week 26 Fixed-Income Securities (IV)

Bond Valuation

Pricing of Bonds

• Bonds are priced based on the present value of future cash flows.

• Cash flows consist of:

  • Periodic interest income (coupon payments).

  • Principal (par value) at maturity.

Basic Bond Valuation Model

• Requires:

  • Annual coupon payment (C).

  • Par value (PV_n, usually $1,000).

  • Years to maturity (N).

  • Market yield (discount rate) (r_i).

Semiannual Compounding

• Most bonds pay interest semiannually.

Measures of Yield and Return

• Metrics to assess bond return:

  • Current Yield.

  • Yield to Maturity.

  • Yield to Call.

  • Expected Return.

Current Yield

• Indicates current income relative to market price.

• Calculated based on annual interest income.

Yield to Maturity (YTM)

• Most important measure of return.

• Rate of return if the bond is held to maturity.

• Assumes reinvestment of coupon payments at the YTM rate.

• Internal rate of return on a bond.

• Using Annual Compounding: Trial-and-error method. Calculators/software can help.

• Using Semiannual Compounding: Bond equivalent yield is twice the semiannual yield.

Yield Properties

• Critical assumptions:

  • Bond is held to maturity.

  • Coupon payments are reinvested at the YTM rate.

Finding the Yield on a Zero

• Equations can be used to solve for Yield to maturity of a zero-coupon bond by ignoring the coupon portion of the equations because for a zero, they will of course equal zero.

Expected Return

• Used for bonds traded actively before maturity.

• Rate of return expected over a holding period less than the bond's life.

• Uses estimated market price at the expected sale date.

Valuing a Bond

• Conservative investors focus on YTM for income.

• Aggressive traders calculate expected return for capital gains.