## Some Thoughts On Gold, Real Yields, And Inflation

TIPS-style inflation-linked bonds (more properly known as Canadian-style) pay a fixed coupon on a principal amount that varies with the price level. In this way, the real value of the principal is protected (you always get back an amount of principal that’s indexed to the price level, floored in the case of TIPS at the original nominal value), and the real value of the coupon is protected since a constant percentage of a principal that is varying with the price level is also varying with the price level. This clever construction means that “inflation-linked” bonds can be thought of as simply bonds that pay fixed amounts in real space.

I have illustrated this in the past with a picture of a hypothetical “cake bond,” which pays in units of pastry. The coupons are all constant-sized cupcakes (although the dollar value of those cupcakes will change over time), and you get a known-sized cake at the end (although the dollar value of that cake might be a lot higher). That’s exactly what a TIPS bond is essentially accomplishing, although instead of cupcakes you get a coupon called money, which you can exchange for a cupcake. This is a useful characteristic of money, that it can be exchanged for cupcakes.

The beauty of this construction is that these real values can be discounted using real yields, and all of the usual bond mathematics work just perfectly without having to assume any particular inflation rate. So you can always find the nominal price of a TIPS bond if you know the real price…but you don’t need the nominal price or a nominal yield to calculate its real value. In real space, it’s fully specified. The only thing which changes the real price of a real bond is the real yield.

All TIPS have coupons. Many of them have quite small coupons, just like Treasuries, but they all have coupons. So in the cake bond, they’re paying very small constant cupcakes, but still a stream of cupcakes. What if, though, the coupon was zero? Then you’d simply have a promise that at some future date, you’d get a certain amount of cake (or, equivalently, enough money to buy that certain amount of cake).