How One-Period Bonds Pay Face Value Rather Than Purchase Price
Summary
This exchange clarifies the meaning of a one-period bond as a claim to one unit of currency at the next date. The promised payoff is its face value, while the bond's price today can differ from that amount because of interest rates, coupons, market demand, and trading conditions. The payoff is therefore not generally the amount originally paid by the investor.
The responses distinguish a bond's contractual payment from its market price. They note that newly issued bonds may be priced at par in some settings, often by adjusting the coupon, while zero-coupon bills with positive rates sell at a discount and secondary-market bonds can trade above or below par. The explanation assumes the unit payoff is certain and does not address default risk or more complex state-contingent claims.
Key ideas
- A one-period bond promises a unit of currency at the end of the period.
- The bond's payoff is set by its face value, not by the investor's purchase price.
- Interest rates and market conditions can make a bond trade above or below par.
- The unit-payoff interpretation assumes the bond will repay as promised.
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Full text
# What does it mean by "A one period bond is a claim to a unit payoff." from Cochrane? # 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)? ## Answer by Dimitri Vulis (score 3, accepted) https://quant.stackexchange.com/a/49384 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. ## Answer by Kevin (score 3) https://quant.stackexchange.com/a/49383 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...
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