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Yield Curve

• Describes how a bond’s term to maturity varies based on its yield

• Shape of the yield curve describes the current state of fixed income market

o Upwards slope means bonds with longer maturities pay higher yields

o Downwards slope means bonds with longer maturities pay lower yields

On-the-run vs. Pure Yields

• Most bonds have cash flows that take place over different periods of time

• To calculate the pure yield for a given period of time, we only want the bond to have cash flows

at that exact period of time

• The pure yield curve is imputed by taking government treasuries, zero-coupon bonds and strips

with different maturities and imputing a curve

• Alternatively, an on-the-run yield curve is imputed by taking on-the-run coupon bonds near their

pay values

• These 2 curves can have substantially different values

Yield Curve and Future Rates

• Yield curve can provide info about the market expectations of future interest rate changes

• In equilibrium, we cannot have arbitrage, we need to have equal cash flows between 2

strategies:

o Buying and holding a bond for a certain period of time

o Buying, holding until maturity, and reinvesting in a series of shorter-term bonds over

that same period of time

• Consider two bonds:

o A 2 year zero-coupon bond with a yield of 6%.

o A 1 year zero-coupon bond with a yield of 5%.

• If we want to buy $1,000 in face value of the 2 year bond, it will cost:

𝑃2=1000

(1.06)2= $890.00

• If we invested that $890 into the 1 year bond instead, we would receive the following face value

after 1 year:

890.00 =𝐹𝑉

1.05 ⇒𝐹𝑉 = $934.50

• For there to be no arbitrage in the 2nd year, we must be able to reinvest that $934.50 from the

1st year and earn exactly $1,000 total. For that to happen, the 1-year yield in year 2 would have

to be:

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