Cash Equivalents and Fixed Income Securities - Bond Yields


Measuring Yield
While the stated (nominal) interest rate on a bond might appear to be the only measure of a bond yield, it is only accurate if you buy a bond at par (or its face value) and hold it until the bond matures. However, many investors buy bonds at prices above or below par, and many sell prior to maturity.
The following measures are used to reflect these circumstances:

  • Yield to Maturity - YTM
    • The return based on the actual purchase price of the bond
    • Takes any premium or discount over par into account and uses the actual time to maturity for the number of compounding periods
    • If an investor buys a bond at a price below its par value (at a discount), then its YTM will be greater than its stated interest rate (also known as its coupon rate).
    • If an investor buys a bond above its par value (at a premium), then its YTM will be lower than its coupon rate.
    • If the bond was purchased at par, the yield to maturity will equal the stated coupon rate.

Example:
For $976 James Smith buys a bond with a face value of $1,000 and a 6% coupon rate. What will his yield to maturity be?

  1. 6%
  2. Less than 6%
  3. More than 6%
  4. Unable to calculate based on given information

Answer: The correct answer is "c". When an investor buys a bond at a discount to its face value, the yield to maturity will exceed the coupon rate.

  • Yield to Call
    • Similar to YTM but uses the call date for the number of compounding periods and incorporates any call premium into the future value

    • A callable bond is one that allows the issuer the right to demand the bond back from an investor prior to maturity. The investor is paid the bond's face value plus a premium to partly compensate the investor for the loss of the future coupon payments on the bond. Typically, the investor must reinvest the proceeds at a lower rate of return than the rate of return earned prior to the call.

    • The YTC on a particular bond usually will be less than its yield to maturity because there are fewer coupon payments and fewer compounding periods.

  • Current Yield
    • Simply, the annual income divided by the market value of the bond
    • If the bond is trading at a premium, the current yield will be less than the nominal yield.
    • If the bond is trading at a discount, the current yield will be greater than the nominal yield.


Current Yield = Annual Income ÷ Market Value


Example:
A bond with a $1,000 face value and a 5.5% coupon rate currently trades at $984. What is its current yield?
Current yield = $55/$984 = .056 or 5.6%.

  • Real interest rate
    • The rate the investor receives after inflation is taken into account; in essence, the real interest rate equals the nominal interest rate minus the inflation rate. (This equation will give you an approximate real interest rate; the precise equation is more complicated but is not needed for the Series 65 exam.)

    • The inflation premium is typically higher for bonds with longer maturities.
Real interest rate = Nominal Interest Rate - Inflation Rate



Exam Tips and Tricks
Consider this sample question:

  1. A client buys a DEF 10% bond at 105. The bond matures in 10 years. What is the current yield?
    1. 10.17%
    2. 9.52%
    3. 9.69%
    4. 9.13%

The correct answer is "b", since current yield is found by dividing the annual interest payment (in this case 10% or $100) by the current market price (in this case 105% or $1,050). Note that bond par values are most often $1,000. Whether or not you know this value, it will not affect the answer, since you can merely divide the coupon in % terms by the price in % terms.

Yield Curves


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