# Short and Sweet question...

Using the following spot rates, what is the price of a three-year bond with annual coupon payments of 6 percent? One-year rate: 4.45% Two-year rate: 5.13% Three-year rate: 6.01%

6/(1.0445) + 6/(1.0513)^2 + 106/(1.0601)^3 100.14

This is a typical “see if there is arbitrage” situation. you discount each CPN payment @ the spot for the appropriate period. you get \$100.14 LETS SAY the market is pricing the bond at 1\$10.23, you have 9c in arbitrage, risk free PROFITS (assuming zero transaction costs). thanks for bringing it up. they did bond arb like this in the 80s, but the markets are too efficient these days for things like this to happen in recurring fashion.

daj, i can’t follow most of the time what you are saying. i am presuming its a good thing for me. How does arbitrage or your 80s theory or zero transaction cost have any relevance in this question

Pepp, Because due to market inefficiency, in the 80s was easier mo make arbitrage buys three annual zero coupon bonds instead of a 3-year bond (or vice versa). Now, due to market technology and efficency, this is very unluckly to happen

Thanks, good to know. Is this information part of curriculum?

I dont think so. But how you create arbitrage YEP.

Arbitrage? of course arbitrage is part of the text:)

Arbritrage yes…but the 80s story not

The question is asking the price of a bond, given 3 different spot rates, for three different years. I don’t see no arbitrage. Can someone please provide the solution.

You are correct Pepp.

This question isn’t about arbitrage; it’s about discounting cash flows. I doubt that in the '80’s you could arb bonds this way anyway. People in the '80’s certainly knew how to price bonds (they did in the 1880’s). STRIPS came out in '85 and I’ll bet the market priced things pretty efficiently the day they came out. Now there were some tax games you could play with zeros then - the investment banks took treasuries and put them in trusts (LYONS, TGRS, etc.) and you didn’t pay tax on accrued interest. I dont know if you could short those trusts, but they were tax advantaged so they were priced differently than coupon bonds.