Controlled Interest Rate Risks For Futures and Forwards

Investment managers and investors utilize swaps, forwards, futures, and volatility derivatives in various ways, including hedging, directional bets, creating desired payoffs, asset allocation, portfolio rebalancing, and gauging current market expectations.

The following table shows that investors and portfolio managers commonly use these derivatives in portfolio management.

$$ \begin{array}{l|l}
{\textbf{Common uses of Swaps, Forwards,} \\ \textbf{and Futures}} & \textbf{Typical Derivatives Used} \\ \hline
{\text{Modifying Portfolio Returns and Risk} \\ \text{Exposures (Hedging and Directional Bets)}} & {\text{Interest Rate, Currency, and} \\ \text{Equity} \\ \text{Swaps and Futures;} \\ \text{Fixed-Income Futures;} \\ \text{Variance Swaps.} } \\ \hline
\text{Creating Desired Payoffs} & {\text{Forwards,} \\ \text{Futures,} \\ \text{Total Return Swaps}} \\ \hline
{\text{Performing Asset Allocation and Portfolio} \\ \text{Rebalancing}} & {\text{Forwards,} \\ \text{Futures,} \\ \text{Total Return Swaps}} \\ \hline
{\text{Performing Asset Allocation and Portfolio} \\ \text{Rebalancing}} & {\text{Equity Index Futures,} \\
\text{Government Bond Futures,} \\ \text{Index Swaps}} \\ \hline
{\text{Inferring Market Expectations for Interest} \\ \text{Rates, Inflation, and Volatility.}} & {\text{Fed Funds Futures} \\
\text{Inflation Swaps} \\
\text{VIX Futures}} \end{array} $$

Altering Risk Exposure Using Swaps, Futures, and Forwards

Financial managers employ swaps, forwards, and futures markets to swiftly and efficiently adjust the risk exposure of their asset portfolios or expected investment transactions.

Managing Interest Rate Risk

Interest Rate Swaps

An interest rate swap is an over-the-counter (OTC) agreement where two parties exchange cash flows based on variable and fixed interest rates, typically on the same currency, and netting unequal payments. This helps parties convert their risk exposure from fixed to floating.

Interest rate swaps are widely employed to mitigate interest rate risk, particularly in managing cash flows related to assets and liabilities. They can also be utilized, alongside futures, to adjust a portfolio’s risk and return characteristics, especially in controlling bond portfolio duration. Financial institutions also use interest rate swaps to hedge against interest rate risk by issuing financial instruments sold to clients.

It's crucial to remember that the hedging instrument and the asset or portfolio being hedged are often not perfect substitutes, leading to a market risk known as basis risk or spread risk. This risk arises from the difference between the market performance of the asset and the derivative instrument used for hedging. When employing an interest rate swap as a hedge, it's possible that fluctuations in the underlying rate of the derivative contract and, consequently, the swap's value may not precisely align with changes in the bond portfolio's value.

Additionally, the bond portfolio may carry other market risks aside from interest rate risk, such as credit spread risk when, for example, corporate bonds are hedged with an interest rate swap. In our analysis, we'll make critical assumptions: the bond portfolio's value change can be estimated using modified duration, a flat yield curve affected solely by parallel shifts, and the assumption of perfect substitution between the portfolio and the derivative contract used for hedging.

Using the following formula, we can find NS, the swap notional principal:

$$ N_S= \left[\frac {MDUR_T-MDUR_P}{MDUR_S} \right](MV_P) $$

Where:

\(N_S\)=Swap notional principal

\(MDUR_T\)= The target modified duration for the combined portfolio

\(MDUR_P\)= The portfolio's modified duration

\(MDUR_S\)= The change in the value of the swap, \(\Delta S\)

\(MV_P\)= The market value of the bond portfolio.

The modified duration of a swap \((MDUR_S)\) is determined by the difference in modified durations between equivalent positions in fixed- and floating-rate bonds. For instance, a pay-fixed party in a pay-fixed, receive-floating swap has a modified duration equivalent to a floating-rate bond minus a fixed-rate bond, considering the matching cash flows. In this context, a pay-fixed, receive-floating swap has a negative (positive) duration when viewed from the perspective of a fixed-rate payer (receiver), which aligns with the expectation that this position would benefit from increasing interest rates due to the positive duration of fixed-rate bonds being more significant than the near-zero duration of floating-rate bonds.

The short-term interest rate derivatives market is large and liquid, involving instruments such as forward rate agreements (FRAs) and interest rate futures. FRAs are over-the-counter (OTC) derivatives primarily used for hedging future loans or interest rate fluctuations. They settle at maturity by accounting for the discounted difference between the contracted interest rate and the prevailing rate at settlement, applied to the notional amount. Short-term interest rate risk can also be managed using interest rate futures contracts, which, unlike OTC forwards and swaps, are standardized and backed by clearinghouses, virtually eliminating counterparty risk.

Forward rate agreements and interest rate futures are commonly employed to mitigate the risk stemming from fluctuations in interest rates between the anticipation and execution of loans or deposits.

To hedge against interest rate risk, institutional investors and bond traders can use interest-rate futures or fixed-income futures (also called “bond futures”). Due to their limited maturities and higher liquidity in nearer-month contracts, interest rate futures are typically used to hedge short-term bonds with up to two to three years left to maturity. Short-term bonds can be hedged using interest rate futures by using a strip of futures contracts and calculating the number needed for each cash flow's interest rate exposure. Due to their high liquidity, fixed-income futures contracts are preferred for hedging bond positions, especially US Treasury bonds.

Fixed Income Futures

Portfolio managers seeking to hedge bond portfolio duration risk typically opt for fixed-income futures. These are exchange-listed standardized forward contracts with a predefined range of deliverable bonds' remaining maturities as their underlying assets.

Bond futures serve two primary purposes: hedgers use them to safeguard their bond portfolios from unfavorable interest rate shifts and arbitrageurs to profit from price variations in equivalent financial instruments.

Fixed-income futures contracts use a basket of deliverable bonds with varying coupon rates and maturity dates as their underlying assets. Typically, these contracts are closed out or rolled over to the next contract month instead of being physically delivered. However, if delivery does occur, the seller should deliver and can choose which bond to deliver. To align with this, the duration of a futures contract typically matches that of the cheapest underlying deliverable bond, known as the cheapest-to-deliver (CTD) bond. The CTD bond's duration influences the price sensitivity of bond futures.

In selecting the cheapest-to-deliver (CTD) bond from the underlying bond basket, the seller chooses the one that results in the highest profit or negligible loss upon delivery. A concept of conversion factor (CF) has been introduced to aid this choice. The conversion factor system allows a more impartial comparison among deliverable bonds because the short side can deliver any eligible security. The amount the futures contract seller receives at delivery depends on the conversion factor, which, when multiplied by the futures settlement price, generates a price reflecting how the deliverable bond would trade if its coupon matched the notional coupon of the futures contract specification (e.g., 6% coupon and 20 years to maturity).

The following equation gives the principal invoice amount at maturity:

$$
\text{Principle invoice amount}=\frac {\text{Futures settlement price}}{100} \times CF \times \text{Contract size} $$

The cheapest-to-deliver (CTD) bond is identified based on duration, price, and yield levels. Typically, a bond with a low coupon rate, long maturity, and, hence, a longer duration is likely to be the CTD bond when the market yield exceeds the notional yield of the fixed-income futures contract. The notional yield typically aligns with the current prevailing interest rate.

The pricing difference between the cash security and fixed-income futures is the basis, calculated as the spot cash price minus the futures price multiplied by the conversion factor. Physical delivery of the underlying asset ensures that futures and spot prices align on the delivery date, as the no-arbitrage condition demands a zero basis on this day. Nevertheless, basis traders seek arbitrage opportunities based on minor pricing discrepancies. When the basis is negative, traders profit by “buying the basis,” involving purchasing the bond and shorting the futures. Conversely, when the basis is positive, traders profit by “selling the basis,” which means selling the bond and buying the futures.

Question

How can the portfolio manager, who holds $60 million in fixed-rate US bonds with an average modified duration of 6.5 and anticipates rising interest rates, achieve a target modified duration of 5.5 without selling any securities? One approach is to create a negative-duration position by engaging in an interest rate swap, in which the manager pays the fixed rate and receives the floating rate. Specifically, a three-year interest rate swap has an estimated modified duration of -3.00 for the fixed-rate payer.
Explain how the manager can utilize this interest rate swap to attain the desired modified duration.

1. $20 Million.
2. $35 Million.
3. $35 Million.

Solution

The correct answer is A.

The portfolio manager aims to achieve a portfolio with a market value of $60 million and a desired modified duration of 5.5 by combining the bonds and the swap. This relationship can be expressed as follows:

$$
$60,000,000(6.50)+(N_S)(MDUR_S)=\$50,000,000(5.5) $$

The notional principal for the interest swap that the manager should use is determined as follows:

$$ N_S= \left[\frac {5.5-6.5}{-3.00} \right] \times \$60,000,000=\$20,000,000 $$

B and C are incorrect. Per the calculations above, the correct value is $20,000,000

Derivatives and Risk Management: Learning Module 2: Swaps, Forwards, and Futures Strategies; Los 2(a) Demonstrate how interest rate swaps, forwards, and futures can be used to modify a portfolio's risk and return