The most comprehensive educational resources for finance

Bootstrapping Spot Rate Curve (Zero Curve)

A spot rate curve, also known as a zero curve refers to the yield curve constructed using the spot rates such as Treasury spot rates instead of the yields. A spot rate Treasury curve is more suitable to price bonds because most bonds provide multiple cash flows (coupons) to the bond holders at different points

Key Rate Duration

Effective duration calculates the approximate change in a bond’s price given a 100 basis point (1%) move in interest rates as part of a parallel shift in the yield curve. When the yield curve shifts in a non-parallel manner, the portfolio’s effective duration cannot be used to estimate the change in portfolio value. Key rate

Yield Curve Construction with Treasuries

The Treasury bond yield curve can be built from several different sources: On the Run Treasuries: This entails plotting the observed yields from the most recently issued Treasuries. On the Run + Selected Off the Run Treasuries: On the run issues may not cover the all time periods needed, particularly for longer maturities, so off

Parallel and Non-parallel Shifts in Yield Curve

Parallel Shift Rates across the maturity spectrum change by a constant amount and the slope of the yield curve remains consistent. Non-Parallel Shifts Twist: The slope of the yield curve becomes flatter (the spread between short and long term yields narrows) or steeper (the spread between short and long term yields widens). Butterfly: Change to

Three Shapes of the Yield Curve

Term Structure of Interest Rates: The term structure of interest rates is the relationship between the spot rate of U.S. Treasury securities and their time until maturing. Yield Curve: The relationship between U.S. Treasury yields and time to maturity. Three Shapes of the Yield Curve Positive Slope: Short term bonds have lower yields than long

Yield Curve Arbitrage

Where can you find the market rates of interest (or equivalently the zero coupon bond prices) for every maturity? This lecture shows how to infer them from the prices of Treasury bonds of every maturity, first using the method of replication, and again using the principle of duality. Treasury bond prices, or at least Treasury