Merits and demerits of credit spread measures

As discussed in the previous LOS, a spread quantifies the yield distinction between comparable yet distinct bonds. Spreads pinpoint particular risk factors, each carrying its distinct narrative. We commence with the benchmark spread.

Benchmark /Government “G-spread”

The basic idea behind using spreads is the benchmark spread. It shows the difference in yields among bonds with different credit risk levels. This spread is calculated by keeping the bond duration and maturity as similar as possible. It indicates how much extra yield a bond with credit risk provides compared to a similar bond without credit risk. This spread is called the G-Spread, where ‘G’ stands for ‘government,’ which usually means no credit risk. Another name for this spread is the nominal spread. For example:

$$ \text{Corporate bondYTM} – \text{Treasury bondYTM} = \text{G-spread} $$

Swap Spreads “I-spread”

The I-spread, like the G-spread, measures credit risk premium. Nevertheless, the I-spread comes into play since commonly used government benchmarks might not be perfectly comparable due to liquidity issues. It compares yields between a corporate bond and a similar swap transaction, addressing liquidity concerns since swaps offer more maturity options for precise calculations.

Remember, while the I-spread tries to mimic the G-spread, they differ. I-spreads often reflect the credit quality of big banks and reliable parties, showing different behavior from corporate issuers, especially during market turbulence.

Zero-volatility Spread “Z-spread”

Similar to the internal rate of return idea, the Z-spread is a single value added to each initial spot rate on the curve. This value helps discount future cash flows to reach the bond's current price.

The Z-Spread formula is as indicated below:

$$ PV=\frac {PMT}{(1+z_1+Z)^1} + \frac {PMT}{(1+z_2+Z)^2} +\dots +\frac {(PMT+FV)}{(1+z_N+Z)^N} $$

The bond price (PV) depends on the coupon (PMT) and principal (FV) payments, using benchmark spot rates \((z_1 \dots z_N)\) from the yield curve, along with a constant Z-spread per period (Z) in the denominator, discounted to the coupon date. While more accurate than G-spread or I-spread, this calculation is complex and typically done by practitioners using spreadsheets or analytical models.

Credit default swap (CDS)

CDS basis is the difference between a specific bond's Z-spread and the CDS spread for the same issuer and maturity. It reflects the relationship between bond and CDS market spreads.

A negative basis indicates a broader yield spread than the CDS, while a positive basis suggests a tighter yield spread. Bond pricing, accrued interest, and contract terms contribute to CDS basis disparities. Unlike asset swaps, CDS contracts are settled after a credit event, eliminating interest rate swap exposure. Like the I-spread and asset swap, the CDS basis is a crucial metric for investors managing credit risk through CDS, as further explained later.

Option Adjusted Spread “OAS”

For bonds without embedded options, nominal spreads suffice. Yet, when dealing with bonds containing embedded options or a mix of such bonds, the appropriate metric is the Option Adjusted Spread (“OAS”). Calculated via an interest rate tree, the OAS identifies the uniform amount that aligns with the bond's present market price when added to each tree node.

Comparable to implied volatility in equity options, the OAS starts by assessing the current market price and endeavors to rationalize it through the implied premium required for discounting.

However, the OAS becomes intricate due to the likelihood of the ‘average path’ differing from the actual path. Consider a young baseball player who hit 20 home runs in his first season and 30 in his second. Though his average was 25, this number was never achieved – merely representing a midpoint. Similarly, the OAS faces this challenge. The interest rate tree might display a feasible real-world path or a purely mathematical path that does not reflect actuality.

Below is a summary of the merits and demerits of key fixed-rate bond credit spread Measures:

$$ \small{\begin{array}{l|l|l|l}
\textbf{Spread} & \textbf{Description} & \textbf{Merits} & \textbf{Demerits} \\ \hline
\text{Yield Spread} &{\text{The variance between a} \\ \text{bond’s yield to maturity} \\ \text{(YTM) and the} \\ \text{corresponding} \\ \text{government benchmark} \\ \text{with a similar maturity.}} & {\text{Easy to compute} \\ \text{and notice.} }& { \text{Maturity misalignment,} \\ \text{slope deviation in the} \\ \text{curve, and temporal} \\ \text{inconsistency.}} \\ \hline
{\text{G Spread} \\ \text{(Government} \\ \text{Spread)} } & { \text{Spread over an} \\ \text{interpolated government} \\ \text{bond}} & {\text{Clear and a} \\ \text{maturity-matched,} \\ \text{default-risk-free} \\ \text{bond.}} & {\text{Susceptible to fluctuations} \\ \text{in demand for government} \\ \text{bonds.}} \\ \hline
{\text{I-spread} \\ \text{(Interpolated} \\ \text{spread}} & {\text{Yield differential} \\ \text{compared to the swap} \\ \text{rate with an identical} \\ \text{maturity.}} & {\text{Differential} \\ \text{compared to the} \\ \text{market-based} \\ \text{(MRR) measure,} \\ \text{frequently employed} \\ \text{for hedging or carry} \\ \text{trading.}} & {\text{Single estimate of the term} \\ \text{structure, applicable only} \\ \text{to bonds without} \\ \text{embedded options.}} \\ \hline
{\text{ASW (Asset} \\ \text{swap)} } & {\text{Differential relative to} \\ \text{the market-based (MRR)} \\ \text{rate for fixed-coupon} \\ \text{bonds.}} & {\text{Tradeable spread} \\ \text{transforms the} \\ \text{present bond coupon} \\ \text{into the Market} \\ \text{Replacement Rate} \\ \text{(MRR) plus an} \\ \text{additional spread.}} & {\text{Tradeable spread instead} \\ \text{of a spread measure} \\ \text{aligned with cashflows} \\ \text{applies exclusively to} \\ \text{bonds without embedded} \\ \text{options.}} \\ \hline
{\text{Z-spread} \\ \text{(Zero} \\ \text{volatility} \\ \text{spread)}} & {\text{Yield differential} \\ \text{compared to a} \\ \text{government (or swap)} \\ \text{spot curve.}} &
{\text{Precisely reflects the} \\ \text{term structure of} \\ \text{government or swap} \\ \text{zero rates.}} & {\text{A more intricate} \\ \text{computation restricted to} \\ \text{bonds without embedded} \\ \text{options.}} \\ \hline
{\text{CDS Basis}} & {\text{Yield differential} \\ \text{compared to the CDS} \\ \text{spread with an} \\ \text{equivalent maturity.}} & {\text{The interpolated} \\ \text{CDS spread} \\ \text{compared to the Z-} \\ \text{spread.}} & {\text{Tradeable spread instead} \\ \text{of a spread measure} \\ \text{aligned with cash flows,} \\ \text{applicable only to bonds} \\ \text{without embedded} \\ \text{options.}} \\ \hline
\text{OAS} & {\text{The yield spread} \\ \text{incorporates the Z} \\ \text{-spread along with bond} \\ \text{option volatility.}} & {\text{Offers a broad} \\ \text{comparison for} \\ \text{assessing option-} \\ \text{free bonds with} \\ \text{riskier bonds} \\ \text{containing} \\ \text{embedded options.}} & {\text{Elaborate computation} \\ \text{reliant on volatility and} \\ \text{prepayment assumptions;} \\ \text{bonds with embedded} \\ \text{options are improbable to} \\ \text{consistently yield a} \\ \text{positive Option-Adjusted} \\ \text{Spread (OAS) over time.}}
\end{array}} $$

Floating-Rate Note (FRN) Credit Spread Measures

Unlike fixed-rate bonds, floating-rate notes (FRNs) offer interest coupons with a variable MRR and a typically stable yield spread. While both fixed-rate and floating-rate bonds see price declines with increasing credit risk, it's important to note that they differ in terms of interest rate risk, and we should pay close attention to the credit spread measurements for FRNs.

Recall the formula for valuing a floating rate bond is as follows:

$$ \begin{align*}
PV & = \frac { \left[\frac {(MRR+QM) \times FV)}{m} \right]}{ \left[1+ \frac { (MRR+DM)}{m} \right]^1 } + \frac { \left[ \frac { (MRR+QM) \times FV}{m} \right]}{\left[1+ \frac { (MRR+DM)}{m} \right]^2 } \\ & + \dots \frac {\left[ \frac {(MRR+QM) \times FV}{m} \right]+FV}{ \left[1+ \frac {(MRR+DM)}{m} \right]^N} \end{align*} $$

Note:

$$
\text{Each Interest Payment}= \frac { (MRR+QM)\times FV}{m} $$

Where:

\(QM\)= Quoted margin.

\(FV\)= Par value.

\(m\)= Number of periods per year.

$$ \text{Periodic discount rate per period}=\frac { (MRR+DM)}{m} $$

Where:

\(DM\)= Discount margin.

Note that MRR is based on the current MRR, assuming a flat forward curve. The QM is the yield spread over the MRR set at issuance, compensating investors for the issuer's credit risk. While some FRN bond agreements may adjust the QM in response to changes in ratings or criteria, it's crucial to understand that the QM usually remains fixed until maturity and does not reflect evolving credit risk.

A summary of the relationship between the QM versus DM and an FRN's price on any reset date is as indicated below:

$$ \textbf{FRN Discount, Premium, and Par Pricing} \\
\begin{array}{l|l|l}
\textbf{FRN} & \textbf{Description} & \textbf{QM vs. DM} \\
\textbf{Price} & & \\ \hline
\text{Par} & {\text{The price (PV) of an FRN equals} \\ \text{its future value (FV).}} & {\text{QM}=\text{DM}} \\ \hline
\text{Discount} & {\text{The trading price (PV) of an FRN} \\ \text{is less than its future value (FV).}} & {\text{QM}\lt \text{DM}} \\ \hline
\text{Premium} & {\text{The trading price (PV) of an FRN} \\ \text{exceeds its future value (FV).}} & {\text{QM} \gt \text{DM}}
\end{array} $$

Zero-discount margin (Z-DM)

The zero-discount margin (Z-DM) integrates forward MRR into calculating yield spread for Floating Rate Notes (FRNs). Similar to the concept of the zero-volatility spread for fixed-rate bonds discussed previously, the Z-DM represents the periodic fixed adjustment applied within the FRN pricing model to determine the market price as observed.

The formula is as follows:

$$ \begin{align*}
PV & = \frac { \left[\frac { (MRR+QM) \times FV}{m} \right]}{ \left[1+ \frac { (MRR+Z_{DM})}{m} \right]^1} + \frac { \left[ \frac { (z_2+QM) \times FV}{m} \right]}{\left[1+ \frac {(z_2+Z_{DM})}{m} \right]^2} \\ & +\dots \frac { \left[\frac { (z_N+QM) \times FV}{m} \right]+FV}{ \left[1+\frac {(z_N+Z_{DM})}{m} \right]^N} \end{align*} $$

Similar to the Z-spread for fixed-rate bonds, the Z-DM is influenced by shifts in the forward curve of MRR. The Z-DM will be lower than the DM in an upward-sloping yield curve. Additionally, the Z-DM operates under the assumption of a constant quality margin (QM) and that the FRN will be held until it matures.

A summary of crucial FRN Credit Spread Measures is as follows:

$$ \small{\begin{array}{l|l|l|l}
\textbf{Spread} & \textbf{Description} & \textbf{Merits} & \textbf{Demerits} \\ \hline
\text{QM} & {\text{Spread in Yield} \\ \text{relative to the MRR} \\ \text{of the original FRN.}} & {\text{Denotes the} \\ \text{periodic spread} \\ \text{associated with} \\ \text{FRN cash flows.}} & {\text{Fails to account for} \\ \text{alterations in credit risk} \\ \text{over time:}} \\ \hline
\text{DM} & {\text{Spread in yield over} \\ \text{the MRR required to} \\ \text{price the FRN at par.}} & { \text{Defines the spread} \\ \text{differential from} \\ \text{the Quoted Margin} \\ \text{(QM) while} \\ \text{maintaining a} \\ \text{constant MRR.}} & {\text{Presumes a constant,} \\ \text{unchanging MRR zero} \\ \text{curve.}} \\ \hline
\text{Z-DM} & {\text{Spread in yield} \\ \text{across the MRR} \\ \text{curve.}} & {\text{Integrates forward} \\ \text{MRR rates into the} \\ \text{calculation of the} \\ \text{yield spread.}} & {\text{It involves a more intricate} \\ \text{computation, and the} \\ \text{resulting yield spread does} \\ \text{not align with the cash flows} \\ \text{of the FRN.}}
\end{array}} $$

The Effect of Yield Spreads on Portfolio Returns

In the case of fixed-rate bonds priced above the benchmark rate, there is a notable increase in the roll-down return stemming from coupon income compared to the bond's initial credit spread. Additionally, the roll-down return due to price appreciation surpasses identical government security, primarily because the higher-yielding bond extends the carry-over period. It's essential to acknowledge that this enhanced return is accompanied by higher risk and relies on the assumption of all promised payments being fulfilled, the bond remaining outstanding without default or prepayment, and no call option being exercised.

Please note that effective spread duration (EffSpreadDur) and effective spread convexity (EffSpreadCon) primarily capture changes in the spread rather than changes in the yield curve. ΔSpread is typically defined as an Option-Adjusted Spread (OAS) alteration.

$$ \text{EffSpreadDur}=\frac { (PV_-)-(PV_+)}{2 \times (\Delta \text{Spread})(PV_0)} $$

The above equation is occasionally known as either “spread duration” or “OAS duration,” depending on whether OAS is the underlying spread. Active portfolio managers estimate alterations in bond portfolio values resulting from spread adjustments using market value-weighted averages as replacements for the duration and convexity metrics.

$$
\text{EffSpreadCon}=\frac { (PV_- )+(PV_+)-2(PV_0)}{(\Delta \text{Spread})^2 \times (PV_0)} $$

$$
\text{Duration Times Spread (DTS)} \approx (\text{EffSpreadDur} \times \text{Spread}) $$

A portfolio's Duration Times Spread (DTS) is calculated as the market value-weighted mean of the DTS for each of its constituent bonds. Furthermore, changes in spread within a portfolio are quantified in terms of percentages (\(\Delta\)Spread/Spread) rather than being expressed in absolute basis point terms.

Active credit managers frequently rely on spread duration-based metrics to evaluate the initial effect of spread fluctuations when assessing the incremental impact of credit-based portfolio choices.

The excess spread return for a spread-based bond is calculated as follows:

$$ \text{ExcessSpread}\approx \text{Spread}_0-(\text{EffSpreadDur} \times \Delta \text{Spread}) $$

\(\text{Spread}_0\) represents the initial yield spread, transforming into (\( \frac { \text{Spread}_0}{\text{Periods Per Year}}\)) for holding periods shorter than one year. It's important to note that this computation assumes no defaults during the specified period. While defaults are relatively uncommon, as the likelihood of a default event increases, the anticipated future cash flows from the bond are affected, causing the bond's value to approach the present value of the expected recovery instead.

Acknowledging the distinction in measuring interest rate sensitivity between Floating Rate Notes (FRNs) and fixed-rate bonds is crucial. The regular resetting of MRRs in the FRN's numerator and denominator results in an almost negligible rate duration for FRNs trading at par just before a reset date.

Alterations in spread (either DM or Z-DM) play a central role in influencing price variations when there is a change in FRN yield as follows:

$$ \text{EffRateDur}_\text{FRN}=\frac { (PV_- )-(PV_+)}{2 \times (\Delta MRR)(PV_0)} $$

$$ \text{EffSpreadDur}_{\text{FRN}}=\frac { (PV_- )-(PV_+)}{2 \times (\Delta DM)(PV_0)} $$

Question

Which spread measures are least likely to be derived by adjusting interest rates to justify current market prices?

1. Option Adjusted Spread.
2. Zero-Volatility Spread.
3. I-Spread.

Solution

The correct answer is C.

I-spread: The difference between a corporate bond yield and a similar swap fixed rate.

A is incorrect. OAS: A trial and error spread calculated using an interest rate tree.

B is incorrect: Z-spread: A trial and error spread calculated using a spot rate curve.

Reading 22: Fixed Income Active Management: Credit Strategies

Los 22 (b) Discuss the advantages and disadvantages of credit spread measures for spread-based fixed-income portfolios and explain why option-adjusted spread is considered the most appropriate measure