Book 4_Fixed_READING 57_THE TERM STRUCTURE OF INTEREST RATES_SPOT, PAR, AND FORWARD CURVES Flashcards
Spot rates
are market discount rates for single payments to be made in the future
The no-arbitrage price of a bond
is calculated using no-arbitrage spot rates:
= coupon/(1+S1) + coupon/(1+s2)^2 + … + (coupon + principal)/(1+Sn)^n
Spot curves
- plots spot rates versus maturity
- To interpret the par yield of a bond as a weighted average of the spot rates applying to each individual cash flow of the bond
- Derived from the prices of instruments offering single payments in the future, such as zero-coupon bonds or stripped Treasury bonds.
Forward rates
are current lending/borrowing rates for short-term loans to be made in future periods.
A spot rate for a maturity of N periods
- Is the geometric mean of forward rates over the N periods.
- The same relation can be used to solve for a forward rate given spot rates for two different periods.
To value a bond using forward rates
discount the cash flows at Periods 1 to N by the product of one plus each forward rate for Periods 1 to N, and sum them
The par curve
shows the coupon rates for bonds of various maturities that would result in bond prices equal to their par values.
A forward curve
is a yield curve composed of forward rates, such as 1-year rates, available at each year over a future period.
In an upward-sloping (normal) yield curve environment,
forward rates will be higher than spot rates, which will be higher than par yields
In a downward-sloping (inverted) yield curve environment
forward rates will be lower than spot rates, which will be lower than par yields
In a flat yield curve environment
forward rates will be equal to spot rates, which will be equal to par yields across all maturities
Quick estimates on the yield
- Spot rate is the average of forward rates
- Par rate is the average of spot rates
