Electron wrote:I'm wondering if your first comment above is applicable to a bond mutual fund since it maintains a perpetual maturity. Holding an individual bond to maturity and dealing with the reinvestment of each coupon might look a little different.

No, it doesn't apply to a bond fund--I already made that point--so yes, holding a bond to maturity is completely different. As I said, it eliminates the impact of terminal yield, which is not the case for a bond fund.

Electron wrote:I've been thinking about Table 2.5 and how it was generated. It appears that they made some assumptions that are not clear. I believe the table applies to a fund or index and not an individual bond.

I don't think so. It seems pretty clear that it applies to a 20-year bond with an initial yield of 5%, held for 10 years.

Electron wrote:As an example, let's say the initial yield was 5%, the reinvestment rate was 6%, and the terminal yield was 5%. It's not clear what happened along the way.

I'm not sure, but I don't think it matters. The reinvestment rate tells us all we need to know about what happened along the way in terms of reinvested interest, and the terminal yield tells us all we need to know about impact on price. For this particular chart, I don't think the path matters. I think that's one of the beauties of this presentation.

If we think of the chart as representing a 10-year holding period, and we assume we bought the bond at par with a 5% coupon (the stated initial yield), the terminal yield is the only additional piece of data we need to calculate the price of the bond when we sell it, so that gives us the return component due to the difference in rates between purchase and sale.

We know what the coupon payments are, so we know that component of the return.

We know the average reinvestment rate, so that gives us the interest on interest component of the return.

What I was thinking of was something similar, but trying to respond to some of the criticisms of the applicability of this chart to an intermediate-term bond fund, like "10 years is not enough time for a 20-year bond to recover from an interest rate increase". OK, well let's use a shorter average maturity, closer to that of an intermediate-term bond fund.

A 10-year bond held for 10 years doesn't work because terminal yield is not relevant. I suspect we'd see similar complaints for a 10-year bond held for five years.

So I was just thinking of a simplified model, not necessarily with all the complexities of a bond fund

The first approximation could be a bond-thingy of some sort with a constant maturity of about 5 years or 7 years or whatever (TBM is 7.4 years, IT Treasury is 5.6 years). You start out with current yield, assume coupon=yield at time 0, and assume this gives you the coupon portion of your return. Then the two dimensions of the table give you the other return components over the selected time period. Terminal yield gives you the price change component, and average reinvestment rate gives you the interest-on-interest component.

I guess the major criticism of this model would be that it doesn't capture gradually changing coupon payments that you'd see as a bond fund rolls over it's bonds to ones with different coupon rates. Maybe a second order model could assume that the average coupon during the holding period was the average of the starting yield and the terminal yield.

I assume anything more complicated than this would get into some if not all of the complexities raised by ogd.

Anyway, perhaps this really warrants another post if anyone is interested in pursuing it, since the main purpose of this post has already been achieved. Current yield for the aggregate bond index is a pretty good predictor of following 10-year returns, but it's not perfect, and we don't really know whether it will be higher or lower, or by how much, but it's likely to be in the ballpark.

Kevin