Bond Prices and Interest Rates

May 19, 2009

Yesterday I posted a piece about inflation expectations and Treasury yields. I ended with a warning that long-term bonds, not stocks, are the riskiest assets in our portfolios today.

A good friend asked me to review some of the logic in more detail. Here you go:

1) The link between rising interest rates and falling bond prices is not just a theory that might or might not be true. It is the definition of an interest rate, or yield. 

For example, In the chart below, if you pay pay the market price of $0.95 to buy a bond (really just an IOU) that promises to pay you $1.00 in one year then we would calculate its yield as r = ($100-$0.95)/$0.95 = $0.05/$0.95 = 5.26%.

If something changes in the marketplace and people lose interest in owning bonds so that their price falls to $0.90 then we would calculate their yield to be r = ($1.00-$0.90)/$0.90 = $0.10/$0.90 = 11.11%.

SO, SAYING THAT INTEREST RATES GO UP (in this case, from from 5.26% TO 11.11%) IS THE EXACT SAME EXACT STATEMENT AS SAYING THAT BOND PRICES ARE FALLING (in this case, from 95 cents to 90 cents).

2) the interest rate, or yield, (which is just a calculation we make by dividing a contractual interest payment by the price we pay for the security) on all sorts of securities rises and falls with inflation (actually expected inflation). The best way to understand this is to think of the inflation rate as the "interest" you receive from owning a tangible asset like a house or a bar of gold. If you buy it for $100 this year and its prices goes up to $110 in one year (10% inflation) then the "yield" on the asset is $10/$100 = 10% (the increase in value divided by what you paid to buy it.) 

The logic is; inflation goes up => "yield" on real goods goes up => that makes the yield on real goods high compared with the yield on bonds and other securities => that makes people sell bonds to buy more houses and other hard assets to capture some of that extra yield => that pushes hard asset prices up and bond prices down => SO YOU DON'T WANT TO OWN BONDS WHEN THEIR PRICES ARE FALLING.

3) Moral of the story--you don't want to own bonds when people start worrying that inflation, hence interest rates, will go up.

NOTE: There is a reason why I used tangible asset prices (think houses or gold bars) in this example rather than consumer goods prices (like the CPI). The logic of the analysis requires us to compare the total return of two assets after holding both for one year. That works fine for houses and gold bars because they don’t disappear during the year (they have low physical depreciation rates and low storage costs). It does not work well for the haircuts, guitar lessons, or the other services that make of 70% of the market basket of goods used to construct the CPI. They disappear the moment you buy them. It doesn’t work well for popsicles, watermelons, or other nondurable consumer goods either. The implication is that there is no reason at all to expect interest rates and inflation measures with the CPI to move together. Surprise!

Dr. John