Bonds, Prices, and Interest Rates in Economics

Understand the relationship between bond pricing and present value.
Define the interrelationship among a bond’s price, coupon rate, current yield, yield to maturity, and holding period return.
Explain determinants of bond prices and their fluctuations.
Identify three major types of bond risk: default, inflation, and interest rate changes.

Bonds are instruments that allow governments and private firms to finance operations.
Origin: Concept traced back to kings borrowing for lifestyles and wars; modern bonds invented by the Dutch; refined by the British; introduced to the U.S. by Alexander Hamilton.
Key topics:
- Relationship between bond prices and interest rates.
- Supply and demand in the bond market.
- Risks associated with bonds.

Standard bonds specify fixed payment amounts and payment dates. Key types include:
1. Zero-Coupon Bonds: Promise a single payment on a future date. (e.g. US Treasury bills)
2. Fixed-Payment Loans: Fixed equal payments at regular intervals (e.g. mortgages, car loans).
3. Coupon Bonds: Periodic interest payments and repayment of principal at maturity (e.g. U.S. Treasury Bonds, corporate bonds).
4. Consols: Make periodic interest payments indefinitely without repaying principal.

Example: U.S. Treasury Bills (T-bills): promise to pay $100 at a future date, sold at a discount (e.g. a $100 T-bill selling for $96).
Formula for price of a zero-coupon bond:
P = \frac{F}{(1 + i)^n} where P = price, F = face value, i = interest rate, n = number of periods.
Example calculations:
- For $100 face value:
- 1-year T-Bill price at 5%: P = \frac{100}{(1 + 0.05)} = 95.24.
- 6-month T-Bill price at 5%: P = \frac{100}{(1 + 0.025)} = 97.56.

Definition: Promise to repay principal with fixed payments included.
Value calculated as the present value of all future payments:
PV = \sum_{t=1}^{n} \frac{Payment}{(1 + i)^t}.

Price formula:
P_{Consol} = \frac{C}{i} where C = yearly coupon payment, i = interest rate.

Represents total return on bond investment.
Relates price changes with yield. Key rules:
- When bond prices increase, YTM decreases.
- If bond price equals $100, YTM equals the coupon rate.
- Use formula: YTM = \frac{Coupon Payment + (Face Value - Price)}{Price}.

Current Yield Formula:
\text{Current Yield} = \frac{\text{Coupon Payment}}{\text{Price Paid}}.
Example: Price of a $100 bond at $99 with 5% coupon gives a current yield of 5.05%.

Return from holding a bond before maturity. Calculated as:
Holding Period Return = \frac{Coupon Payment + (Selling Price - Purchase Price)}{Purchase Price}.
Illustrative example of bond selling at different prices before maturity impacts return significantly.

Supply and Demand govern bond prices.
As prices rise, supply increases, while demand decreases. Conversely, lower prices raise demand and decrease supply.

Government borrowing, business conditions, and expected inflation shift supply curve to the right, increasing quantity supplied but decreasing equilibrium price, thus raising yields.

Wealth, economic expectations, perceived risk, and liquidity influence demand. A shift to the right raises equilibrium price and lowers yield.

Risk of issuer failing to pay. Measured through the default risk premium, calculated as the difference between yield to maturity (YTM) and risk-free rate.

Fixed dollar payments can lose purchasing power. Understanding of nominal vs. real interest rates crucial.

Longer-term bonds exhibit greater sensitivity to interest changes. Risk rises with uncertainty around market interest rate movements.

Understanding these concepts provides insight into the bond market dynamics, pricing, and associated risks, which are essential for both investors and borrowers.