Valuation Factors of Fixed Income Securities

Why fixed-income valuation matters on the Series 66

Fixed income shows up in more Series 66 questions than any single equity topic, and there's a reason: the bond market is the adviser's main instrument for managing portfolio risk, generating income, hedging inflation, and matching a retirement-stage client to the right risk profile. Understanding how bonds are valued is what lets you answer the suitability question correctly — not just "is this a good bond?" but "is this the right bond for this client right now?"

The next five sections lay the framework down brick by brick: bonds as present-value calculations, the four yield measures and when each one applies, duration and convexity, the major bond types and how they're taxed, and the six risk categories every fixed-income investor lives with.

A bond is a present-value calculation

A bond is a promise of fixed cash flows: a run of coupon payments at regular intervals, plus the return of face value (par, usually $1,000) at maturity. The bond's price today is simply the present value of all those future cash flows, discounted at a market-determined yield:

Here r is the market yield per period and n is the total number of periods. That right-hand side is the engine behind every other idea in the chapter — the inverse relationship, the yield hierarchy, duration. Each one is really just asking: what happens to this present value when one input moves?

Three intuitions to anchor:

• The coupon rate is fixed at issuance and never changes. A 5% coupon bond pays $50 per year on a $1,000 face, period, regardless of what happens to the bond's price.
• The yield (r) is the market's required return today. It changes constantly with interest rates, credit perception, and economic conditions. When yields rise, the denominators grow, the present value falls, and the bond's price drops.
• At issuance, the coupon rate equals the market yield, and the bond trades at par. Once issued, market yields move but the coupon doesn't — the price has to adjust instead.

Why prices move inversely to yields

The inverse relationship between bond prices and yields isn't a market custom you have to memorize — it's a direct arithmetic consequence of the PV formula. Push the discount rate r up and every term in the present-value sum shrinks, so the price has to fall.

Make it concrete. A bond pays $50 in coupons a year for 10 years, then returns $1,000 at maturity. Discount that stream at 4% and the price comes out near $1,081 — a premium. Discount the same cash flows at 6% and the price falls to about $926 — a discount. Nothing about the bond changed; only the rate you discounted at did.

This is the single most-tested relationship in all of fixed income. Any time the exam says "rates rose" or "rates fell," the very next thing it cares about is bond prices — and they always move the opposite way.

The Inverse Relationship: Prices and Yields

Start with the most fundamental bond fact of all: when interest rates rise, bond prices fall, and when rates fall, prices rise. That single seesaw is the interest rate risk every fixed-income investor lives with.

Yield Measures

• Coupon rate: The stated annual interest rate on the bond (fixed at issuance)
• Current yield: Annual coupon payment ÷ current market price
• Yield-to-maturity (YTM): Total return if held to maturity, accounting for coupon payments, current price, par value, and time remaining
• Yield-to-call (YTC): Total return if the bond is called at the earliest call date — relevant for callable bonds trading at a premium

The four yield measures

The same bond has four different yields, each answering a different question — and the Series 66 cares about which one you quote in which situation.

Advisers are required to quote a customer the lowest applicable yield — the "yield to worst." For a callable bond trading at a premium, that's almost always YTC, since the issuer has every reason to refinance. For a callable bond trading at a discount, YTM is the lower number, because calling early would actually speed up the investor's return. Knowing which to quote is a frequently-tested advisory-practice point.

The yield hierarchy — premium, par, discount

Tax-equivalent yield — comparing munis and taxables

Because municipal bond interest escapes federal income tax, you can't compare a muni yield against a taxable yield head-to-head — you'd be comparing after-tax to pre-tax. The fix is the tax-equivalent yield (TEY): the pre-tax yield a taxable bond would have to hit to leave the investor with the same after-tax return as the muni.

Run the numbers. A 3.0% muni held by an investor in the 32% federal bracket has a tax-equivalent yield of 3.0% ÷ (1 − 0.32) = 3.0% ÷ 0.68 = 4.41%. In other words, a taxable bond would need to yield 4.41% just to match the after-tax return of that 3% muni. So if comparable taxable corporates yield only 4.0%, the muni actually wins after tax — even though its headline number is lower.

Two layers of tax matter:

• Federal. Muni interest is always federally tax-exempt; corporate and Treasury interest is fully federally taxable. Use the investor's federal marginal rate in the formula.
• State. Most states exempt interest from munis issued within the state (in-state munis are "double tax-exempt" for residents). Out-of-state munis are still federally exempt but state-taxable. For a true comparison, use combined federal + state marginal rate.

The Series 66 always tests the federal-only version. The intuition to carry: the higher the tax bracket, the higher the TEY, and the more attractive munis become — while in a low bracket, munis often lose out to slightly higher-yielding taxables.

Worked example — the three yields on one bond

A 6% coupon, 10-year bond is trading at $920 (a discount). Step through each yield measure to see how they relate.

The pattern Coupon (6.00%) < CY (6.52%) < YTM (~7.10%) confirms the discount-bond hierarchy: yields step up from coupon to YTM. The mechanical reason: a discount bond delivers the coupon stream plus an additional return from price pulling back to par, which the coupon rate by itself doesn't capture.

Duration — the price-sensitivity number

Duration boils a bond's price sensitivity down to one number: how much its price moves for a small change in yield. It's quoted in years, and it reads almost literally:

What the Series 66 wants is the feel for what pushes duration up or down. Three relationships do the work:

This runs straight into portfolio construction. A client who needs to keep interest-rate risk down should hold shorter-maturity, higher-coupon bonds; a client making a directional bet on falling rates wants the opposite — long-maturity, low- or zero-coupon bonds, where duration is highest.

Duration

Duration measures how sensitive a bond's price is to interest-rate changes. Quoted in years, it tells you roughly how much the price will move for a 1% change in rates — a duration of 5 means about a 5% price swing per 1% rate move.

• A bond with a duration of 5 years will lose approximately 5% in value if rates rise 1%
• Longer maturity = higher duration = more price sensitivity
• Higher coupon = lower duration = less price sensitivity
• Zero-coupon bonds have duration equal to their maturity (maximum duration)

Duration factors at a glance

Convexity — the duration approximation's correction

Duration draws the price change as a straight line — a 1% rate rise gives a 5% price drop on a duration-5 bond. But the real price-yield relationship is a curve, not a line, and that curvature has a name: convexity.

For small moves (10–30 basis points), duration is essentially right. Over bigger moves, two systematic biases show up — and both run the same way:

• When rates fall, bond prices rise more than duration predicts. The curve bends up faster than the straight-line approximation.
• When rates rise, bond prices fall less than duration predicts. The curve flattens out compared to the linear approximation.

Both biases land in the bondholder's favor, which is why more convexity is generally a good thing to own. The Series 66 won't make you compute it, but it does test the concept: positive convexity is favorable, and duration on its own understates the gain when rates fall while overstating the loss when they rise.

U.S. Treasury securities

Treasuries are direct obligations of the U.S. federal government, and they set the credit-risk benchmark for the entire bond universe. They come in four flavors, sorted by maturity:

• Treasury bills (T-bills) — 4 to 52 weeks, sold at a discount, no coupons. Covered in detail in the cash-equivalents chapter.
• Treasury notes (T-notes) — 2 to 10 years, pay semi-annual coupons. The "10-year" yield financial media reference is this instrument.
• Treasury bonds (T-bonds) — 20 to 30 years, pay semi-annual coupons. Longest-maturity Treasury issuance.
• STRIPS (Separate Trading of Registered Interest and Principal Securities) — Treasury notes and bonds with the coupon payments stripped off and sold separately. Each piece becomes a zero-coupon Treasury security. Maximum duration for a given maturity; phantom income tax treatment.

Whatever the maturity, every Treasury shares three features the Series 66 likes to test:

• Interest is fully federally taxable but exempt from state and local income taxes — the same rule as T-bills.
• Credit risk is effectively zero for purposes of the exam (and for the entire risk-free-rate framework).
• Quoted in 32nds. A Treasury price of 101-16 means 101 and 16/32 (i.e., 101.50) percent of par, or $1,015.00 on a $1,000 face. Corporate bonds are quoted as decimal percentages of par.

TIPS — Treasury Inflation-Protected Securities

TIPS are Treasury notes and bonds whose principal adjusts with inflation, tracked by the Consumer Price Index (CPI). The coupon rate stays fixed, but the dollar amount of each coupon shifts, because it's figured against that inflation-adjusted principal.

Mechanics:

• Principal rises when CPI rises (the standard case) and falls if CPI falls (deflation). At maturity, the investor receives the higher of the inflation-adjusted principal or the original par.
• Coupon rate is fixed, but coupon dollar amounts grow with inflation because they're percentage-of-adjusted-principal.
• Inflation adjustments are taxable at the federal level in the year accrued, even though the investor doesn't receive the principal until maturity. This "phantom income" feature makes TIPS most attractive in tax-advantaged accounts (IRAs, 401(k)s).
• Real yield, not nominal yield, is the quoted yield. TIPS price relative to ordinary Treasuries reveals the market's inflation expectations: the gap between the nominal-Treasury yield and the TIPS yield is the implied inflation rate.

The Series 66 leans on recognition here — what TIPS do and how they differ from plain Treasuries — more than on mechanics. The suitability point is the one to keep: TIPS fit clients worried about inflation eating their real returns, retirees on fixed-income portfolios most of all.

Municipal bonds

Municipals are debt issued by state and local governments, agencies, and authorities, and their defining feature is tax: interest is exempt from federal income tax, and often from state and local tax too for in-state residents. Two main types, split by what stands behind the bond:

Two more categories are worth a mention:

• Insured municipal bonds — backed by private bond insurance (AGM, Build America Mutual, etc.) that pays principal and interest if the issuer defaults. Pre-2008 these were common; post-2008 the muni insurance industry shrank dramatically and most current issuance is uninsured.
• Bank-qualified municipal bonds (BQ) — small-issue munis (≤$10M annual issuance) that banks can hold with favorable tax treatment. Mostly an institutional concern; the Series 66 may mention but rarely tests.

Corporate bonds — callable and convertible features

Corporate bonds are debt of private companies — semi-annual coupons, par back at maturity, and interest that is fully taxable at the federal, state, and local levels. Beyond the plain-vanilla version, two embedded features can reshape the bond's economics:

Bond tax treatment at a glance

In-state munis are the only category fully exempt from all three layers ("triple tax-exempt") for the issuing state's residents. Treasuries are best for high-state-tax residents who want federally-taxable but state-exempt income. Corporates carry the heaviest tax burden but tend to offer the highest pre-tax yields as compensation.

Accrued interest at the trade date

Bonds pay coupons on a schedule (usually semi-annually), so a buyer who steps in between coupon dates owes the seller a slice of the next coupon — the part the seller earned while holding the bond. That's accrued interest, and it gets added to the price at settlement.

• Corporate and municipal bonds use a 30/360 day count (months treated as 30 days, year as 360).
• Treasury bonds use actual/actual (real calendar days).
• The price quoted is "clean" (without accrued interest); the total paid is "dirty" (with accrued interest).

The buyer gets that accrued interest back at the next coupon date, when the full coupon is paid to whoever now holds the bond. So it's a settlement adjustment, not a true cost — but it makes the amount payable bigger than the quoted price, which catches newer investors off guard. The Series 66 tests recognition over calculation: the trade settles at price plus accrued, and the buyer recovers it on the next coupon date.

Six bond risks the Series 66 tests

Bond Ratings and Credit Spread

Bond ratings size up credit quality — how likely the issuer is to pay on time and in full:

• Investment grade: BBB/Baa and above
• Non-investment grade (high-yield/junk): BB/Ba and below
• Major agencies: Moody's, S&P, Fitch

Credit spread is the yield gap between a corporate bond and a same-maturity Treasury. It's what investors are paid for taking on credit risk:

• Wider spreads = higher perceived credit risk
• Spreads widen during economic downturns (flight to quality)
• Spreads narrow during economic expansions

Credit ratings and credit spread

Credit ratings estimate how likely an issuer is to pay interest and principal in full and on schedule. Three agencies dominate U.S. ratings — Moody's, S&P, and Fitch — and while their notation differs slightly, the categories line up.

The credit spread is the yield difference between a corporate (or municipal) bond and a comparable-maturity Treasury. It's the extra return investors demand for taking credit risk on top of the risk-free rate. Three behaviors to anchor:

• Spreads widen during economic downturns — "flight to quality" pushes investors out of corporates into Treasuries, raising corporate yields relative to Treasuries.
• Spreads narrow during economic expansions as default expectations decline and investors stretch for yield.
• Lower-rated bonds have wider spreads, all else equal — the credit-quality difference is exactly what the spread compensates.