Yield Curves
Yield curves, a graphical representation of the interest rates on debt for a range of maturities, are typically upward-sloping. This means that they show diminishing marginal yield-to-maturity increases at longer tenors, becoming flatter at longer maturities. For instance, the yield curve for U.S. Treasury bonds typically slopes upwards, reflecting higher yields for longer-term investments.
Nominal yields-to-maturity incorporate an expected inflation premium. Therefore, a positively sloped yield curve aligns with market expectations of rising or stable future inflation and relatively strong economic growth. For example, if investors expect inflation to rise in the future, they would demand higher yields for long-term bonds, leading to an upward-sloping yield curve.
Static Yield Curve and Portfolio Management
Static Yield Curve and how a portfolio manager can generate excess returns from a static or stable yield curve can be achieved by increasing risk by adding either duration or leverage to the bond portfolio.
For instance, if we consider the US Treasury yield curve, when it is upward-sloping, longer duration exposure will result in a higher yield-to-maturity over time. This is due to the “repo carry” trade, which is the difference between a higher-yielding instrument purchased (like a 10-year Treasury bond) and a lower-yielding (financing) instrument (like a 3-month Treasury bill). This trade can generate excess returns.
Strategies for Generating Excess Returns
$$ \begin{array}{l|l|l|l}
\textbf{Strategy} & {\textbf{Investment} \\ \textbf{Approach}} & {\textbf{Expected} \\ \textbf{Returns}} & {\textbf{Market} \\ \textbf{Conditions}} \\ \hline
{\textbf{Buy-and-}\\ \textbf{Hold} \\ \textbf{Strategy}} & {\text{Buying bonds with} \\ \text{durations above} \\ \text{the benchmark} \\ \text{and holding them} \\ \text{without active} \\ \text{trading during a} \\ \text{subsequent period.}} & {\text{Higher returns from} \\ \text{incremental duration} \\ \text{if the relationship} \\ \text{between long-} \\ \text{and short-term} \\ \text{yields-to-} \\ \text{maturity remains} \\ \text{stable.}} & {\text{Stable interest} \\ \text{rate} \\ \text{environment} \\ \text{between long-} \\ \text{and short-term} \\ \text{maturities.}} \\ \hline
{\textbf{Rolling} \\ \textbf{Down the} \\ \textbf{Yield} \\ \textbf{Curve}} & {\text{Investing in bonds} \\ \text{to capture not only} \\ \text{the coupon income} \\ \text{but also the} \\ \text{additional returns} \\ \text{due to the} \\ \text{passage of time as} \\ \text{the bond matures} \\ \text{and moves down} \\ \text{the yield curve.}} & {\text{Accumulation of} \\ \text{returns from} \\ \text{coupon income and} \\ \text{the potential sale of} \\ \text{the bond at a} \\ \text{higher price} \\ \text{(lower yield-to-} \\ \text{maturity) at the} \\ \text{end of the} \\ \text{investment} \\ \text{horizon.}} & {\text{Upward-sloping} \\ \text{yield curve and} \\ \text{a stable rate} \\ \text{environment} \\ \text{over the} \\ \text{investment} \\ \text{period.}} \\ \hline
{\textbf{Repurchase} \\ \textbf{Agreement} \\ \textbf{or Repo} \\ \textbf{Trade}} & {\text{Buying a long} \\ \text{-term security} \\ \text{and financing it} \\ \text{with a short} \\ \text{-term loan at a} \\ \text{rate below the} \\ \text{long-term} \\ \text{yield, planning} \\ \text{to sell the bond} \\ \text{and unwind the} \\ \text{repo at the end} \\ \text{of the trade} } & { \text{Earning positive} \\ \text{“repo carry” from} \\ \text{the difference} \\ \text{between the long-} \\ \text{-term yield and the} \\ \text{short-term} \\ \text{financing rate.} } & {\text{Stable or} \\ \text{predictable} \\ \text{interest rate} \\ \text{environment,} \\ \text{favorable for} \\ \text{short-term} \\ \text{loans at rates} \\ \text{below long-} \\ \text{term yields.}}
\end{array} $$
Cash-Based Static Yield Curve Strategies
These strategies are a part of fixed income portfolio management, focusing on the stability of interest rates and the shape of the yield curve. For instance, a more sophisticated approach might involve investing in less liquid and higher-yielding government bonds, such as those that are not in the current issuance cycle. Despite the low portfolio turnover, this strategy can be quite aggressive due to the introduction of liquidity risk.
Buy-and-Hold Strategy
- This strategy might involve investing in less liquid and higher-yielding government bonds, such as US Treasury bonds issued in previous years.
- Although it may seem passive due to the low portfolio turnover, it can be quite aggressive as it introduces liquidity risk.
Price Appreciation
- Benefiting from price appreciation by selling a shorter-dated bond at a premium when rolling down the yield curve depends on a reasonably static and upward-sloping yield curve, similar to the US yield curve in early 2020.
- Under this yield curve scenario, the repo carry will be maintained and will generate excess return due to the reduced cash outlay versus a term bond purchase.
Active managers, such as those at BlackRock or Vanguard, with an investment mandate that extends to the use of synthetic means to increase risk by adding duration or leverage to the portfolio might consider using derivatives-based strategies to increase duration exposure beyond a benchmark target.
Long Futures and Receive-Fixed Swap
- The long futures strategy is similar to rolling down the yield curve, but it relies solely on price appreciation rather than bond coupon income.
- The receive-fixed swap is similar to the cash-based repo carry trade, but the investor receives the fixed swap rate and pays a market reference rate (MRR), often referred to as “swap carry”.
Derivatives Contracts
- Global exchanges, such as the Chicago Mercantile Exchange, offer a wide range of derivatives contracts across swap, bond, and short-term market reference rates for different settlement dates.
- Over the counter (OTC) contracts may be uniquely tailored to end user needs, such as a specific hedge fund’s risk profile.
- The discussion here is limited to futures and swaps and will extend to options in a later section.
Margining and Derivatives
Margining, traditionally confined to exchange-traded derivatives, has now extended to over-the-counter (OTC) derivatives due to the advent of derivatives central counterparty (CCP) clearing. This was a regulatory mandate post the 2008 financial crisis to reduce counterparty risk. Active managers dealing with both exchange-traded and OTC derivatives need to maintain adequate cash or eligible collateral to meet margin or collateral requirements. They also need to incorporate any resulting foregone portfolio return into their overall performance.
Implicit Leverage in Derivatives
Derivatives carry a high degree of implicit leverage as the initial cash outlay for a derivative is restricted to initial margin or collateral, unlike the full price for a cash bond purchase. A minor shift in price/yield can significantly impact a derivative’s mark-to-market value (MTM) compared to the margin posted. This outsized price effect makes derivatives effective tools for fixed-income portfolio management.
Bond Futures
Bond futures are contracts to take delivery of a bond on a specific future date. The changes in the futures contract value mirror those of the underlying bond’s price over time, allowing an investor to create an exposure profile similar to a long bond position by purchasing this contract with a fraction of the outlay of a cash bond purchase. Most government bond futures are traded and settled using the least costly or cheapest-to-deliver (CTD) bond among those eligible for future delivery.
Basis Point Value (BPV) of a Futures Contract
The basis point value (BPV) of a futures contract is determined using the following approximation: \(\text{Futures BPV} \approx \frac {\text{BPV}}{\text{CF}}\), where CF is the conversion factor for the CTD security. For government bond CTD futures with a fixed basket of underlying bonds, the futures BPV simply equals the BPV of an underlying basket of bonds.
$$\text{Futures BPV} \approx \frac{\text{BPV}_{\text{CTD}}}{\text{CF}_{\text{CTD}}}$$
Where:
- \(\text{BPV}_\text{CTD}\) is the Basis Point Value of the Cheapest-to-Deliver (CTD) security
- \(\text{CF}_{\text{CTD}}\) is the Conversion Factor for the Cheapest-to-Deliver (CTD) security
Interest Rate Swaps
An interest rate swap involves the net exchange of fixed-for-floating payments. The fixed rate (swap rate) is derived from short-term market reference rates for a given tenor. The fixed-rate receiver is “long” a fixed-rate term bond and “short” a floating-rate bond. This gives rise to an exposure profile that mimics a “long” cash bond position by increasing duration.
\(\text{Swap BPV} = \text{ModDur}_{\text{Swap}} \times \frac {\text{Swap Notional}}{10,000}.\)
Dynamic Yield Curve
The Dynamic Yield Curve is a crucial concept in understanding the changes in the yield-to-maturity of bonds over time. These changes are reflected in the level, slope, and curvature of rates across different maturities. The primary focus is on how these changes in instantaneous yield-to-maturity affect the expected change in price due to investor’s view of benchmark yields.
For active fixed-income managers who anticipate a divergent rate level view, the primary objective is to position the portfolio in a way that maximizes profit when yield levels decrease and minimizes losses when yield levels increase. This divergent rate level view implies an expectation of a parallel shift in the yield curve.
Since 2007, there has been a general decline in bond yield levels, also known as a bull market. This trend began in late 1981 when the 10-year US Treasury yield-to-maturity peaked at nearly 16%, due to the contractionary US Federal Reserve monetary policy where the short-term federal funds rate was raised to 20% to combat double-digit inflation.
Strategies for Active View on Rates
- Receive-fixed swaps or long futures positions can be used as alternatives to a cash bond strategy for taking an active view on rates.
- Option-free bonds are generally preferred over callable bonds by most fixed-income managers when taking a divergent rate level view, due to their greater liquidity.
- However, an exception arises when portfolio positioning strategies are based on expected changes in interest rate volatility.
Impact of Economic Conditions on Yield Levels
For instance, during the COVID-19 pandemic in 2020, yields reached new lows due to a sharp economic slowdown, leading to additional monetary and fiscal policy stimulus. If analysts predict a strong economic rebound that could increase yield levels, they might aim to mitigate the negative impact of higher rate levels by reducing duration.
Active Portfolio Positioning
An active portfolio can be strategically positioned to minimize downside exposure to higher yields-to-maturity compared to the index. To limit changes to the bond portfolio, the manager may opt for a swap strategy. It’s crucial to note that many active managers prefer using derivatives over short sales to establish a short bond position due to the uncertain cost and availability of individual bonds to borrow and sell short. Derivatives also allow for duration changes without disrupting other active bond strategies within a portfolio.
Portfolio managers often use average duration and yield level changes to estimate bond portfolio performance in broad terms. However, these approximations are only reasonable if we assume a parallel yield curve shift.
Divergent Yield Curve Slope View
The yield curve, a graphical representation of interest rates on debt across various maturities, can exhibit different slopes under diverse economic conditions. The slope of the yield curve can significantly fluctuate due to changes in monetary policy, growth expectations, and inflation, affecting yields across the term structure differently.
Yield Curve Slope Changes
A steepening yield curve implies that long-term interest rates are rising faster than short-term rates, while a flattening yield curve indicates a decreasing difference between long-term and short-term interest rates.
Bond portfolio managers often employ a barbell strategy to prepare their portfolios for yield curve slope changes. This strategy involves holding positions in both short-term and long-term securities, which may move in opposite directions.
The barbell strategy is effective for positioning a portfolio for yield curve slope changes or twists. Managers can combine long or short positions in either maturity segment to capitalize on expected yield curve slope changes. These changes may be duration neutral, net long, or short duration, depending on the anticipated steepening or flattening of the curve.
In some cases, the investment policy statement may permit managers to use bonds, swaps, and/or futures to achieve this objective. However, it’s crucial to note that not all strategies are cash neutral. The focus here is solely on portfolio value changes due to yield changes, ignoring any associated funding or other costs.
Yield Curve Steepener Strategies
Yield curve steepener strategies aim to profit from an increase in the yield curve slope. This can be achieved by combining a “long” position in a shorter-dated bond with a “short” position in a longer-dated bond. For example, an active manager might purchase a 2-year Treasury bond and sell a 10-year Treasury bond, both priced at par, to benefit from yield curve steepening with a net zero duration.
Establishing a Rate View
The different scenarios that can affect the yield curve and how they impact fixed-income manager strategies. It also explains how to calculate portfolio duration and BPV.
Bull Steepening Scenario
- This scenario occurs when short-term yields-to-maturity fall more than long-term yields-to-maturity. It’s often seen when the central bank lowers benchmark rates to stimulate economic activity during a recession.
- For instance, during the 2008 global financial crisis, the UK gilt yield curve experienced bull steepening as the Bank of England cut interest rates to stimulate the economy.
Bear Steepening Scenario
- This scenario happens when long-term yields-to-maturity rise more than short-term yields-to-maturity. It can occur when there’s an increase in long-term rates due to higher growth and inflation expectations, while short-term rates remain unchanged.
- An analyst might expect the next central bank policy change to be a monetary tightening to curb inflation in this scenario.
Impact on Fixed-Income Manager Strategy
Expectations of bull or bear steepening will influence the strategy of an active fixed-income manager. For example, if a manager anticipates a bull steepening, they might increase their position in 2-year long Treasury bonds by $50 million to capitalize on an expected greater decline in short-term yields-to-maturity.
Yield Curve Flattening
Yield curve flattening involves an anticipated narrowing of the difference between long-term and short-term yields-to-maturity.
There are two basic variations of yield curve flattening.
The yield curve is a graphical representation of the interest rates on debt for a range of maturities. It can flatten due to monetary policy actions influenced by changing growth and inflation expectations. A real-world example of this is a bear flattening scenario, which typically follows a bear steepening move. This move is often seen when policymakers respond to rising inflation expectations and higher long-term rates by raising short-term policy rates.
During periods of high market uncertainty, investors often sell higher risk assets and buy default risk-free government bonds in a flight to quality. This behavior often contributes to bull flattening, where long-term rates fall more than short-term rates.
Implementing Flattener Strategies
Flattener strategies can be implemented using a barbell strategy. This strategy reverses the exposure profile of a steepener, which involves a “short” short-term bond position and a “long” long-term bond position. For instance, if an investor expects the government yield curve to flatten over a certain period, they may choose a duration neutral flattener using available government zero-coupon securities.
The initial portfolio Bond Price Value (BPV) close to zero indicates that parallel yield curve shifts will have little effect on portfolio value. However, the short 2-year and long 10-year trades position the manager to profit from a decline in the current spread between 2- and 10-year yields-to-maturity.
After a certain period, the portfolio may experience changes due to factors such as a decline in economic growth and inflation expectations. The return of the portfolio is comprised of rolldown return and yield changes.
Rolldown Return in Zero-Coupon Bonds
Our focus is on the concept of Rolldown Return, particularly in relation to zero-coupon bonds. These bonds are distinctive as they typically appreciate over time, assuming constant rates and a positive yield-to-maturity. However, when yields-to-maturity are negative, the bond’s premium amortization often leads to a negative rolldown return.
\(\Delta\) Price Due to Benchmark Yield Changes
Understanding how benchmark yield changes affect price is crucial. For instance, consider a scenario where the yield difference declines from 69 basis points (bps) to 43 bps, primarily due to a 24 bp decrease in the 10-year yield-to-maturity. It’s important to note that the Excel DURATION and MDURATION functions return a #NUM! error for negative yields-to-maturity.
Divergent Yield Curve Shape
The yield curve shape, also known as curvature, explains the relationship between short-term, medium-term, and long-term yields-to-maturity across the term structure. For instance, consider the US Treasury yield curve which plots the yields of US Treasury notes of varying maturities. The butterfly spread, a measure of this relationship, is typically positive as the difference between short- and medium-term rates is usually greater than that between medium- and long-term rates.
Changes in yield curve curvature can be influenced by several factors, separate from rate level or curve slope changes. The segmented markets hypothesis provides one explanation, suggesting that different market participants face unique regulatory or economic constraints. For example, the Federal Reserve’s quantitative easing policy, which involves purchasing Treasury securities at specific maturities, could impact the volatility of the butterfly spread.
Yield Curve Curvature Strategy: The Butterfly Strategy
The butterfly strategy is a common yield curve curvature strategy. It involves combining a long bullet with a short barbell portfolio (or vice versa) to take advantage of expected yield curve shape changes. The short-term and long-term bond positions of the barbell form the “wings,” while the intermediate-term bullet bond position forms the “body” of the butterfly.
In bond portfolio management, an active manager might foresee an increase in the butterfly spread due to a decrease in 2- and 10-year yields-to-maturity and an increase in the 5-year Treasury yield-to-maturity. To capitalize on this, the manager might implement a combined short (5-year) bullet and long (2-year and 10-year) barbell strategy, similar to how a hedge fund manager might adjust their portfolio based on market predictions.
Portfolio Positions and Duration
Despite the sum of portfolio positions indicating a net “short” bond position, the strategy can be confirmed as duration neutral. This can be done by either adding up the position Basis Point Values (BPVs).
If 2- and 10-year Treasury yields-to-maturity fall by 25 bps each and the 5-year yield-to-maturity rises by 50 bps, the portfolio performance can be estimated by multiplying each position BPV by the respective yield change. The formula for this calculation is:
Butterfly Spread Changes
The portfolio gain in this example coincides with an increase in the butterfly spread from -50 bps to +100 bps. The specific view of an active manager on how the yield curve shape will change will dictate the details of the combined bullet and barbell strategy. This can be seen in both the negative butterfly view and a positive butterfly, which indicates a decrease in the butterfly spread due to an expected rise in short- and long-term yields-to-maturity combined with a lower medium-term yield-to-maturity.
Yield Curve Volatility Strategies
The subject of Yield Curve Volatility Strategies revolves around the significance of volatility in active fixed-income management, specifically in the realm of option-only strategies. These strategies, although playing a minor role in overall yield curve management, are crucial in markets like the United States. Here, a large portion of outstanding fixed-income bonds, such as asset-backed securities, have embedded options. Investors often use these cash bond positions with embedded options more frequently than stand-alone options to manage volatility.
For instance, as of 2019, about 30% of the Bloomberg Barclays US Aggregate Bond Index was made up of securitized debt, which primarily includes bonds with embedded options. The purchase of a bond call (put) option provides an investor the right, but not the obligation, to buy (sell) an underlying bond at a pre-determined strike price.
An active manager’s decision between purchasing or selling bonds with embedded call or put options versus an option-free bond with similar characteristics depends on expected changes in the option value and whether the investor is “short” volatility (i.e., has sold the right to call a bond at a fixed price to the issuer), as in the case of callable bonds, or “long” volatility (i.e., owns the right to sell the bond at a fixed price to the issuer), as for putable bonds.
Effective Duration and Convexity
Effective duration and convexity are the relevant summary statistics when future bond cash flows are contingent upon interest rate changes. The formulas for Effective Duration (EffDur) and Effective Convexity (EffCon) are as follows:
$$ \text{EffDur} = \frac{(PV_-) – (PV_+)}{2 \times (\Delta \text{Curve}) \times (PV_0)}$$
$$ \text{EffCon} = \frac{(PV_-) + (PV_+) – 2 \times (PV_0)}{(\Delta \text{Curve})^2 \times (PV_0)}$$
Yield Curve Volatility Strategies
Yield curve volatility strategies are a set of financial strategies that are often constrained by the availability of liquid callable or putable bonds. However, there are several stand-alone derivatives strategies that provide the investor with the right, but not the obligation, to adjust portfolio duration and convexity based on an interest rate-sensitive payoff profile. These strategies are typically used in the bond market.
Interest rate put and call options are typically based on a bond’s price, not its yield-to-maturity. For instance, if an investor purchases a bond call option for a 10-year US Treasury bond, they have the right, but not the obligation, to acquire the bond at a pre-determined strike price. This adds convexity to the portfolio and will be exercised if the bond price appreciates beyond the strike price. Conversely, a purchased bond put option benefits the owner if prices fall beyond the strike prior to expiration.
Sale of Bond Put and Call Options
Selling a bond put or call option limits an investor’s return to the up-front premium received, in exchange for assuming the potential cost of exercise if bond prices fall below or rise above the pre-determined strike. The option seller must post margin based on exchange or counterparty requirements until expiration.
An interest rate swaption involves the right to enter into an interest rate swap at a specific strike price in the future. This instrument grants the contingent right to increase or decrease portfolio duration. A purchased payer swaption, for instance, might be bought by a manager to benefit from higher rates using an option-based strategy.
Options on Bond Futures Contracts
Options on bond futures contracts are liquid exchange-traded instruments frequently used by fixed-income market participants to buy or sell the right to enter into a futures position. Long option, swaption, and bond futures option strategies are commonly used.
Key Rate Duration for a Portfolio
The key rate duration, also known as partial duration, is a crucial concept in portfolio management. It measures the sensitivity of a portfolio to changes in interest rates at specific maturity points along the yield curve. This tool is used to evaluate changes in the yield curve level, slope, and curvature. The sum of key rate durations equals the effective duration of the portfolio.
Key Rate Duration Calculation
The key rate duration is calculated using the formula:
$$ \text{KeyRateDur}_k = \frac{1}{PV} \times \frac{\Delta PV_k}{\Delta r_k}$$
Where:
- \(\text{KeyRateDur}_k\): Key rate duration for the kth maturity point.
- \(\Delta PV_k\): Change in portfolio value for the kth maturity point.
- \(\Delta r_k\): Change in the kth key rate.
- \(PV\): Total portfolio value.
The sum of all key rate durations equals the effective duration of the portfolio:
$$\sum_{k=1}^{n} \text{KeyRateDur}_k = \text{EffDur},$$
Shaping Risk
Key rate durations help identify “shaping risk” for a bond portfolio. This refers to a portfolio’s sensitivity to changes in the shape of the benchmark yield curve. By breaking down a portfolio into its individual duration components by maturity, an active manager can pinpoint and quantify key exposures along the curve.
Key Rate Duration Differences
Comparing the key rate or partial durations for specific maturities across different portfolios can provide more detailed information regarding the exposure differences across maturities. For instance, negative differences for certain maturities indicate that one portfolio has lower exposure to short-term rates than another. Conversely, a large positive difference in a certain tenor shows that one portfolio has far greater exposure to yield-to-maturity changes for that tenor.
Practice Questions
Question 1: Yield curves are a crucial tool for investors and active managers in understanding the market expectations and positioning their portfolios. An upward-sloping yield curve typically indicates certain market expectations and influences the strategies of active managers. If an active manager’s forecasts align with the current yield curve, what kind of strategies will they likely choose to implement in their portfolio management?
- Strategies that are consistent with a volatile or changing yield curve.
- Strategies that are consistent with a static or stable yield curve.
- Strategies that are inconsistent with the current yield curve.
Answer: Choice B is correct.
If an active manager’s forecasts align with the current yield curve, they will likely choose to implement strategies that are consistent with a static or stable yield curve. An upward-sloping yield curve typically indicates that the market expects interest rates to rise in the future. If an active manager agrees with this expectation, they would likely implement strategies that take advantage of this anticipated increase in interest rates. This could include investing in short-term bonds that will mature before interest rates rise, or in floating-rate notes whose interest payments will increase as rates rise. The manager might also avoid long-term fixed-rate bonds, whose prices would fall as interest rates rise. By aligning their strategies with the current yield curve, the manager is positioning their portfolio to benefit from the expected changes in market conditions.
Choice A is incorrect. Strategies that are consistent with a volatile or changing yield curve would be appropriate if the manager expected the yield curve to change significantly in the future, not if their forecasts align with the current yield curve. These strategies might involve investing in instruments that benefit from changes in interest rates, such as options on bonds or interest rate swaps.
Choice C is incorrect. If the manager’s forecasts align with the current yield curve, it would not make sense for them to implement strategies that are inconsistent with the current yield curve. Doing so would likely result in poor performance, as their investments would not be positioned to benefit from the expected changes in market conditions.
Question 2: A portfolio manager is considering a “buy-and-hold” strategy for his bond portfolio. This strategy involves buying bonds with duration above the benchmark without active trading during a subsequent period. Under what condition would this strategy reward the manager with a higher return from the incremental duration?
- If the yield curve is downward-sloping
- If the relationship between long- and short-term yields-to-maturity remains stable over this period
- If the yield curve is flat
Answer: Choice A is correct.
A “buy-and-hold” strategy for a bond portfolio would reward the manager with a higher return from the incremental duration if the yield curve is downward-sloping. In a downward-sloping yield curve, long-term interest rates are lower than short-term rates. This is also known as an inverted yield curve. When a portfolio manager buys bonds with a duration above the benchmark, they are essentially buying long-term bonds. If the yield curve is downward-sloping, these long-term bonds will have lower yields than short-term bonds. However, as time passes and the bonds move towards maturity, their yields will increase (since bond prices and yields move inversely). This increase in yield will result in a higher return for the portfolio manager. Therefore, a downward-sloping yield curve is the condition under which a “buy-and-hold” strategy would reward the manager with a higher return from the incremental duration.
Choice B is incorrect. If the relationship between long- and short-term yields-to-maturity remains stable over this period, the return from the incremental duration would also remain stable. This is because the yield curve would not change, and therefore the yields on the long-term bonds in the portfolio would not increase. As a result, the portfolio manager would not earn a higher return from the incremental duration.
Choice C is incorrect. If the yield curve is flat, this means that short-term and long-term interest rates are the same. In this case, buying bonds with a duration above the benchmark would not result in a higher return from the incremental duration. This is because the yields on the long-term bonds would not increase over time, as they would in a downward-sloping yield curve. Therefore, a flat yield curve is not the condition under which a “buy-and-hold” strategy would reward the manager with a higher return from the incremental duration.
Glossary
- Yield Curve: A graphical representation of the interest rates on debt for a range of maturities.
- Yield-to-Maturity (YTM): The total return anticipated on a bond if it is held until maturity.
- Active Management: The use of a human element, such as a single manager, co-managers or a team of managers, to actively manage a fund’s portfolio.
- Repo Carry: The difference between the yield of a higher-yielding instrument purchased and a lower-yielding (financing) instrument.
- Liquidity Risk: The risk that an investor will not be able to sell an asset quickly enough to prevent or minimize a loss.
- Derivatives: Financial instruments whose value is derived from the value of another asset.
- Implicit Leverage: The risk exposure that exceeds the initial investment.
- Barbell Strategy: A strategy that involves combining positions in both short-term and long-term securities.
- Portfolio Convexity: A measure of the curvature in the relationship between bond prices and bond yields.
- Conversion Factor: A factor used to adjust the futures price to reflect the cheapest to deliver security.
Portfolio Management Pathway Volume 2: Learning Module 5: Yield Curve Strategies;
LOS 5(b): Formulate a portfolio positioning strategy given forward interest rates and an interest rate view that coincides with the market view.
LOS 5(c): Formulate a portfolio positioning strategy given forward interest rates and an interest rate view that diverges from the market view in terms of rate level, slope, and shape.
LOS 5(d): Formulate a portfolio positioning strategy based upon expected changes in interest rate volatility.
LOS 5(e): Evaluate a portfolio’s sensitivity using key rate durations of the portfolio and its benchmark.