 # Zero Coupon Bonds

Hey guys, Zero coupon bonds always sell below their par value, or at a discount prior to maturity. The amount of the discount may change as interest rates change, but a zero coupon bond will always be priced less than par. Can someone please explain in a little better way as to why zero coupon bonds will always sell at a discount prior to maturity even if the interest rates (market yields) go down?

anupamjain008 Wrote: ------------------------------------------------------- > Hey guys, > > Zero coupon bonds always sell below their par > value, or at a discount prior to maturity. The > amount of the discount may change as interest > rates change, but a zero coupon bond will always > be priced less than par. > > Can someone please explain in a little better way > as to why zero coupon bonds will always sell at a > discount prior to maturity even if the interest > rates (market yields) go down? It’s pretty simple. A ZC offers a single fixed payment at some point in the future. The price at any time prior to maturity is the present value of the single future cash flow, discounted at the required rate of return (i.e. the market yield or market interest rate). Actually, the price of ANY security should be the PV of the expected future cash flows. PV is always less than FV (unless the discount rate is negative, which would be really, really weird). So, price < par value for a ZC.

They pay no coupons and you are discounting one future cash flow, which is the par value e.g. 100 or 1000. Nominal Value/(1+x)^T is less than the Nominal Value if X>0 and T>0

Hmm… A zero could sell at a premium if it had some embedded option like say to convert to stock or if interest rates until maturity were negative (happens sometimes) or some strange tax rule (remember Flower Savings Bonds that allowed you to pass money without estate tax).

I did add x>0 if postive interest rates. Option features would imply the price of a convertible zero coupon would equal = Price of straight zero coupon bond - price of issuer call option on bond (if any) + bondholder option on stock + bond holder put option (if any). Using Black Scholes or some other valuation technique for Stock Option valuation. If interests rates were positive and the bond were putable as well as callable and convertible a premium would need the put and stock options to dominate the negating impacts of the call option on price (over and above the initially discount) and send the price above par.

Are you planning to lend someone cash with negative interest rate? Zero coupon bond trades below par because it has no coupon payment and pays par value at maturity. It is possible for the bond to trade above par if it has option to convert the bond into stock.

I’ve traded Euroyen and repo at negative interest rates. Negative interest rates happen.

If you can answes this question, then you’ll understand w first of all keep in mind a zero coupon bond makes only one payment which is the Par. Now lets assume that Par is \$100: 1) if you buy the bond a 90 you are making a profit of \$10 2) if you buy the bond at \$110 you are loosing \$10 Now let’s assume that the interest rate goes up, you’ll still make \$10 under conditioin one and loose \$10 under condition 2 Assuming the interest rate goes down, you’ll still make \$10 under condition one and loose \$10 under condition 2. Now can you tell me any reason why you will buy a this bond under condition 2? \$10 profit represent a 5 percent interest, if the market rate goes above 5 the bond will trade under 90 percent(the only way for an investor to make profit). If the maket rate goes below 5percent, the bond will trade above 90 but below 100(since it pays 5 percent interest rate). Now keys to understand all this is that, Zeron coupon bond is what is call a PURE DISCOUNT BOND. the amount of money you make on a pure discount bond is Par-purchase price. the Par being fixed the only way to affect the value of the bond is to play with the purchase price. a) If you purchase price is equal to the par you’ll make no money and you’ll loose no money. b) if the pruchasse price is above Par(meaning the bond was traded at premium), you are surely loosing money. Conclusion: Since the first rule of investment is: never loose money, that mean no one will buy go for option 1 and option a, meaning a zero coupon bond will never trade at premium. Hope this help.