Bonds and Interest Rates
Bonds and Interest Rates: Comprehensive Study Notes
Understanding Bonds: Fundamentals and Key Terms
/
Bond Definition: A debt contract representing an interest-only loan. This means the borrower (issuer) pays interest periodically and repays the principal (face value) at maturity.
Example: An AMR.GF bond with a coupon, maturity on , non-callable, a CCC+ S&P rating, and a price quote of on approximately . This implies a bond with specific characteristics relevant to its valuation.
Face Value (Par Value, F):
The principal amount promised to be paid to the bondholder at maturity.
Quoted bond prices are typically based on a face value of . However, for corporate bonds, the actual face value is usually .
Coupon Percent Rate (c):
The stated annual interest rate on the bond, usually set at the time of issue.
Often, the coupon rate is chosen to be equal to the yield to maturity at the time of issue, meaning the bond sells at par.
Coupon Payment (C):
The dollar amount of interest paid per year.
Calculated as the coupon percent rate multiplied by the face value: .
Number of Coupon Payments per Year (m):
Determines the frequency of interest payments.
for annually paid coupons.
for semiannual coupons, which is common for corporate bonds.
Maturity Date (T):
The specific date on which the face value of the bond must be repaid to the bondholder.
represents the number of years remaining until this repayment date.
Yield to Maturity and Bond Valuation
Yield to Maturity (y):
The total return an investor expects to receive if they hold the bond until maturity and it does not default.
It is the discount rate used to calculate the present value of all future bond payments (coupons and face value).
Represents the market's required return for bonds with comparable risk and maturity.
Typically quoted as an Annual Percentage Rate (APR), also known as Bond Equivalent Yield (BEY).
Similar to the coupon rate, at issue, the yield to maturity is often equal to the coupon rate.
Bond Value (B):
The present value of all future cash flows from the bond, which consist of an annuity of coupon payments and a single lump-sum payment of the face value at maturity.
Expressed as: .
When using a financial calculator or present value formulas, the following variables are used:
(total number of coupon payments)
(the current bond price/value)
(the coupon payment per period)
(the face value repaid at maturity)
(the yield to maturity per period)
Inverse Relationship between Bond Prices and Yields: As market interest rates (yields) increase, the present value of a bond's future cash flows decreases, leading to a fall in bond prices. Conversely, as yields decrease, bond prices rise.
Discount, Par, and Premium Bonds
Discount Bonds:
Sell for less than their par value: B < ext{Face}.
This occurs when the bond's coupon rate is less than the prevailing yield to maturity in the market (c < y).
Examples include zero-coupon bonds (which pay no periodic interest and technically have a coupon rate of ), T-Bills (pure discount, zero-coupon bonds), and US Savings Bonds.
Bonds Selling at Par:
Sell for exactly their par value: .
This happens when the bond's coupon rate is equal to the market's yield to maturity ().
Premium Bonds:
Sell for more than their par value: B > ext{Face}.
This occurs when the bond's coupon rate is higher than the prevailing yield to maturity (c > y).
Example: An SKS.GF bond with a coupon rate and a maturity on had a yield to maturity of on roughly . Since the coupon rate () was significantly higher than the yield to maturity (), this bond would have been selling at a premium.
To calculate the present value (PV) for such a bond, the same financial calculator variables are used: , , , , and then solve for .
Bond Values Over Time
Convergence to Par: As a bond approaches its maturity date, its market price tends to converge towards its par value.
Smooth Approach (if yields are constant):
For a Premium Bond (c > y), the bond's price will gradually decrease over time, moving from above par down to the par value at maturity.
For a Discount Bond (c < y), the bond's price will gradually increase over time, moving from below par up to the par value at maturity.
A bond originally issued at Par () will maintain its par value if yields do not change until maturity.
Interest Rate Risks
Price Risk:
The risk that changes in market interest rates will cause bond prices to fall.
Impact of Interest Rate Increases: When interest rates rise, bond prices fall because existing bonds with lower fixed coupon rates become less attractive compared to new bonds offering higher rates.
Sensitivity Factors:
Maturity: Longer-term bonds have higher price risk than short-term bonds because their cash flows are discounted over a longer period, making them more sensitive to interest rate changes.
Coupon Rate: Bonds with lower coupon rates have higher price risk than those with higher coupon rates. This is because a larger proportion of their total return comes from the principal repayment at maturity, which is discounted more heavily over time, making them more like zero-coupon bonds in their sensitivity.
Reinvestment Rate Risk:
The risk that income generated from a bond (coupon payments) will have to be reinvested at a lower interest rate than the bond originally offered, leading to a reduction in total return.
Impact of Interest Rate Decreases: When interest rates fall, coupon payments received must be reinvested at these lower rates.
Sensitivity Factors:
Maturity: Long-term bonds tend to have higher reinvestment rate risk than short-term bonds because they generate coupon payments for a longer duration, providing more opportunities for reinvestment at potentially lower rates.
Coupon Rate: Bonds with higher coupon rates have higher reinvestment rate risk than those with lower coupon rates because they generate larger periodic cash flows that need to be reinvested.
Characteristics of Bonds Affecting Required Yields
Investors demand higher yields for bonds with characteristics that imply higher risk or less favorable terms. Here are some key characteristics:
Registered vs. Bearer Bonds:
Registered Bonds: Ownership is recorded by the issuer or its agent; payments are sent directly to the registered owner. These are more common today.
Bearer Bonds: Ownership is not recorded; physical possession of the bond certificate determines ownership, and payment is made to whoever presents the coupon.
Secured versus Unsecured Bonds:
Secured Bonds: Backed by specific assets.
Collateral Bonds: Secured by financial securities (e.g., stocks, other bonds).
Mortgage Bonds: Secured by real property, typically land and buildings.
Unsecured Bonds: Not backed by specific assets.
Debentures: Unsecured corporate bonds.
Notes: Typically short to medium-term unsecured debt.
Senior vs. Junior Subordinated Debt:
Senior Debt: Has priority over other debts in the event of liquidation.
Junior Subordinated Debt: Lower priority in claim to assets during liquidation, thus higher risk and often higher yields.
Sinking Fund Provisions or Balloon Payments:
Sinking Fund: An account managed by the bond trustee for early bond redemption, reducing default risk by requiring the issuer to retire a portion of the bonds periodically.
Balloon Payment: A large payment (often the full principal) due at the end of the loan term, differing from a sinking fund where payments are staggered.
Protective Covenants:
Provisions in the bond indenture designed to protect bondholders' interests, such as restrictions on dividend payments, further borrowing, or asset sales. More protective covenants generally imply lower risk and thus lower required yields.
Credit Quality (S&P Ratings):
Ratings agencies (e.g., S&P, Moody's, Fitch) assess the default risk of bonds.
Yields are highly sensitive to credit ratings.
Investment Grade: AAA, AA, A, BBB (Lower default risk, lower yields).
Speculative (Junk) Grade: BB, B, CCC, CC, C, D (Higher default risk, higher yields).
Callable Bonds vs. Non-Callable Bonds:
Callable Bonds: Give the issuer the right to repurchase (call) the bond before maturity, usually at a specified call price. This is beneficial to the issuer if interest rates fall, allowing them to refinance at a lower rate. Consequently, callable bonds generally offer higher yields to compensate investors for this call risk.
Call Provisions: Can vary based on how early the bond can be called, and the call premium (additional amount paid above par).
Put Bonds vs. Non-Put Bonds:
Put Bonds: Give the investor the right to sell the bond back to the issuer before maturity, usually at par. This is beneficial to the investor if interest rates rise or the issuer's credit quality deteriorates. Put bonds therefore offer lower yields than comparable non-put bonds.
Convertible Bonds vs. Non-Convertible Bonds:
Convertible Bonds: Can be exchanged for a specified number of shares of the issuer's common stock. This equity feature offers potential upside to investors, so they typically offer lower yields than non-convertible bonds.
Income Bonds vs. Non-Income Bonds:
Income Bonds: Coupon payments are contingent on the issuer's earnings. If the company does not earn enough, it may not pay interest. This makes them riskier and typically requires higher yields.
Floating Rate Bonds vs. Fixed Rate Bonds:
Floating Rate Bonds: Coupon payments adjust periodically based on some market interest rate index (e.g., LIBOR, Treasury rates). This reduces interest rate risk for investors.
With a Collar: Some floating rate bonds have a