Bond valuation and yields are key concepts in fixed income investing. They help investors understand how bonds are priced and what returns they can expect. These tools are essential for making informed decisions in the bond market.

Calculating bond prices involves discounting future cash flows. Yield to maturity measures the total return if a bond is held to maturity. The inverse relationship between bond prices and yields is crucial for understanding market dynamics and investment strategies.

Bond Valuation and Yields

Bond price calculation

• Bond price calculation formula: $P = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2} + ... + \frac{C}{(1+r)^n} + \frac{F}{(1+r)^n}$
  • $P$ represents the bond price, the present value of all future cash flows
  • $C$ denotes the coupon payment, the periodic interest payment made to bondholders (semi-annual for most bonds)
  • $r$ is the periodic interest rate, calculated by dividing the yield to maturity by the number of periods per year (2 for semi-annual coupon payments)
  • $n$ represents the total number of periods until the bond matures (20 for a 10-year bond with semi-annual coupons)
  • $F$ is the face value (par value) of the bond, the amount paid to the bondholder at maturity ($1,000 for most corporate bonds)
• Bond pricing based on the present value of future cash flows discounts each cash flow back to its present value using the yield to maturity as the discount rate
  • Coupon payments are the regular interest payments made to bondholders, typically semi-annually (every 6 months)
  • Face value is the amount paid to the bondholder at maturity, also known as the par value or principal ($1,000 for most corporate bonds)

Yield to maturity determination

• Yield to maturity (YTM) is the total return expected on a bond if held until maturity, expressed as an annual percentage rate
  • Assumes all coupon payments are reinvested at the same YTM rate, although reinvestment rates may vary over time
• YTM calculation involves solving for $r$ in the bond price formula, which requires trial and error or the use of a financial calculator (HP-12C or TI BA II Plus)
  • Goal is to find the discount rate that equates the present value of all future cash flows to the current bond price
• Factors affecting YTM include:
  1. Current bond price: Higher prices lead to lower YTMs, while lower prices result in higher YTMs
  2. Coupon rate: Higher coupon rates generally lead to higher YTMs, all else being equal
  3. Time to maturity: Longer maturities typically result in higher YTMs due to increased interest rate risk
  4. Face value: The amount paid to the bondholder at maturity ($1,000 for most corporate bonds)

Bond price vs yield relationship

• Bond prices and yields have an inverse relationship, meaning they move in opposite directions
  • When bond prices rise, yields fall, as investors are willing to accept lower returns for the same cash flows
  • When bond prices fall, yields rise, as investors demand higher returns to compensate for the lower price
• Reasons for the inverse relationship:
  • Fixed coupon payments: As bond prices change, the fixed coupon payments represent a different percentage of the bond's price (higher price = lower yield, lower price = higher yield)
  • Opportunity cost: Higher yields on newly issued bonds make existing bonds with lower yields less attractive, causing their prices to fall as investors sell them to buy the new, higher-yielding bonds

Current yield and yield to call

• Current yield is the annual coupon payment divided by the bond's current price, expressed as a percentage
  • Formula: $Current Yield = \frac{Annual Coupon Payment}{Current Bond Price}$
  • Provides a simple measure of the bond's annual income return, but does not consider capital gains or losses from price changes
  • Example: A bond with a $60 annual coupon and a current price of $950 has a current yield of 6.32% ($60 / $950)
• Yield to call (YTC) is the yield earned by a bond if it is called (redeemed) by the issuer before maturity
  • Relevant for callable bonds, which give the issuer the right to redeem the bond at a specified call price on or after a specific date
  • YTC calculation is similar to YTM but uses the call date and call price instead of the maturity date and face value
  • Example: A 10-year bond with a 6% coupon, a current price of $1,050, and a call price of $1,020 in 5 years has a YTC of 4.97%
• Implications for bond investors:
  • Current yield is a useful metric for comparing the income generated by different bonds, especially for investors focused on regular income
  • YTC is important to consider when investing in callable bonds, as it may differ from the YTM if the bond is called before maturity, impacting the investor's total return