Last time I posted about simulating monthly bond returns.
The results were okay but a bit disappointing.
Someone pointed out to me that I was using the Barclays Intermediate Treasury Total Return Index and comparing it to a bond fund that held maturities between 4 and 10 years. Yet the maturity of the simulated fund doesn’t necessarily match the average maturity of the index…doh.
That’s totally true. I was lazy and didn’t even think to check the details of the index I was using. I haven’t yet found a precise definition of the index but a summary from SPDR says:
The Index includes all publicly issued, U.S. Treasury securities that have a remaining maturity of greater than or equal to 1 year and less than 10 years, are rated investment grade, and have $250 million or more of outstanding face value.
That’s quite a bit different from the fund I was simulating. This Index doesn’t have any 10 year bonds. It holds bonds less than 10 years. And the maturities go all the way down to 1 year.
Barclays Intermediate Term Treasury Index (take 2)
Armed with this, let’s take another crack at things. This is what we had before.
Let’s try simulating a bond fund that more closely matches the index. This time we’ll make a 10–1 fund.
That’s definitely an improvement but still pretty far off from the index. Remember we said that the index has bonds less than 10 years? We’re still using 10 years bond at the top of our ladder. Let’s try changing that as well.
Still not great. Okay, let’s just resort to brute force and try a bunch of different variants and see what falls out.
There are several that are clearly bad: 10–1 (the black line at the bottom) and 1–1 (the blue line with circles at the top) are the worst. Let’s narrow it down to just the three best.
The 4–1 does pretty well from about 1985–2010. But it does worse before and after that. That kind of instability is a bit worrisome. The 5–1 looks like a better overall choice. And when we check the geometric means, the 5–1 is definitely closer:
I feel a little dirty about “chart hacking” like that but it looks like the 5–1 simulation gives us results that are the closest to the actual index over a 40+ year period.
If we look back at where we started, we’ve made a big improvement in our index tracking accuracy.
Barclays 5–10 Treasury Index
We seem to have done okay matching one Barclays Treasury Index. Let’s try another one and see how we go. (Barclays has a lot of indexes, don’t worry, I’m not going to try this for all of them!)
Let’s check out a bunch of variants first.
And then narrow it down to the best fitting ones.
If we look at the geometric mean return it says that the 10–3 is actually ever so slightly closer than than the 10–2 model. But I’d rather have a model slightly underestimate returns than slightly overestimate returns — after all, we’re already ignoring transaction costs and fund expenses here — so I think 10–2 is the better choice here.
Unfortunately, this Barclays index is relatively new, with data only going back to 1992. That gives us only 24 years of data to work with, so we should be a bit less certain of this result than our first one.
Again, we’ve seen that we need to go with a shorter average maturity (10–2) than we would have naively expected in order to match the index.
Barclays 1–5 Treasury Index
This is a shorter maturity index but has data going back to 1976. At this point, we’re not surprised when it looks like we need a shorter maturity in order to match the index.
The 3–1 seems to have the most consistent fit and checking the geometric mean confirms that.
We have a decent level of confidence is three models matching three indexes:
- The 3–1 Sim matches the Barclays 1–5 Treasury Index
- The 10–2 Sim matches the Barclays 5–10 Treasury Index
- The 5–1 Sim matches the Barclays Intermediate Term Treasury Index
We consistently had to shorten the maturity used in our model in order to match the index returns. To be honest, I don’t have a great answer for why that is. A small part of the answer is the differing end points used.
- When Barclays says “5–10” they mean it includes 5 year bonds but excludes 10 year bonds
- When we say “5–10” we mean that it includes 5 year bonds and also includes 10 year bonds.
We know that Barclays doesn’t include 10 year bonds but it isn’t clear what they do include. When a new 10 year bond is issued, do they start including it one week later (when it is 9 years and 51 weeks old)? Or do they only add things when they initially come up for auction? Do they sell a bond the exact day it reaches the minimum maturity? Do they sell at the beginning of the month or the end of the month?
We also know that Barclays indexes are cap-weighted rather than equally weighted by year. If the Treasury has an auction for 7-year bonds, they get added to the index. And since the Treasury auctions off 2-, 3-, 5-, and 7- years bonds regularly, it seems plausible that that causes the index to skew towards a shorter maturity than our naive ladder.
Finally, the Barclays indexes appears to often include more than just basic Treasury Bonds. There are things like STRIPS and TIPS out there. Or issues with less than $250 million in face value remaining.
Here’s the spreadsheet with the underlying data.
