I would like to learn some basic information about treasury bonds. The following questions are of interest to me:
- How the coupon rate is determined?
- How the yield is determined?
- What’s the relationship between yield and price?
- The relationship between yield and interest rate?
- From a macroeconomic perspective, what’s the status of the treasury bond market of USA, China, and Japan?
We refer to these lectures.
Treasury Bonds are debt securities issued by the government to finance its operations. They are known for their stability and are key instruments in the financial markets. Below is a structured explanation of the key concepts related to Treasury Bonds.
1. Intrinsic Properties of Treasury Bonds
Treasury Bonds have two intrinsic properties:
Face Value (Principal):
The amount paid to the bondholder at maturity. Typically, the face value is $1,000, though this may vary.Coupon Rate:
The fixed annual interest rate set at the time of issuance, expressed as a percentage of the face value.- Example: A bond with a face value of $1,000 and a coupon rate of 5% will pay $50 in interest annually.
2. How Treasury Bonds Work
When you hold a Treasury Bond, you receive:
- Periodic Coupon Payments: These payments are based on the bond’s coupon rate. Payments are typically made semi-annually.
- Face Value at Maturity: At the end of the bond’s term, the face value is returned to the holder.
Illustration: Bond Payment Timeline
|--------------------|--------------------|--------------------| Maturity
$25 $25 $25 $1,000
(Coupon Payment) (Coupon Payment) (Coupon Payment) (Face Value + Coupon Payment)
3. Market Trading: Price and Yield
Treasury Bonds are traded in the secondary market, and their price and yield vary based on market conditions.
Price: The price of a bond is what investors are willing to pay for it. It may differ from the face value due to changes in interest rates and demand.
- If market interest rates fall below the bond’s coupon rate, the bond price rises (a premium).
- If market interest rates rise above the bond’s coupon rate, the bond price falls (a discount).
Yield: The return an investor earns if they buy the bond at the current price and hold it until maturity.
- Inverse Relationship: Price and yield move in opposite directions. When the bond price goes up, the yield goes down, and vice versa.
4. Calculating Bond Price and Yield to Maturity
The price of a bond is calculated as the present value of all future cash flows (coupon payments and face value) discounted by the yield to maturity (YTM).
Formula:
\[ P = \sum \frac{C}{(1 + YTM)^t} + \frac{F}{(1 + YTM)^T} \]Where:
- \(P\): Price of the bond
- \(C\): Coupon payment
- \(F\): Face value
- \(t\): Each payment period
- \(T\): Total number of periods
Illustration: Bond Pricing
Consider a bond with:
- Face Value (\(F\)) = $1,000
- Coupon Payment (\(C\)) = $50 (5% annual coupon rate, paid semi-annually)
- Yield to Maturity (YTM) = 4% (annualized)
- Maturity = 10 years (20 semi-annual periods)
Using the formula, you calculate the present value of all cash flows to determine the price.
5. Interest Rates and Bond Prices
- Bond prices are influenced by interest rate expectations. When market participants anticipate future interest rate changes, they adjust bond prices accordingly.
- Future Predictions: Because bond prices reflect expected interest rates, they serve as indicators of long-term interest rate trends.
6. Spot Rate vs. Yield to Maturity
- Spot Rate: The yield for a specific period in the future. It applies to zero-coupon bonds, where no intermediate payments are made.
- Yield to Maturity (YTM): The average annual return if the bond is held to maturity, considering all future cash flows.
7. Treasury Bonds as Predictors of Economic Trends
Treasury Bonds are closely watched because their yields provide insights into investor expectations about the economy. The yield curve, which plots the yield of bonds against their maturity, is a key tool for this purpose.
a. Normal Yield Curve (Positive Slope)
- Definition: In a normal yield curve, long-term yields are higher than short-term yields.
- Reason: Investors demand a higher return for lending money over longer periods to compensate for risks such as inflation and uncertainty.
- Economic Signal: Indicates a healthy, growing economy.
Example:
- 2-year Treasury yield: 2.5%
- 10-year Treasury yield: 3.5%
- 30-year Treasury yield: 4.0%
Illustration:
Yield (%)
|
| *
| *
| *
| *
|___________________
1Y 5Y 10Y 30Y
Maturity
Interpretation:
Investors expect stable growth, and the higher yields on long-term bonds reflect a normal expectation of risk and inflation over time.
b. Inverted Yield Curve (Negative Slope)
- Definition: In an inverted yield curve, short-term yields are higher than long-term yields.
- Reason: Investors expect economic slowdowns or recessions, causing them to shift money into long-term bonds for safety. This increased demand for long-term bonds lowers their yield.
- Economic Signal: Often a precursor to a recession. Historically, an inverted curve has predicted recessions in the U.S. with high accuracy.
Example:
- 2-year Treasury yield: 4.5%
- 10-year Treasury yield: 3.0%
- 30-year Treasury yield: 2.5%
Illustration:
Yield (%)
|
| *
| *
| *
| *
|___________________
1Y 5Y 10Y 30Y
Maturity
Interpretation:
Investors expect the economy to weaken in the near term, reducing inflation and interest rates over time.
Last modified on 2025-01-20