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Monday, November 22, 2010
The DIY investor needs to become comfortable with the relationship between bond prices and interest rates. Especially today, with rates at historically low levels.
I start one of my intro to macroeconomics classes each semester with the announcement that tonight my students will earn their MBAs. This, of course, is tongue-in-cheek; but it does give a hint to the importance of the concept to be discussed - present value. After all, present value is at the foundation of finance.
I begin by sketching out a problem on the board that involves figuring out how much to pay for an apartment building. There is a stream of rental payments, a need to factor in costs, and the estimating of inflation involved.
Later I stress the similarity to a bond and even to stocks. In fact, it comes to the point where students realize the need to value a future stream of payments is all around us. I jokingly point out that with their MBA they can go out and consult at $600/hour on valuing businesses - not far from the truth.
Before the night is over, though, we get into some mathematics. We talk about compound interest and derive the formula FV = PV(1+r)^t (where FV is future value and PV is present value) and then flip it around to solve for the all important present value PV = FV/(1+r)^t.
I'm a firm believer that students have to get their hands dirty to gain understanding. I have seen too many students over the years who thought they understood concepts until they had to apply them. In other words, it looks easy up at the board. Along these lines, I give them a homework assignment based on a group who won a $1 million lottery. The story is that a bunch of old guys pooled their money and when they showed up for the prize they were told it was $50,000/year for 20 years. The assignment is to calculate the present value of the 20-year income stream using a discount rate of 3% and again using 4%.
This illustrates forcefully the difference between cash in hand and a stream of future payments. It also illustrates why the old guys proceeded directly to court on the grounds of misleading advertising.
The real point of the exercise is to get at how bonds work - it shows, in a fun sort of way, the important idea that the value of a stream of payments moves in the opposite direction of interest rates. In particular, it is why bond prices fall when interest rates rise and bond prices rise when interest rates fall - a concept that is difficult for some investors and students to grasp.
The clever DIYer can extend the exercise to show why longer maturity bond prices are more volatile, the impact of discounting using yields on the yield curve etc.