"When the zero curve is upward-sloping, the zero rate for a...

Name: Problem 18, Chapter 4: Options, Futures, and Other Derivatives
Uploaded: 2021-05-10T02:35:19-08:00
Duration: 1 min 7 s
Channel: Sandile Ndlovu
Description: "When the zero curve is upward-sloping, the zero rate for a particular maturity is greater than the par yield for that maturity. When the zero curve is downward-sloping the reverse is true." Explain why this is so.

"When the zero curve is upward-sloping, the zero rate for a particular maturity is greater than the par yield for that maturity. When the zero curve is downward-sloping the reverse is true." Explain why this is so.

Key Concepts

Par Yield

The par yield is the coupon rate that makes the price of a coupon-bearing bond equal to its face value at issuance. It is determined by setting the present value of a series of coupon payments plus the face value repayment to be equal to par, which means it is computed as a weighted average of the applicable zero rates over the bond’s life.

Zero-Coupon Bond Pricing

A zero-coupon bond, which pays no interim coupons and only a single payment at maturity, is priced using its zero rate, the yield to maturity that equates the bond’s single cash flow to its current price. This zero rate is a fundamental building block for understanding the term structure of interest rates and is used as the basis for discounting other cash flows in finance.

Yield Curve Slope

The yield curve, which plots interest rates across different maturities, reflects market expectations and risk conditions. When the zero curve is upward sloping, longer maturities command higher zero rates compared to shorter ones; conversely, a downward sloping curve indicates lower rates for longer maturities. The slope of the yield curve impacts the relationship between the zero rates and the par yields.

Discounting and Weighted Average Effects

The par yield is essentially an average of the zero rates over the periods of a bond’s cash flows. In an upward sloping zero curve, later cash flows are discounted at higher rates, but earlier cash flows are discounted at lower rates, resulting in a par yield that is lower than the zero rate corresponding to the bond’s maturity. Conversely, in a downward sloping curve, the later cash flows face lower discount rates compared to earlier ones, leading the par yield to exceed the zero rate for the same maturity.

Transcript

Please give Ace some feedback