Liability- Based Strategies

Consider a portfolio manager at a defined benefit pension plan with a PBO (Projected Benefit Obligation) of $2.57 billion. The effective duration of this obligation is calculated to be 9.35, resulting in a BPV (Basis Point Value) of liabilities as follows:

PBO = $2.57 billion Effective Duration = 9.35 BPV of Liabilities (BPVL) = $2,402,950

The plan assets amount to $3.07 billion, consisting of 60% equity and 40% bonds. The manager decides to hold a laddered bond portfolio composed of one-to-five-year Treasury and investment-grade corporate bonds. While this portfolio doesn't perfectly match the cash flows of the liabilities, it offers high liquidity and can be sold to meet near-term plan distributions. The duration of these bonds is only 2.85, leading to a BPV of assets (BPVA) as follows:

Plan Assets = $3.07 billion Asset Allocation in Bonds = 40% Bond Duration = 2.85 BPV of Assets (BPVA) = $349,980

To address the duration gap, the manager plans to use Treasury bond contracts. These contracts are based on a $100,000 par value. The Cheapest to Deliver (CTD) bond has a BPV of 128.98, a duration of 13.53, and a conversion factor of 0.9436. The BPV of the contract \((BPV_{\text{Futures}})\) is calculated as follows:

BPV of CTD Bond = 128.98 Conversion Factor = 0.9436 BPV of Futures Contract \((BPV_{\text{Futures}}) =\frac {128.98 }{ 0.9436} = 136.6893\)

Now, the manager has various options based on their interest rate outlook:

1. No View (Full Hedge): If the manager has no particular interest rate view, they may choose to fully hedge the duration gap.
2. Negative Interest Rate View (Over Hedge): If the manager anticipates a decrease in interest rates, they may decide to over-hedge the duration gap.
3. Positive Interest Rate View (Under Hedge): Conversely, if the manager expects an increase in interest rates, they may opt to under-hedge the duration gap.

These strategies allow the manager to adjust the portfolio in response to their interest rate expectations.

Manager Has No View

In the case that the manager has no view on interest rates, they could choose to construct a 100% hedge to remove the duration gap they will buy contracts to increase the asset duration:

NF for a 100% hedge = 2,402,950 – 349,980 / by 136.6893 = 15,019 contracts to buy

Manager Has Negative Interest Rate View – Over Hedge

Assuming that the manager has discretion to over hedge or under hedge by up to 10% and believes that interest rates will decline, they would profit from this opportunity by buying more contracts than would be required for a 100% hedge. To set the asset duration above the liability duration they will buy:

NF for a 100% hedge = 1.1 x 15,019 = 165,212 contracts to buy

Manager Has Positive Interest Rate View – Under Hedge

Now assume instead that the manager believes that interest rates will increase period to profit from this they will buy fewer contracts than would be required for a 100% hedge to set the asset duration below the liability duration they will buy:

NF for a 90% hedge = 0.9 x 15,019 = 135,172 contracts to buy

Hedging with futures

An alternative approach for managers is hedging with futures contracts, but this strategy carries operational and practical risks. Here's what you need to know:

1. Daily Margin Adjustments: When hedging with futures, managers must post the margin and adjust it daily. This means that any gains or losses on the futures contracts are settled in cash on a daily basis.
2. Impact of Price Changes: A small change of 1/32 in the contract price results in a gain or loss of $31.25 on each contract. While successful hedging offsets changes in the liability's value, these changes are unrealized and do not involve actual cash flows.
3. Rare Use of 100% Hedges: Due to these issues, fully hedging 100% of liabilities is rare in practice. Most managers opt for partial hedges to reduce the duration gap more effectively.

In summary, while hedging with futures is a viable option, the need for daily margin adjustments and the impact of contract price changes make partial hedges a more common choice for managers looking to manage duration gaps effectively.

Hedging With Interest Rate Swaps

Using interest rate swaps is an alternative method to manage the duration gap, and it offers advantages:

1. OTC Instruments: Interest rate swaps are over-the-counter (OTC) instruments, which can help avoid the margin cash flow complexities associated with futures.
2. Effect on Portfolio Duration: Consider these points:
   • A received fixed swap increases the portfolio's duration, adding a positive duration effect.
   • A pay-fixed swap reduces the portfolio's duration, creating a negative duration effect.
   • The net duration of the swap is determined by the difference between fixed and floating-rate bonds that replicate the swap's future coupon flows.

Let's delve into an example:

• A 10-year swap is available, and the manager has the flexibility to hedge between 30% to 70% of the duration gap, with 50% considered a neutral position.
• The duration gap remains at 205,297 BPV (based on earlier calculations), and the asset duration is lower.
• The replicating fixed and floating sides of the swap have durations of 9.1 and 0.25, respectively.
• The value per basis point value swap (VBPVS) per 100 notional for each side of the net swap duration is determined.

Let's calculate the notional swap principal needed for a 100% hedge:

• Fixed-side BPV = 0.0918.
• Floating-side BPV = 0.0025.
• Net swap BPV = 0.0893.

Now, to close the duration gap entirely, we divide the duration gap in BPV by the swap BPV per basis point value (BPV per 1 BP). Keep in mind that BPV is per 100, so we divide it by 100 to get BPV per one basis point (BP):

$$ \text{Notional Swap Principal} = \frac { \text{Duration Gap in BPV}}{\text{Swap BPV per 1 BP}} $$

To increase the asset duration, you can enter a receive fixed swap.

Assuming the manager expects rates to increase and given the hedging constraints, what hedge would be used?

With increasing rates expected, the manager will leave asset duration as low as permitted for a 30% hedge he will enter a receive fixed swap of 0.3 X 2.3 equals 0.69 billion NP.

Assuming the manager just entered the 30% hedge and now believes rates will decline, what hedge would be used?

If the manager has recently initiated a 30% hedge and foresees a decline in interest rates, they will aim to maximize asset duration by opting for the maximum allowable hedge of 70%. In this scenario, they would seek a fixed swap of 0.7 x 2.3, equaling 1.61 billion NP. To achieve this, an additional fixed swap of 1.61 – 0.69, which is 0.92 billion NP, would be necessary.

Swaptions Overview

Swaptions, an alternative to traditional swaps, offer flexibility for managing a portfolio. A receiver swaption, for instance, is acquired by paying an initial premium. This provides the option to initiate a receive fixed swap at a predetermined swap fixed rate, also known as the swaptions strike rate. The cost is limited to the initial premium.

• Over time, the swaption's value is assessed by comparing the swaptions strike rate (CFR) to the current market CFR for new swaps. If the market CFR is lower, the swaption has value. It grants the right to receive payments at a rate above the current market rate, increasing the portfolio's BPV and total assets.
• Conversely, if the market CFR rises, the swaption loses value and may expire unused. In contrast, using a traditional swap would result in escalating losses on a received fixed swap.
• Now, let's discuss the concept of a “swaption collar.”

A “swaption collar” is a financial strategy that combines two swaptions, one to protect against rising interest rates and the other to guard against falling interest rates. It's essentially a combination of a receiver swaption and a payer swaption.

Here's how it works:

• Receiver Swaption: This component provides the right to enter into a receive fixed interest rate swap at a predetermined rate if market interest rates fall below that rate. In other words, it protects against declining interest rates. If rates drop, the receiver swaption allows the holder to lock in a higher fixed interest rate, which can be advantageous.
• Payer Swaption: This component, on the other hand, grants the right to enter into a pay fixed interest rate swap at a predetermined rate if market rates rise above that rate. It serves as protection against increasing interest rates. If rates climb, the payer swaption enables the holder to secure a lower fixed interest rate, reducing interest expenses.

By combining these two swaptions, a swaption collar provides a way to manage interest rate risk in both directions. It's a strategy used by organizations and investors to hedge against the uncertainty of interest rate movements while allowing for some flexibility and cost control.

Choosing an Optimal Strategy

The manager's choice of the best strategy depends on their outlook for interest rates. Let's consider a defined benefit (DB) plan facing a duration gap and a need to increase asset duration. This means the plan is vulnerable to interest rate declines because the assets won't increase as much as the liabilities, causing the plan surplus to decrease.

The manager has three swap-based hedging options:

1. Receive Fixed Swap vs. Pay Libor: In this strategy, the plan would enter into a swap where it receives a fixed interest rate and pays the floating Libor rate.
2. Receiver Swaption: This involves acquiring a receiver swaption, which grants the right to enter into a receive fixed interest rate swap if market rates fall.
3. 0-Cost Collar: This strategy combines buying a receiver swaption and selling a payer swaption, creating a collar to manage interest rate risk.

All these strategies have the same notionals and payment frequency, with all floating payments based on Libor. The manager has been advised that any gains or losses from these swaptions will be recorded in the sponsor's financial statements. This means she can evaluate the swaptions as if they are marketable securities when making decisions. She must use one of these hedges because the duration gap is too large and risky for the plan's surplus. Unhedged is not an option. Here is the relevant data she has gathered:

$$ \begin{array}{c|c}
& \textbf{Cost} \\ \hline
\text{2.5% fixed-rate swap} & \text{None} \\ \hline
\text{2.3% receiver swaption} & 75 BP \\ \hline
\text{3.3% payer swaption} & 75 BP
\end{array} $$

The first choice will be optimal if the manager believes that the new SFR will be at or below 2.5%.

The second choice is suboptimal because there is an initial cost, and the 2.3% fixed rate received by the plan is lower.

The collar is also suboptimal as the 2.3% fixed rate received by the plan is lower.

Question

Duration is most accurate for measuring?

1. Parallel shifts and yield curve twists.
2. Parallel shifts only.
3. Yield curve twists only.

Solution

The correct answer is A.

This statement is accurate. Duration is a useful measure for assessing both parallel shifts and yield curve twists. When there’s a parallel shift in the yield curve (i.e., when interest rates across all maturities change by the same amount), duration can help estimate the change in the bond’s price. Similarly, for yield curve twists (non-parallel shifts where rates on different maturities move by different amounts), duration remains a useful measure for assessing the bond’s price sensitivity.

B is incorrect. This statement is partially correct. Duration is very accurate for measuring the price sensitivity to parallel shifts in the yield curve. In the case of a parallel shift, the accuracy of duration is quite high. However, it may not be as accurate in the presence of yield curve twists.

C is incorrect. This statement is incorrect. While duration can provide a rough estimate of the price sensitivity to yield curve twists, it is not as accurate for this purpose as it is for measuring parallel shifts. Yield curve twists introduce more complexity because different parts of the yield curve move in different directions, and duration’s simplifying assumption that yield changes are uniform across all maturities does not hold in such cases. In the presence of yield curve twists, other measures like key rate duration or convexity are often used for more accurate sensitivity assessments.

Reading 20: Liability-Driven and Index-based Strategies

Los 20 (e) Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio’s objectives