Fixed Income Valuation Factors

Each factor answers a different question: duration answers "how sensitive," yield answers "what do I actually earn," rating and spread answer "how risky," and DCF ties them together into a single fair-value estimate.

How Does Duration Work as a Valuation Tool?

Duration is both a bond characteristic and a valuation factor that helps determine fair value by quantifying interest rate sensitivity:

• Portfolio duration = weighted average of individual bond durations
• Longer duration = greater price change per 1% interest rate move
• A portfolio with duration of 7 will lose approximately 7% of its value if rates rise 1%

Advisers adjust portfolio duration based on interest rate outlook:

• Expect rates to rise - shorten duration (reduce price sensitivity)
• Expect rates to fall - lengthen duration (maximize price appreciation)

Immunization = matching portfolio duration to the investment time horizon, neutralizing both interest rate risk and reinvestment risk. If rates rise, bond prices fall but future coupons reinvest at higher rates. If rates fall, bond prices rise but future coupons reinvest at lower rates. Matching duration to the target date is meant to make those two effects offset each other.

Practical example: An adviser managing a bond portfolio for a client who needs funds in 5 years would target a portfolio duration near 5 years, immunizing against interest rate changes.

Exam Tip: Gotchas

• Duration is an approximation, not an exact prediction. It works well for small rate changes (1-2%), but becomes less accurate for large moves because of convexity.
• Zero-coupon bonds have duration equal to their maturity (no interim cash flows to shorten it). This makes them the most price-sensitive bonds for a given maturity.

How Does Maturity Affect Value?

Maturity is the date when the bond's principal is repaid. It directly affects a bond's risk profile and required return:

• Longer maturity = greater price sensitivity to rate changes (but duration is the more precise measure)
• Longer-maturity bonds require higher yields to compensate for greater risk (reflected in a normal yield curve)

Term structure of interest rates (yield curve) shows the relationship between maturity and yield:

• Inverted yield curve is historically a reliable recession predictor
• Yield curve shape reflects market expectations about future interest rates and economic conditions

Think of it this way: The longer you lend money, the more uncertainty you face. More things can go wrong over 30 years than 2 years, so investors demand higher returns for longer commitments.

When Should You Use Yield to Call?

• Annualized return assuming the bond is called at the first call date
• Uses the call price (not par) and years to call (not years to maturity)
• Most relevant when a bond trades at a premium and calling is likely
• Generally lower than yield to maturity (YTM) for premium bonds (shorter time to receive return, plus loss of premium is accelerated)

When to use YTC vs. YTM:

When Should You Use Yield to Maturity?

• Total annualized return if the bond is held to maturity and all coupons are reinvested at the YTM rate
• Accounts for coupon, price gain/loss, and reinvestment
• The most commonly used yield measure for comparing bonds

YTM and pricing relationship:

Think of it this way: The coupon is fixed, so price is the part that adjusts. If new bonds are offering 7.5% and an older bond only pays a 6% coupon, investors will not pay full par for that lower income stream. The older bond's price falls below par until the combination of coupon income plus the built-in gain back to par produces a 7.5% yield to maturity.

The reverse happens when the coupon is above the market's required yield. If a bond pays a 6% coupon when investors only require 4.8%, buyers are willing to pay more than par for the higher income stream. That premium creates a built-in loss back to par at maturity, which pulls the total return down to the 4.8% yield.

How Do the Yield Measures Rank Against Each Other?

The full set of yield measures used to evaluate fixed income securities and how they relate to each other:

Current yield calculation example:

• $1,000 par bond, 5% coupon, trading at $900
• Bond prices are often quoted as a percentage of par rather than in dollars: "trading at 90" or "quoted at 90" means 90% of the standard $1,000 par value, or $900. It is not a literal $90 price.
• Use par value to turn the coupon rate into dollars ($1,000 x 5% = $50), then use the current market price as the denominator for current yield.
• Current yield = $50 / $900 = 5.56% (higher than nominal because price is below par)

Yield hierarchy for a DISCOUNT bond (coupon < market rate):

• Nominal yield < Current yield < YTM < YTC

Yield hierarchy for a PREMIUM bond (coupon > market rate):

• Nominal yield > Current yield > YTM > YTC

Yield hierarchy for a PAR bond (coupon = market rate):

• Nominal yield = Current yield = YTM

Memory Aid: Discount Climbs, Premium Dips

Read the ladder by the comparison signs, not just by the left-to-right order:

• Discount bond: yields climb as you move right: Nominal < Current < YTM < YTC
• Premium bond: yields dip as you move right: Nominal > Current > YTM > YTC
• Par bond: yields stay flat: Nominal = Current = YTM

Think of it this way: For discount bonds, each yield measure adds more return because it accounts for additional gains. For premium bonds, each measure subtracts more because it accounts for additional losses.

Exam Tip: Gotchas

• The yield hierarchy is one of the most heavily tested fixed income concepts. Memorize both directions: Nominal < CY < YTM < YTC for discount; reversed for premium.
• YTC only exists for CALLABLE bonds. Yield to worst is always the LOWEST possible yield.

How Does the Coupon Rate Affect Value?

The coupon rate is the fixed annual interest rate stated on the bond that determines periodic cash flows:

• Higher coupon = lower duration = lower price volatility (more cash flow received sooner reduces sensitivity)
• Lower coupon = higher duration = higher price volatility
• Zero coupon = duration equals maturity (maximum price sensitivity)

A bond's coupon rate never changes after issuance. What changes is the market's required yield, which drives the bond's price above or below par.

Exam Tip: Gotchas

• Higher coupon = LESS price volatility, not more. This is counterintuitive. Larger, earlier cash flows reduce a bond's duration and its sensitivity to rate changes.

How Do You Value Convertible Bonds?

Applies to convertible bonds and convertible preferred stock, securities that can be exchanged for a fixed number of common shares:

Key formulas:

Example: $1,000 par convertible bond, conversion price = $25

• Conversion ratio = $1,000 / $25 = 40 shares
• If stock trades at $30: conversion value = 40 x $30 = $1,200 (conversion is profitable)
• If stock trades at $20: conversion value = 40 x $20 = $800 (conversion is NOT profitable; bond trades on its bond value)

Key characteristics:

• Convertible bonds offer lower coupon rates than equivalent non-convertible bonds (the conversion privilege has value)
• The bond will trade at the greater of its straight bond value (based on coupon/yield) or its conversion value
• When stock price is well below conversion price, the convertible trades like a regular bond (bond floor)
• When stock price is well above conversion price, the convertible trades like equity (tracks the stock)
• Convertible bonds have less downside risk than common stock (bond floor) but less upside than stock (conversion premium)

Forced conversion: Issuers call the convertible bond when conversion value exceeds the call price, forcing holders to convert rather than accept the lower call price. Investors do not lose money; they convert to stock worth more than the call price.

Exam Tip: Gotchas

• Always use par value ($1,000) to calculate conversion ratio, not the current market price. Conversion terms are set at issuance.
• When conversion value EXCEEDS the call price, the issuer will call the bond to FORCE conversion. This is a common exam scenario.

How Do Bond Ratings Affect Value?

Rating agencies (Moody's, Standard & Poor's (S&P), Fitch) assess credit risk (default risk), the likelihood the issuer will fail to make interest or principal payments. Credit ratings directly affect required yield and market price.

• Investment-grade: BBB-/Baa3 or higher; suitable for risk-averse and institutional investors
• High-yield (junk): BB+/Ba1 or lower; higher coupon to compensate for default risk
• Many fiduciary accounts, pension funds, and insurance companies are restricted to investment-grade bonds only
• Ratings assess credit risk only; they do NOT measure interest rate risk, liquidity risk, or market risk

Rating changes affect bond prices:

• Downgrade = price falls, yield rises (investors demand more compensation for increased risk)
• Upgrade = price rises, yield falls (lower risk requires less compensation)
• Investment-grade bonds trade at lower yields (tighter spreads) than high-yield bonds because of their lower default risk

Memory Aid: The dividing line is BBB (S&P) / Baa (Moody's). At or above = investment grade. Below = junk. A downgrade from BBB to BB ("falling angel") can cause a sharp price decline because institutional investors are forced to sell.

What Is a Credit Spread and Why Does It Move?

The credit spread is the yield difference between a bond and a comparable-maturity risk-free Treasury security, expressed in basis points (100 bps = 1%):

• Measures the additional yield investors demand for taking on credit risk
• Wider spread = higher perceived risk
• Narrower spread = lower perceived risk

Credit spreads by rating:

Credit spreads and the economy:

• A corporate bond's required yield has two pieces: the comparable Treasury yield plus the credit spread.

• Those pieces can move in opposite directions. In a recession, Treasury yields may fall as investors buy safe Treasuries, while the credit spread may widen because investors demand more compensation for corporate default risk.

• Example: if the comparable Treasury yield falls from 4% to 3%, but the corporate bond's credit spread widens from 1% to 3%, the corporate bond's required yield rises from 5% to 6%. A higher required yield means a lower corporate bond price, even though Treasury prices are rising.

• Spread duration measures how much a bond's price changes for a 1% change in credit spread

• Credit spreads are a key component of discounted cash flow analysis for bonds

Exam Tip: Gotchas

• During a recession, credit spreads WIDEN even if Treasury yields are falling. This means corporate bond prices can fall even when Treasury prices are rising. Do not confuse interest rate movements with spread movements.

How Does Discounted Cash Flow Analysis Value a Bond?

A bond's intrinsic value is the present value of all future cash flows (coupons + principal) discounted at the required rate of return:

• C = each periodic coupon payment
• FV = face value (principal) repaid at maturity
• r = discount rate (required rate of return)
• n = number of periods to maturity

Only four inputs appear in that equation: the coupon, the face value, the discount rate, and the number of periods. Bond rating is not one of them. A rating is a qualitative credit assessment; it influences the discount rate an investor should demand (a lower rating implies a wider credit spread, which raises r), but it never enters the DCF math directly.

• Required rate of return = risk-free rate + credit spread
• DCF incorporates the time value of money: a dollar received today is worth more than a dollar received in the future
• Higher discount rate → lower present value → lower bond price

Using DCF for valuation decisions:

• If DCF value > market price: bond is undervalued (buy)
• If DCF value < market price: bond is overvalued (sell)
• YTM is the discount rate that sets DCF value = market price

Think of it this way: A bond is simply a stream of future cash payments. DCF asks: "What is that stream of payments worth today, given what I could earn elsewhere?" The answer is the bond's fair price.

Exam Tip: Gotchas

• DCF is the theoretical foundation for all bond pricing. The required rate of return combines the risk-free rate (Treasuries) plus the credit spread for that bond's risk level.
• If DCF value exceeds market price, the bond is undervalued: buy. If it is below market price, the bond is overvalued: sell.

What Should You Check on Exam Day?

• Match the yield to the price: YTC for premium bonds likely to be called, YTM for discount bonds unlikely to be called.
• Memorize the yield hierarchy in both directions and recall that yield to worst is always the lowest of the available yields.
• Remember that a bond's coupon rate is fixed at issuance; only its price and yield move with the market.
• Use par value, never the current market price, when calculating a convertible bond's conversion ratio.
• Know the investment-grade cutoff (BBB-/Baa3) and that ratings measure credit risk only, not interest rate or liquidity risk.
• Separate rate moves from spread moves: a recession can widen credit spreads even while Treasury yields fall.
• Recall that DCF depends on coupon, face value, discount rate, and periods to maturity, and that rating is not a direct input.