The Relationship Between the Spot and Forward Rates In general T-year zero, the spot rate is r T-year zero the spot rate is 7>T Infer the forward rate f the interest rate between Tand T rT-rT f Charles cao 11
11 Charles Cao The Relationship Between the Spot and Forward Rates ◼ In general: ◼ T-year zero, the spot rate is r ◼ T * -year zero, the spot rate is r * ◼ T * > T ◼ Infer the forward rate, f , the interest rate between T and T * T T r T rT f − − =
The Zero-coupon Yield curve It is a curve that shows the relationship between the spot rate and maturity The term structure The upward-sloping yield curve The downward-sloping yield curve Charles cao
12 Charles Cao The Zero-coupon Yield Curve ◼ It is a curve that shows the relationship between the spot rate and maturity ◼ The term structure ◼ The upward-sloping yield curve ◼ The downward-sloping yield curve
Treasury yield curve 6 5432 0 13 6 1 yr 2 yr 3 yr 5 yr 7 yr 10 20 momo mo yr yr Source: Wall Street Journal, 11 / 12/2003 Charles cao 13
Treasury Yield Curve 0 1 2 3 4 5 6 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr % 13 Source: Wall Street Journal, 11/12/2003 Charles Cao
Treasury Bond and Treasury Note Futures They are traded on the CBot Treasury bond futures are based on T-bonds with maturities of at least 15 years Long-term contracts Treasury note futures are based on T-notes with maturities of 2, 5 and 10 years Intermediate-term contracts Charles cao 14
14 Charles Cao Treasury Bond and Treasury Note Futures ◼ They are traded on the CBOT ◼ Treasury bond futures are based on T-bonds with maturities of at least 15 years ◼ Long-term contracts ◼ Treasury note futures are based on T-notes with maturities of 2, 5 and 10 years ◼ Intermediate-term contracts
Price quotes of the t-bond T-bonds are quoted in dollars and 32nd of a dollar The quoted price is for a bond with a face value of $100 A price o93-14i931432,or934375 If the face value of the t-bond is $100, 000 the price of the bond is $93,437.50 cash price quoted price accrued interest since last coupon date Charles cao
15 Charles Cao Price quotes of the T-bond ◼ T-bonds are quoted in dollars and 32nd of a dollar ◼ The quoted price is for a bond with a face value of $100 ◼ A price of 93-14 is 93 14/32, or 93.4375 ◼ If the face value of the T-bond is $100,000, the price of the bond is $93,437.50 cash price = quoted price + accrued interest since last coupon date