# What does it mean by “A one period bond is a claim to a unit payoff.” from Cochrane?

In the textbook Asset Pricing by John Cochrane, on p. 19 (corresponding table on p. 18), he claims that

A one period bond is of course a claim to a unit payoff."

What does he mean by "a unit payoff"? In my understanding, wouldn't one period bond pay the original price (maybe plus the interest) of the bond back to the investor (i.e. on p. 19, the corresponding cell should be $$p_t$$ instead of 1)?

• Cochrane is a theorist, the bonds he has in mind are Zero Coupon Bonds. He considers coupon bonds are just "packages" of zero coupon bonds. – Alex C Oct 27 '19 at 15:54

A bond repays its notional face value (plus interest sometimes), not the original purchase price. Do not assume the the price you pay for a bond is its face value.

Sometimes a law or a regulation (pretty useless, in my humble opinion:) does require that a bond newly issued in primary market be sold at exactly 100% par price (face value). Then the coupon needs to be tweaked to price the bond exactly to par under the current market conditions and bond invesntor demand.

If the bond pays no coupon (zero-coupon bonds such as T-bills) and the interest rates are positive then of course no one would willingly buy such a bond at face value. It has to be sold at a discount.

Of course once the bond is being bought and sold in secondary market, it is unlikely that it is traded exactly at par.

If regulations don't require the new bond to be sold exactly at par, then the originators will often set the coupon so the price is expected to be close to par, for convenience, but then price at whatever the bond investors will pay - perhaps some people are willing to pay 101? Alternatively sometimes the originators will "tap" an existing issue - issue more bond with the same maturity, coupon, and other terms and conditions as an existing bond, selling at whatever price the market dictates.

• But it is a one-period bond. Wouldn't the principal also be paid back? Also I think it makes a general statement here instead of referring to a specific bond, so why the payoff has to be one unit of currency? – Aqqqq Oct 27 '19 at 15:33
• Yes, the principal (notional, face value) is promised to be repaid in a predictable way (if the bond issuers keep their promise to pay back). We can assume the repayment to be \$1 for convenience. You might then plan, "I need \$X at the end of the period, so I will spend \$P on bonds". The price \$P that you pay to buy the bond in the market is generallly not exactly the same amount that is promised to be repaid (but is usually close, like 99.1%). You sound like you wanted to assume the bond price to always be 1, which isn't right. – Dimitri Vulis Oct 27 '19 at 17:45
• "You sound like you wanted to assume the bond price to always be 1" because I thought that principal is paid back at the end of period 1, since it is a one-period bond. If the bond issuers do not pay the principal back at the end of period 1, when will they pay the principal back? – Aqqqq Oct 27 '19 at 22:03
• The bond investor pays P for the bond and later receives 1 from the bond issuer. – Dimitri Vulis Oct 27 '19 at 22:57
• (Separate question, really) Lots of possible motivations. For example, the bond buyer might hope that a central bank (as economic stimulus) would buy the bond before its maturity at an even higher price . – Dimitri Vulis Oct 29 '19 at 9:52

That simply means that a bond pays one unit of the currency in any state (regardless what happens in the future, i.e. there is no default risk about the payoff of a bond).

So you will receive 1 in the next period (regardless what you paid for it). Of course, today you probably pay less than 1 due to time value of money...

• But it is a one-period bond. Wouldn't the principal also be paid back? Also I think it makes a general statement here instead of referring to a specific bond, so why the payoff has to be one unit of currency? – Aqqqq Oct 27 '19 at 15:32
• @Aqqqq In the academic literature, it is often assumed that a bond is normed, i.e. its principal (nominal) equals 1. So you’re right, the bond does pay back its nominal but it is simply one. – KeSchn Oct 27 '19 at 15:53