate-term U.S. Treasury fund. We buy 10-year U.S. Treasuries and sell them when they hit 7 years.

The current 10-year rate is 1.48%. If the yield curve doesn't change, in 3 years it will be a 7-year bond. But 7-year bonds yield 1.26%!

20/ So what happens to our bond? To prevent arbitrage, the price must go up until the yield-to-maturity goes down to 1.28%.

But if we sell it at the higher price and go back and buy a 10-year UST again, we've captured some return.

This is roll yield.

21/ If we include roll yield estimates into our yield curve, we may find certain points much more attractive than they were previously.

For the current 7-year US Treasury, roll yield is almost as large is the coupon yield itself!

22/ This is especially true on a risk-adjusted basis!

As a rough, first-order approximation, we can divide carry by duration to get a risk-adjusted carry measure.

https://twitter.com/choffstein/status/1419998535949377538

23/ (For a constant duration bond fund, the first order approximation of volatility is duration times the volatility of the underlying rate.

...

24/ And if we accept that level shifts across the curve represent a disproportionate amount of yield curve variance, we can kind of just hand wave and say “volatility across the curve is proportionate to duration”)

25/ What this all means is that if you’re buying, say, a 7-year U.S. Treasury today and levering it up 2.5x to get the same duration as a 20+ UST, you’re getting almost *double* the expected carry.

26/

TL;DR: Declining rates had less to do with the bond bull than high starting yields did.

Carry is our expected return. That’s yield + roll yield.

Leverage can help you exploit risk-adjusted return opportunities.