10. Bonds
Table of Contents
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 bondβs 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 twoyear bond:
$r_1$ = current interest rate on a oneyear bond $E(r_2)$ = Expected future shortterm rate = Oneyear rate, one year from now
$$ (1+y_n)^n = (1+y_{n1})^{n1}(1+f_n) $$
2. Liquidity Preference Theory
To hold longerterm bonds, investors may require a liquidity premium.
 Why?
 Investors in general prefer shortterm bonds, which have higher liquidity.
 May need to sell bonds before maturity
 Longer maturity bonds have higher interest rate risk
 Investors in general prefer shortterm bonds, which have higher liquidity.