Treasury Markets
Kevin Crotty
BUSI 448: Investments
Where are we?
Last time:
- Empirical facts about equities
Today:
- Treasury market basics
- Term structure
- Spot rates
Treasury Securities
Bills
- Bills
- Maturity of 1 year or less (1, 3, 6, 12 months)
- Usually issued as discount securities
- Taxes – exempt from state and local income taxes
- Small denomination – can purchase in $100 increments from Treasury Direct
Bonds and Notes
- Notes
- Maturity between 2 years and 10 years (2, 3, 5, 7, 10 years)
- Coupon securities (semiannual)
- Bonds
- Maturity greater than 10 years (20, 30 years)
- Coupon securities
TIPS and STRIPS
- Treasury inflation protection securities (TIPS)
- Principal is indexed to consumer price index
- Maturities of 5, 10, 30 years
- STRIPS (Separate Trading of Registered Interest and Principal Securities)
- Allows individual component of Treasuries to be traded
- Improves liquidity for zero-coupon Treasury markets
Historical yields
- can pull data from FRED at St. Louis Fed
- 3-month Tbill series
Treasury Curve
Term structure of rates
- Interest rates (yields) of different maturity bonds are generally different
- For instance, 10-year bond may have a different yield than a 2-year note
- The yield curve is the plot of yields as a function of time to maturity
- The term structure of rates is the relation between yields and maturity
Key aspects of the term structure
- Level
- Slope
- Curvature
Historical Yield Curves
Time-series of yields
- What do you notice prior to the shaded recessions?
Some fixed income empirical facts
Size of the market
Stocks, bonds, and gold returns
Spot rate curve
Spot rates
- Spot rates are the discount rates associated with CFs of a particular maturity.
Two methods to get them:
- Use zero-coupon bonds (i.e., Tbills or STRIPS)
- Bootstrap them from coupon bonds
Bond pricing revisited
If z1, z2, …, zT are maturity-specific riskless spot rates, then the bond price is:
P(z)=C/m(1+z1)+C/m(1+z2)2+...+C+FACE(1+zT)T
P(z)=T∑t=1C/m(1+zt)t+FACE(1+zT)T
where
- C/m is the periodic coupon payment
- m is the compounding periods per year
- T is the total number of payments (# years ⋅m)
Spot rates from zero-coupon bonds
- A zero-coupon bond pays no coupons P(zt)=FACE(1+zt)t
- Using traded prices, we can solve for zt zt=(FaceP(zt))1/t−1
Spot rates from coupon bonds
Bootstrapping: method of extracting spot rates from coupon bond prices.
Iterative procedure: 1st solve for z1, then z2 using z1…
To get spot rate zt, we must know z1,z2, …, zt−1: zt=(CFtPV(CFt))1/t−1
PV(CFt)=Pt−∑t−1i=1CFi(1+zi)i
Pt is the price of the coupon bond maturing at time t.
Example
| Bond | Price | Coupon Rate | Maturity | Face Value |
| A | 97.5 | 0% | 0.5 | 100 |
| B | 95 | 0% | 1.0 | 100 |
| C | 955 | 2.5% | 1.5 | 1,000 |
| D | 1,000 | 5.75% | 2 | 1,000 |
Assume semiannual coupon payments and no credit risk.
- Determine the spot rates for the four periods
- What is the fair price of a 2-year 10% coupon bond with a face value of $1,000 if it pays annual coupons?
For next time: Arbitrage
BUSI 448
Treasury Markets Kevin Crotty BUSI 448: Investments