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## Yield Curve Risk

We know that the bond prices are sensitive to changes in interest rates. When interest rates increase, the bond prices fall and vice versa. A bond’s maturity also influences its price sensitivity to interest rate changes. When we are looking at a single bond, measuring the interest rate risk (sensitivity) is relatively easier because we

## 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

## LIBOR Swap Rate Curve

The London Inter-bank Offered Rate (LIBOR) is the U.S. dollar borrowing rate for high quality banks among one another, outside the U.S. Swap Rates: The fixed interest rate in a swap contract where two parties have agreed to exchange fixed rate and floating rate payments based on a notional principal. LIBOR is commonly used as

## 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

## Understanding Yield Curve

The yield curve refers to the relationship between the interest rates and the time to maturity of a debt. For example, if we plot the interest rate offered by U.S. Treasury for different maturity debt, what we will get is the Yield Curve. The yield curve will have the maturity on the X-axis, and interest