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charliebonds,

You wrote, Yes, the example was unfortunate. Subtracting 5% from the nominal YTM returned a value that suggested I had made a mistake with my math.

So let's walk through another example. Let's buy GE's 6.75's of 06/15/32 on 08/24/08 for 102.500. Using Excel's YIELD formula, the nominal YTM would be about 6.5%. If inflation runs 5%, then mere subtraction suggests that the inflation-adjusted YTM would be 1.5%. But if both par and the income-stream are discounted (as I do it), then the adjusted YTM drops to a negative -1.2%.

For short time-frames, the former method is a good-enough approximation. For longer times-frames, it isn't, due to compounding.

Nonsense. Let's assume inflation is 5%. If I loan a friend \$1,000 and they give me \$50/year for 25 years and then return the original \$1,000, have I lost purchasing power on my original investment?

I would say NO - though that answer depends on some assumptions I've made. Naturally I will have lost purchasing power if I just stick the \$50/year in a jar and wait for it all to come back to me. But if I redeploy it at 5%/year (or actually use it for purchases), my purchasing will remain unchanged.

The use or redeployment of that \$50/year income stream is not my friend's responsibility - he's done everything he can to make me whole. The redeployment is my responsibility and I can't just assume I will let the money sit idle - I have to at least assume I can meet inflation (the discount rate) with it. Some analysis functions (such as YTM) also assume you can reinvest the income at the same rate of return as the original investment vehicle. These assumptions may turn out to be unrealistic, but you have to make some assumptions.

In the case of your example, if the reinvestment rate is the same as the original investment, you should get a real annual rate of return of 1.5%. If you assume it will only be the same as inflation, the real rate of return is probably something less than 1.5%, but more than 0%.

BTW, the analysis you're doing is Net Present Value or the NPV() function in Excel. Unfortunately Excel's NPV() doesn't provide you a real rate of return. Instead it provides you the discounted present value of some future income stream. If the NPV of an investment (discounted for inflation) is greater than the present value of the proposed investment, you stand to make a real return. You might notice though that the NPV() of a bond with a 5% YTM, discounted for a 5% inflation rate will give you back it's current par value.

And FWIW, none the math changes just because the investment is for 80 years instead of 20.

- Joel

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