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 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