While a big fan of Longinvest's bond fund simulator and methodology for treasuries, I've been troubled by the way it models Total Bond Market using Bond 10-2 (rolling 10 year treasury bonds sold 1 year prior to maturity). The rub is that unlike Treasuries, we know that the Barclays Capital US Aggregate Bond Index includes corporate bonds and mortgage back securities. Yet the longinvest model uses simulated yields solely from Shiller's treasury yields, and we have good reason to think that at least some of the index's returns in the corporate bonds are due to Credit and Beta. The good news is we have Shiller's stock data going back to 1871 which could be incorporated into the bond simulator. Nothing about Longinvest's model of simulated yield curves incorporates this Beta; so for fun I decided to give a quick run.

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Sp500, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being cloned by

**4.9% Sp500, 54.2% STT, 26.1% ITT, and 14.8% LTT.**(Since they come from a snippet of history, these numbers should be taken with a grain of salt but will do for our purposes.)

Longinvest's bond simulator contains models for ITT (Bond 10-4 ten year treasuries sold three years from maturity) and many other funds. I used his Bond 4-2 for STT and his Bond30-11 for LTT. I then came up with a weighted average for the Factor Model (FM) based on weighted average of the funds above. (Here's my Google spreadsheetsheet , though the charts seem to get messed up if you download to excel.)

On its face, the Factor Model does seem to simulate Total Bond Fund moderately better than the Bond 10-2 used in the Simba spreadsheet. Here's the Telltale chart for 1976 on, comparing Longinvest 10-2 model versus the Factor Model, where 1.0 would mean total correspondence:

How much difference would this make going backwards? Quite a bit actually:

(What to make of the outlier of 1928? The two models differ by 50% that year, due to the record 48% stock return, but the actual difference is between 3.1% simulated returns for FM versus 0.7% for the 10-2 model--not quite as dramatic as the telltale chart shows.)

In fact, a case could be made for using units of Standard Deviation as the comparison to help normalize rather than telltale charts. Here's a chart showing the difference between 10-2 and Factor Model from AGG, shown in units of AGG's standard deviation:

And we see that there is indeed quite a difference between the two models going backwards, with half a sd or even a full sd difference not uncommon.

Could an even closer fit be had? Just in terms of correlation, substituting Bond 3-1 (3 year bonds sold at maturity) produced superficially better results (see second tab in spreadsheet). And further substituting for LTT a Bond 24-2 (24 year bonds sold a year prior to maturity) or Bond 20-2 for Longinvest's/Simba Bond 30-11 increases the overall correlation with AGG even further, to 0.959:

But visually the telltale doesn't really show that to be as meaningful as one might think; so I ended up just leaving the existing Longinvest/Simba LTT=30-11 and STT=4-2 since I liked the first telltale better.

So what to make of all this? Should the Simba Backtesting Spreadsheet substitute the Factor Model for Total Bond Fund rather than the existing Bond 10-2? Not necessarily. To state the obvious, the constitution of the Total Bond Index has changed over time with corporates representing different degrees of the index. Beta risk is not the same as credit risk. The simplicity of the initial model gets muddied as well. However, given the intuitive appeal of incorporating a little TSM into the simulation when we know TBM has lots of corporates, further investigation is warranted. I've included my spreadsheet if folks want to play around like I did.