Fixed Income Characteristics

These characteristics work together, not in isolation. A callable, zero-coupon municipal bond combines four separate risk profiles at once, and the exam tests whether you can layer them correctly rather than recall each one alone.

How Are Different Bonds Taxed?

Different bond types have different tax treatment:

Municipal bond tax exemptions:

• Double-exempt: Federal + state tax exempt if the investor resides in the issuing state
• Triple-exempt: Federal + state + city tax exempt in certain jurisdictions (e.g., New York City residents holding NYC munis)
• Private activity bonds may trigger the Alternative Minimum Tax (AMT)

Zero-coupon bonds and Original Issue Discount (OID):

• Zero-coupon bonds create annual taxable income even though no cash is received (phantom income)
• OID bonds are issued below par; the discount is accreted and taxed as ordinary income annually
• De minimis exception: if the total discount is under 0.25% of the redemption price for each full year to maturity, the OID is treated as zero rather than accreted annually
• This makes zero-coupon bonds poor choices for taxable accounts but excellent for tax-deferred accounts (IRAs, 529 plans)

Market discount bonds:

• Bonds purchased in the secondary market below par
• The discount is taxed as ordinary income at sale or maturity (not capital gains)
• The same de minimis threshold applies: below 0.25% per full year to maturity, the market discount is treated as zero and any gain is a capital gain instead

Premium amortization:

• Investors who buy bonds above par may amortize the premium to reduce taxable interest income annually
• For municipal bonds, amortization is mandatory

Taxable Equivalent Yield (TEY):

• Compares tax-exempt municipal bond yields to taxable bond yields
• Formula: TEY = Tax-exempt yield / (1 - marginal tax rate)
• Example: 3% muni yield for an investor in the 37% bracket = 3% / (1 - 0.37) = 3% / 0.63 = 4.76% TEY
• Higher tax bracket = greater benefit from tax-exempt bonds
• When a muni is also state-tax exempt, add the state rate to the federal rate in the denominator

Exam Tip: Gotchas

• Zero-coupon bond holders owe tax on phantom income EVERY YEAR even though they receive NO cash until maturity. This makes zero-coupon bonds poor choices for taxable accounts but excellent for tax-deferred accounts (IRAs, 529 plans).
• Market discount bonds are taxed as ordinary income, not capital gains. Do not confuse secondary market discount with OID; both are ordinary income above the de minimis threshold, and both drop to capital gain treatment below it.

How Liquid Is a Bond?

Liquidity is the ease of buying or selling a bond without significantly affecting its price:

Factors affecting bond liquidity:

• Issue size - larger issues are more liquid

• Credit quality - higher-rated bonds are more liquid

• Maturity - shorter maturities are generally more liquid

• Age - newly issued ("on-the-run") bonds are more liquid than older ("off-the-run") bonds

• Illiquid bonds trade at a wider bid-ask spread, increasing transaction costs

• Liquidity risk = the risk of being unable to sell a bond quickly at a fair price

Exam Tip: Gotchas

• Municipal bonds are the least liquid major bond type. They trade in a fragmented market with thousands of issuers, so investors may face wider bid-ask spreads and difficulty finding buyers.

Who Gets Paid First in a Liquidation?

In the event of issuer bankruptcy or liquidation, bondholders are paid before equity holders:

• Secured bonds have a claim on specific assets (real estate, equipment)
• Debentures are backed only by the issuer's general creditworthiness
• Subordinated debentures are paid after all senior debt is satisfied
• Bondholders have no ownership rights (no voting), but have priority over stockholders in liquidation

Memory Aid: Think "Debt before equity, secured before unsecured." Even subordinated debenture holders are paid BEFORE any equity holders (including preferred stockholders) in liquidation.

How Do Call and Put Features Work?

• Callable bond: Issuer has the right to redeem the bond before maturity at a specified call price (typically par + a call premium)
• Issuers call bonds when interest rates fall to refinance debt at lower rates (same concept as mortgage refinancing)
• Call protection period: A set number of years during which the bond cannot be called (e.g., 10-year bond with 5-year call protection)
• Call premium: Amount above par the issuer pays when calling (e.g., call at 102 = $1,020 per $1,000 bond); declines as the bond approaches maturity

Impact on investors:

• Callable bonds carry reinvestment risk - when called, investors must reinvest at lower prevailing rates
• Callable bonds offer higher coupon rates than comparable non-callable bonds to compensate for call risk
• Price compression - callable bond prices are capped near the call price when rates fall (unlike non-callable bonds that rise freely). This is also called negative convexity
• Yield to call (YTC) is the relevant yield measure when a bond is trading above the call price

Puttable bonds (opposite of callable):

• Give the bondholder the right to sell the bond back to the issuer at par before maturity
• Beneficial when interest rates rise - investor can put the bond back and reinvest at higher rates
• Puttable bonds offer lower coupon rates than comparable bonds (the put feature benefits the holder)

Exam Tip: Gotchas

• Callable bonds benefit issuers, not investors. Issuers call bonds when rates fall. The bond's price will NOT rise significantly above the call price because the issuer will simply call it (price compression / negative convexity).
• For a premium callable bond likely to be called, use YTC (not Yield to Maturity (YTM)) as the relevant yield, since it gives the more conservative, worst-case estimate of return.

How Do Coupon and Zero-Coupon Bonds Differ?

Coupon bonds:

• Pay fixed semi-annual interest payments
• Price fluctuates with interest rates but less than zero-coupon bonds
• Higher coupon = lower duration = lower price volatility

Duration is not just "time until maturity." It is the weighted-average time to receive the bond's cash flows. A higher-coupon bond sends more cash back to the investor earlier, so less of its value depends on the final principal payment. That shorter weighted-average wait lowers rate sensitivity.

Zero-coupon bonds:

• Pay no periodic interest
• Purchased at a deep discount to par value; investor receives full par value at maturity
• Return comes entirely from the difference between purchase price and par
• Examples: T-Bills, Treasury STRIPS, zero-coupon corporate bonds
• Duration equals years to maturity (maximum sensitivity to interest rates)
• Greatest price volatility of any bond type
• No reinvestment risk (nothing to reinvest) but highest interest rate risk
• Treasury STRIPS and zero-coupon corporate bonds are subject to phantom income taxation (the discount is accreted and taxed as ordinary income every year, even though no cash is received)
• T-Bills mature in a year or less, so an individual holder's discount is ordinary income recognized at sale or maturity, not accreted annually the way a multi-year zero-coupon instrument is
• Best suited for tax-deferred accounts or for matching a specific future liability (immunization)

Think of it this way: A zero-coupon bond locks you into one rate for the entire holding period. If rates rise, you are stuck with the lower implied rate and cannot reinvest along the way.

Exam Tip: Gotchas

• Zero-coupon bonds have no reinvestment risk but the highest price volatility. These seem contradictory but both are true: nothing to reinvest (no coupons), but maximum sensitivity to rate changes (duration equals maturity).
• A zero-coupon bond's duration EQUALS its maturity. A 20-year coupon bond always has duration LESS than 20 years because coupon payments return value before maturity.
• T-Bills are zero-coupon by structure but not taxed like STRIPS. Because a T-Bill matures within a year, its discount is ordinary income at sale or maturity, not multi-year phantom income accreted annually the way Treasury STRIPS and zero-coupon corporate bonds are taxed.

What Is Duration and How Does It Work?

Duration measures a bond's price sensitivity to changes in interest rates, expressed in years. It is the weighted average time to receive all of a bond's cash flows (coupons + principal).

Types of duration:

Key duration relationships:

• Zero-coupon bond: duration = maturity (maximum duration for a given maturity)
• Coupon bond: duration is always less than maturity

Duration formula (approximate price change):

• % price change = roughly -duration x change in yield (in percentage points)
• Example: Bond with duration 7, rates rise 1% - price falls approximately 7%

Convexity (supplemental to duration):

• Measures the curvature of the price-yield relationship
• Duration alone underestimates price increases when rates fall and overestimates price decreases when rates rise
• Positive convexity (non-callable bonds) - prices rise faster than they fall for equal rate changes; this benefits the bondholder
• Negative convexity (callable bonds, mortgage-backed securities (MBS)) - price upside is capped because the issuer will call when rates fall
• Convexity matters most for large interest rate changes

Exam Tip: Gotchas

• Modified duration does NOT account for embedded options (call/put features). For callable bonds, you MUST use effective duration. A callable bond's effective duration is SHORTER than its modified duration because the call compresses the bond's life when rates fall.
• Higher coupon = lower duration (counterintuitive). More cash flow received sooner reduces a bond's sensitivity to rate changes.

What Is Accrued Interest?

When a bond trades between coupon payment dates, the buyer owes the seller accrued interest: the interest the bond has earned since the last coupon date but has not yet paid out.

• The buyer pays the seller the bond's quoted (clean) price plus accrued interest at settlement
• The seller earned that interest by holding the bond, so the buyer compensates the seller for it up front
• The buyer then collects the full next coupon payment, which recovers the accrued interest paid at purchase

Exam Tip: Gotchas

Accrued interest is separate from the bond's quoted price. If a question describes a bond trading "plus accrued interest," it is describing the normal purchase price on a settlement date between coupon dates, not an extra fee or a red flag.

How Are Bonds Priced at Par, Premium, and Discount?

The inverse relationship: Bond prices and yields move in opposite directions:

• When market rates rise, existing bonds with lower coupons become less attractive; prices fall (discount)
• When market rates fall, existing bonds with higher coupons become more attractive; prices rise (premium)

Memory Aid: See-Saw

Picture a see-saw with rates on one end and bond prices on the other. When rates go up, prices go down. When rates go down, prices go up. The two ends always move in opposite directions.

Premium bonds:

• Premium is amortized over the life of the bond, reducing cost basis toward par
• Example: an investor buys a $1,000 par bond for $1,080. That extra $80 premium is gradually written down. If the bond is held to maturity, the adjusted basis ends at $1,000 because that is what the investor will receive back.
• At maturity, the bondholder receives par (less than purchase price), so the premium is a built-in loss of principal offset by above-market coupon income

Discount bonds:

• Discount is accreted over the life of the bond, increasing cost basis toward par
• Example: an investor buys a $1,000 par bond for $920. That $80 discount is gradually added to basis. If the bond is held to maturity, the adjusted basis ends at $1,000 because the investor receives par.
• At maturity, the bondholder receives par (more than purchase price), so the discount is a built-in gain

Cost basis here means adjusted basis, not the original trade price frozen forever:

• The investor still paid $1,080 or $920 in cash.
• The accounting/tax basis changes because each period assigns part of the total return to coupon income, premium amortization, or discount accretion.
• For a premium bond, part of each above-market coupon is treated as recovery of the extra $80 paid, so adjusted basis walks down.
• For a discount bond, part of the eventual $80 gain is recognized over time, so adjusted basis walks up.

How the pull toward par looks over time:

Market rates can still push a bond's market price up or down before maturity. The par-convergence idea means that, as the maturity date gets closer, the remaining premium or discount has less time left to be absorbed. If the issuer pays as promised and the bond is held to maturity, the final redemption amount is par.

Bond price quotation:

• Corporate bonds: quoted as a percentage of par (e.g., 98.5 = $985)
• Treasury notes and bonds: quoted as a percentage of par in 32nds (e.g., 98-16 = 98.50% = $985); agency bonds use the same 32nds convention
• Treasury bills: quoted on a discount yield basis, not as a price
• Municipal bonds: serial bonds are quoted in terms of yield (basis points); term bonds ("dollar bonds") are quoted as a percentage of par

Exam Tip: Gotchas

• Bond prices and interest rates move in OPPOSITE directions. This is the single most important fixed income concept. If you see "rates rise," think "bond prices fall" and vice versa.
• Every bond converges to par at maturity. Premium bonds lose value over time (amortization); discount bonds gain value over time (accretion).
• T-bills are quoted on a discount yield basis, not as a dollar price or percentage of par like other Treasury securities. Do not apply the 32nds convention to T-bills.

What Risks Do Fixed Income Investors Face?

Interest rate risk vs. reinvestment risk:

• These two risks work in opposite directions
• When rates rise: bond prices fall (interest rate risk) BUT reinvestment income increases
• When rates fall: bond prices rise BUT reinvestment income decreases (reinvestment risk)
• Duration matching (immunization) balances these two opposing risks

How duration matching works:

• Match the bond portfolio's duration to the investor's time horizon
• If rates rise, the portfolio's market value falls, but coupons can be reinvested at higher rates
• If rates fall, the portfolio's market value rises, but coupons are reinvested at lower rates
• When duration and time horizon are matched, the price effect and reinvestment effect are designed to offset each other by the target date

Exam Tip: Gotchas

• Interest rate risk and reinvestment risk are INVERSELY related. A bond with HIGH interest rate risk (long-term, low-coupon) has LOW reinvestment risk, and vice versa.
• Zero-coupon bonds have the HIGHEST interest rate risk but ZERO reinvestment risk (no coupons to reinvest).

What Should You Check on Exam Day?

• Match tax treatment to bond type: Treasuries are state-exempt, munis are federally exempt, corporates are fully taxable, and OID/market discount below the 0.25% de minimis threshold escapes ordinary-income treatment.
• Confirm the liquidation order (secured, unsecured, subordinated, preferred, common) and that all bondholders rank above all stockholders.
• Read call and put features from the issuer's or holder's perspective: issuers call when rates fall, holders put when rates rise.
• Remember that a zero-coupon bond's duration equals its maturity, while a coupon bond's duration is always shorter.
• Use effective duration, not modified duration, whenever a call or put feature is embedded.
• Keep the price/yield see-saw straight: rates up means prices down, and every bond still converges to par at maturity.
• Know which quotation convention applies: percentage of par for corporates, 32nds for Treasury notes/bonds and agencies, discount yield for T-bills, and yield or percentage of par for munis depending on serial versus term structure.