Hello, Im getting crazy about my misanderstood of bond forward pricing… Suppose a 5 year, $1,000 ZC bond for sale at $700 with RFR = 5% The 5 year forward is F(5) = $700 * 1,05^5 = $893.39 Basically, i will pay $893,39 in 5 years to receive $1,000 in 5 years ??? How could this sorcery be possible?
It’s possible because the $700 price today is absurdly low.
The price should be $783.53.
Where’d you get this stupid problem?
The RFR is 5% but the YTM would be 7,39% because of credit risk for example. I just checked your website and you use quite the same example, but you compute for a shorter forward. If I compute for the expiration forward, we have the same weird result : "Suppose that a 10-year, €1,000 par, zero coupon bond sells for €744.09 (a YTM of 3%). If the (effective) risk-free rate is 2.5%, then the price of a 90-day forward contract on this bond is: F(10) = 744,09 * 1,025^10 = €952,49 Basically, i will pay €952,49 to receive €1000 ! it seems easier to make money as i thought !
Sorry, but your calculations are wrong. One thing is the maturity of the underlying asset (the bond in this case) and other much different the maturity of the forward. You said a forward of 90 days, so it would be 744.09 x 1.025 ^ (90/360) This means I will pay that price for a 10-year bond in 90 days. If in 90 days the bond is trading at higher price, I won; otherwise I lose money.
No . . . you pay €952.49 to receive €1,000 with a probability of 0.95249, and €0 with a probability of 0.04751.
Or have you forgotten about the credit (i.e., default) risk?
Indeed it seems logical to have a discount on the future price for the credit risk that the futures buyer will support during 10 years ! However, what if the RFR was 10% ? F(10) = 744,09 * 1,10^10 = _€_1929.97 € I accept to pay 1929.97 € to get 1000 € in 10 years ? ***Edit*** I just realized it is not possible because if RFR was 10%, then the price of the bond would not be 744,09€ ^^
If RFR is 10 then the YTM will be at least 10%. You can’t assume RFR 10% and YTM 3%.