# 10. Bonds

## A. Concept Checks

• What is yeild to maturity?

• The discount rate that makes the PV of a bond’s payments equal to its price.

$$\text{Bond Value} = \Sigma^T_{t=1} \frac{\text{Coupon}}{(1+r)^t} + \frac{\text{Par Value}}{(1+r)^T}$$

• Bond prices and YTM are positively or inversely related?

• Inversely related
• What are Premium and Discount bonds?

• Bonds selling above/below par value
• Premium bonds – Bond prices are higher than par value
• Discount bonds – Bond prices are lower than par value
• Bond prices are less sensitive to interest rate if bond has shorter maturity and higher YTM

• An increase in a bond’s YTM results in a smaller price change than a decrease in yield of equal magnitude

## B. Yield Curve

The relation between yields and time to maturity.

• Also called term structure of interest rates.

### 1. Expectations Hypothesis

Long term rates equal cumulative expected future short term rates.

Interest rate on a two-year bond:

$r_1$ = current interest rate on a one-year bond $E(r_2)$ = Expected future short-term rate = One-year rate, one year from now

$$(1+y_n)^n = (1+y_{n-1})^{n-1}(1+f_n)$$

### 2. Liquidity Preference Theory

To hold longer-term bonds, investors may require a liquidity premium.

• Why?
• Investors in general prefer short-term bonds, which have higher liquidity.
• May need to sell bonds before maturity
• Longer maturity bonds have higher interest rate risk
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