Fixed Income Analysis

Bond Characteristics at Advisory Depth

Fixed-income securities (bonds) are debt instruments that obligate the issuer to make periodic interest payments and return the principal at maturity. For investment adviser representatives, understanding bonds goes far beyond basic definitions. Advisers must evaluate bonds in the context of client portfolios, assess interest rate risk, analyze credit quality, and construct bond allocations that serve specific client objectives such as income generation, capital preservation, and liability matching.

A bond's key characteristics include its par value (face value, typically $1,000), coupon rate (the annual interest rate paid on the par value), maturity date (when the principal is repaid), and issuer credit quality. These characteristics interact to determine the bond's market price and its sensitivity to changes in interest rates, credit conditions, and economic expectations.

Bond Pricing Theorems

Several fundamental relationships govern how bond prices behave. These theorems, articulated by Burton Malkiel, are essential for advisers managing fixed-income portfolios:

1. Bond prices move inversely to interest rates. When market interest rates rise, existing bond prices fall, and vice versa. This is the most fundamental relationship in fixed-income investing.
2. Longer-maturity bonds are more sensitive to interest rate changes than shorter-maturity bonds. A 30-year bond will experience a much larger price change for a given interest rate movement than a 2-year bond.
3. Price sensitivity increases at a decreasing rate as maturity increases. The difference in sensitivity between a 5-year and a 10-year bond is greater than the difference between a 25-year and a 30-year bond.
4. Lower-coupon bonds are more sensitive to interest rate changes than higher-coupon bonds of the same maturity. A zero-coupon bond has the highest interest rate sensitivity of any bond with the same maturity because all cash flow is concentrated at maturity.
5. The price increase from a rate decrease is larger than the price decrease from an equivalent rate increase. This asymmetry is known as convexity and is discussed in detail below.

Yield Calculations

Yield is the return an investor earns from a bond. There are several yield measures, each providing different information. The Series 65 expects you to understand, calculate, and compare these yield measures.

Current Yield

Current yield is the simplest yield measure, relating the annual coupon payment to the bond's current market price:

Current Yield = Annual Coupon Payment ÷ Current Market Price

For a bond with a $50 annual coupon trading at $950: Current Yield = $50 / $950 = 5.26%. Note that current yield does not account for capital gains or losses at maturity, nor does it consider the time value of money. For a discount bond, current yield will always be higher than the coupon rate. For a premium bond, current yield will be lower than the coupon rate.

Yield to Maturity (YTM)

Yield to Maturity is the most comprehensive yield measure and the one most commonly used to compare bonds. YTM represents the total annualized return an investor will earn if the bond is held to maturity and all coupon payments are reinvested at the same rate. YTM accounts for the coupon payments, capital gain or loss (difference between purchase price and par value), and the time value of money.

YTM cannot be solved with a simple formula; it requires iteration or a financial calculator. However, the Series 65 tests your understanding of YTM relationships rather than complex calculations:

• For a discount bond: Coupon Rate < Current Yield < YTM (the investor earns the coupon plus capital appreciation)
• For a premium bond: Coupon Rate > Current Yield > YTM (the investor earns the coupon but loses capital at maturity)
• For a par bond: Coupon Rate = Current Yield = YTM

Yield to Call (YTC)

Yield to Call applies to callable bonds and measures the yield assuming the bond is called at the earliest possible call date. Callable bonds give the issuer the right (but not the obligation) to redeem the bond before maturity, typically at a specified call price (par or a small premium). YTC is calculated the same way as YTM but uses the call date instead of the maturity date and the call price instead of par value.

When a callable bond trades at a premium, YTC is typically lower than YTM because early call would deprive the investor of premium coupon payments over the remaining life. The relevant yield for premium callable bonds is the yield to worst, which is the lower of YTM and YTC. Issuers tend to call bonds when interest rates decline because they can refinance at lower rates.

Yield Spread

A yield spread is the difference in yields between two bonds, usually expressed in basis points (1 basis point = 0.01%). The most common spreads include:

• Credit spread: The yield difference between a corporate bond and a Treasury bond of similar maturity. Wider credit spreads indicate increased perceived risk of default or economic uncertainty.
• Nominal spread: The difference between a bond's yield and the yield on a benchmark Treasury bond of similar maturity.
• Option-adjusted spread (OAS): Adjusts the nominal spread for embedded options (calls, puts). OAS provides a more accurate comparison between bonds with different embedded option features.

Duration

Duration is one of the most important concepts in fixed-income analysis. It measures a bond's sensitivity to changes in interest rates, expressed in years. A bond with a duration of 5 years will experience approximately a 5% price change for every 1% change in interest rates. Duration is essential for advisers managing interest rate risk in client portfolios.

Macaulay Duration

Macaulay duration is the weighted average time to receive a bond's cash flows, where each cash flow is weighted by its present value as a proportion of the bond's total present value (price). It is expressed in years. For a zero-coupon bond, Macaulay duration equals the bond's maturity because there is only one cash flow (at maturity). For coupon-paying bonds, Macaulay duration is always less than maturity because some cash flows are received before maturity.

Modified Duration

Modified duration adjusts Macaulay duration to directly estimate the percentage price change for a given change in yield:

Modified Duration = Macaulay Duration ÷ (1 + YTM/n)

Where n is the number of compounding periods per year (typically 2 for semi-annual coupon bonds). The approximate percentage price change for a bond is:

% Price Change ≈ −Modified Duration × Change in Yield

For example, if a bond has a modified duration of 7 years and interest rates increase by 0.50% (50 basis points), the estimated price decline is approximately 7 × 0.50% = 3.5%. The negative sign indicates that price moves in the opposite direction of yield changes.

Dollar Duration

Dollar duration (also called DV01 or dollar value of a basis point) measures the dollar change in a bond's price for a 1 basis point change in yield. It is calculated as modified duration multiplied by the bond's market value divided by 10,000. Dollar duration is useful for portfolio managers who need to know the absolute dollar impact of interest rate changes on a portfolio rather than the percentage change.

Factors Affecting Duration

• Maturity: Longer maturity = higher duration (more sensitivity to rates)
• Coupon rate: Higher coupon = lower duration (more cash flow received sooner)
• Yield level: Higher yield = lower duration (present values of distant cash flows are reduced more)
• Zero-coupon bonds: Duration equals maturity (highest duration for a given maturity)

Convexity

Convexity measures the curvature of the price-yield relationship for a bond. Duration provides a linear approximation of price changes, but the actual relationship between bond prices and yields is curved (convex). Convexity captures this curvature and improves the accuracy of duration-based price estimates, particularly for large yield changes.

For a bond with positive convexity (which includes all standard non-callable bonds), the price increase when yields fall is larger than the price decrease when yields rise by the same amount. This asymmetry benefits the bondholder: they gain more from falling rates than they lose from rising rates. More convexity is generally better for investors, all else being equal.

Negative convexity occurs with callable bonds and mortgage-backed securities. When rates fall, the issuer is likely to call the bond (or homeowners are likely to refinance mortgages), capping the price appreciation. This means the bondholder captures less of the upside from falling rates while still bearing the full downside from rising rates. Negative convexity is unfavorable for investors.

Credit Analysis

Credit risk is the risk that a bond issuer will fail to make scheduled interest or principal payments. Credit analysis evaluates the likelihood and severity of default and is critical for advisers constructing fixed-income portfolios.

Credit Ratings

The three major credit rating agencies — Moody's, Standard & Poor's (S&P), and Fitch — assign ratings based on an issuer's creditworthiness. Ratings range from highest quality to default:

The dividing line between investment grade and non-investment grade (also called "high yield" or "junk" bonds) is BBB-/Baa3. Many institutional investors (pension funds, insurance companies) are restricted to investment-grade bonds. When a bond is downgraded from investment grade to junk status, it is called a "fallen angel," and the resulting forced selling can cause sharp price declines.

Spread Analysis

Credit spreads widen and narrow in response to economic conditions and market sentiment. During economic expansions and periods of optimism, investors are willing to accept lower credit spreads (tighter spreads) because perceived default risk is low. During recessions and periods of stress, spreads widen dramatically as investors demand more compensation for the increased risk of default. Monitoring credit spread trends helps advisers gauge market sentiment and adjust portfolio positioning.

Yield Curve Analysis

The yield curve plots the yields of bonds with identical credit quality but different maturities. The most commonly referenced yield curve uses U.S. Treasury securities. The shape of the yield curve provides valuable information about market expectations for future interest rates, economic growth, and inflation.

Yield Curve Shapes

• Normal (upward sloping): Longer maturities offer higher yields than shorter maturities. This is the most common shape and reflects the expectation that investors require higher yields for tying up their money for longer periods (the liquidity premium) and expectations of future economic growth and inflation.
• Inverted (downward sloping): Shorter maturities yield more than longer maturities. An inverted yield curve is considered one of the most reliable recession predictors. It occurs when the market expects the Fed to cut rates in the future due to economic weakness, causing long-term rates to fall below short-term rates.
• Flat: Yields are approximately equal across all maturities. A flat curve often signals a transitional period between normal and inverted curves and suggests uncertainty about the economic outlook.
• Humped: Medium-term maturities yield more than both short-term and long-term maturities. This is relatively rare and may occur during periods of market uncertainty.

Interest Rate Theories

Several theories explain why the yield curve takes different shapes:

1. Expectations Theory (Pure Expectations): Long-term interest rates reflect the market's expectation of future short-term rates. If investors expect short-term rates to rise, the yield curve slopes upward. If they expect rates to fall, the curve slopes downward or inverts. This theory does not account for risk premiums and implies that bonds of all maturities are perfect substitutes.
2. Liquidity Preference Theory: Investors prefer shorter-term, more liquid investments and require a premium (the liquidity premium) to hold longer-term bonds. This theory builds on the expectations theory by adding a risk premium that increases with maturity. It explains why the yield curve is normally upward sloping even when rate expectations are neutral, and it is generally considered the most widely accepted theory.
3. Market Segmentation Theory: Different maturity segments of the yield curve are driven by supply and demand from different types of investors. For example, banks prefer short-term bonds, while pension funds and insurance companies prefer long-term bonds. Each segment operates independently, and yield differences reflect the relative supply and demand in each segment rather than expectations about future rates.

Bond Portfolio Strategies

Advisers use several strategies to structure bond portfolios based on client objectives, risk tolerance, and interest rate outlook.

Laddering

A bond ladder involves purchasing bonds with staggered maturities (e.g., 1-year, 2-year, 3-year, 4-year, and 5-year bonds). As each bond matures, the proceeds are reinvested at the longest maturity, maintaining the ladder structure. Benefits include diversification of interest rate risk across the yield curve, a steady stream of maturing bonds providing liquidity, and reduced reinvestment risk because not all bonds mature at the same time. Laddering is one of the most commonly recommended strategies for individual clients.

Barbelling

A barbell strategy concentrates investments at both extremes of the maturity spectrum, holding short-term and long-term bonds but avoiding intermediate maturities. The short-term bonds provide liquidity and reduced interest rate sensitivity, while the long-term bonds provide higher yields. This strategy outperforms a bullet strategy when the yield curve flattens or when short- and long-term rates move favorably.

Bulleting

A bullet strategy concentrates bonds around a single target maturity date. This approach is used when an adviser knows the client has a specific future liability to fund (such as college tuition in 10 years or a retirement date). By concentrating maturities around the target date, the portfolio minimizes reinvestment risk for that specific time horizon. Bullet strategies work well when the yield curve is expected to shift in a parallel fashion.