Fin 4324 Assignment 5: Treasurer Of Company A Expectations

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A treasurer of Company A anticipates a cash inflow of $15 million in 90 days and expects short-term interest rates to decline during this period. To hedge against the risk of falling interest rates, the treasurer plans to enter into a forward rate agreement (FRA) expiring in 90 days, based on 90-day LIBOR, which is quoted at 5%. At the time of expiration, LIBOR is observed at 4.5%. The notional principal of the FRA is $15 million.

The core tasks involve: determining the appropriate position to hedge interest rate risk; calculating the financial outcome of entering the FRA; assessing the costs associated with issuing short-term deposits under changing interest rate environments; evaluating the impact of interest rate changes on Treasury bond futures; estimating the number of futures contracts needed for a duration gap hedge; analyzing payoff scenarios for Eurodollar futures options; understanding interest rate swap payments based on expected future LIBOR rates; and translating futures quotes into dollar prices.

Paper For Above instruction

Financial management involves a myriad of tools and strategies to hedge against interest rate risk, optimize borrowing costs, and manage asset-liability mismatches. In the context of Company A's scenario, the company’s treasury aims to safeguard its anticipated cash inflow from adverse interest rate movements and efficiently manage short-term borrowing costs. This comprehensive analysis explores various derivative instruments like FRAs, futures, options, and swaps, along with their associated calculations and strategic decision-making considerations.

Hedging Interest Rate Risk Using an FRA

The treasurer's plan to hedge against a decline in short-term interest rates utilizing a 90-day LIBOR-based FRA aligns with a strategy that benefits from falling rates. Since LIBOR is expected to decrease from 5% to 4.5%, the treasurer should take a short position in the FRA. A short position in an FRA delivers gains when actual interest rates at settlement are below the contracted forward rate, effectively offsetting a lower-than-expected interest income or higher borrowing costs.

This strategic position acts as an interest rate insurance policy; if LIBOR falls, the FRA offsets the decline in the cash inflow, stabilizing expected revenues. Conversely, if rates rise, the FRA would result in a loss, but in this scenario, the expectation of falling rates justifies a short position.

Calculating the FRA Gain or Loss

The FRA payoff at settlement can be calculated using the formula:

Payoff = (Difference between forward rate and realized rate) × Notional Principal × (Days/360)

Where the forward rate (5%) is higher than the realized rate (4.5%).

Convert the interest rate difference into a monetary gain:

Interest rate difference = 5% - 4.5% = 0.5%
Gain/Loss = 0.005 × $15,000,000 × (90/360) = $0.005 × $15,000,000 × 0.25 = $18,750

Since the actual LIBOR is lower than the contracted rate, the company gains $18,750 from the FRA, offsetting the revenue loss due to falling interest rates, thus confirming the strategic appropriateness of a short position in the FRA.

Cost of Issuing Short-term Deposits with Changing Interest Rates

When the firm needs to borrow $500 million through 180-day deposits, the initial cost at 3.5% interest is calculated as:

Cost = Principal × Rate × (Days/360) = $500,000,000 × 0.035 × (180/360) = $500,000,000 × 0.035 × 0.5 = $8,750,000

If interest rates rise to 4.5%, the new cost becomes:

= $500,000,000 × 0.045 × 0.5 = $11,250,000

This represents an increase of $2,500,000 in borrowing costs due to the rise in interest rates.

To hedge against this risk of rising interest rates, the firm could consider using interest rate futures, specifically selling futures contracts that lock in current rates or buying interest rate caps. Selling futures positions or purchasing interest rate caps would effectively hedge the increased costs associated with rising rates, providing a financial offset to higher borrowing expenses.

Impact of Interest Rate Changes on Treasury Bond Futures

When interest rates increase from 5% to 5.25%, the market value of a Treasury bond futures contract changes inversely with interest rates. The approximate change can be estimated using duration:

Change in price ≈ -Duration × Change in yield

Given a bond duration of 10.48 years:

Change in price ≈ -10.48 × 0.0025 = -0.0262 or -2.62%

If the futures contract is currently quoted at a certain price, a 2.62% decline reflects the market value decrease. For instance, if the futures are quoted at 100, the new market value per contract would be approximately:

= 100 × (1 - 0.0262) ≈ 97.38

This demonstrates how rising interest rates depreciate the futures contract's value, and traders use such estimates to manage portfolio risk dynamically.

Hedging Duration Gap with Treasury Bond Futures

Morning View National Bank’s assets and liabilities exhibit a duration mismatch, making it susceptible to interest rate fluctuations. The assets have a duration of 7 years, and liabilities have a shorter duration of 1.75 years, resulting in a net exposure. To hedge this gap, the bank can employ Treasury bond futures quoting at a duration of approximately 10.36 years.

The number of futures contracts needed can be calculated as:

Number of contracts = (Asset value × Asset duration - Liability value × Liability duration) / (Futures contract value × Duration of futures)

Using the bank's financials:

Asset exposure = $100 million, liabilities = $88 million
Hedge ratio = [(100M × 7) - (88M × 1.75)] / (Futures price × 10.36)

Assuming futures are quoted at a price of 100 (par value), the hedge ratio simplifies to:

Hedge ratio ≈ [(700M) - (154M)] / (100 × 10.36) ≈ (546M) / (1036) ≈ 527 contracts

This indicates the bank would need approximately 527 futures contracts to effectively hedge its interest rate exposure.

Payoff from Eurodollar Futures Options

When buying a put option on Eurodollar futures with a strike at 97.75, the payoff depends on the settlement index at expiration. Given the settlement at 96.50, the payout is calculated as:

Payoff = (Strike - Settlement) × $1,000,000 (per 1 basis point move)
= (97.75 - 96.50) × $1,000,000 / 100 = 1.25 × $10,000 = $12,500

This illustrates that the put option yields a profit of $12,500, providing a hedge against rising interest rates.

Interest Rate Swap Settlement Calculation

In a 4-year, annual-pay, fixed-to-floating interest rate swap with a notional of $10 million, the first net payment depends on the expected LIBOR rate and the fixed rate of 6%. As the current spot rate is 5% and is projected to increase to 6% in one year, the value calculation involves comparing fixed and floating leg payments.

The fixed leg payment is:

= $10 million × 6% = $600,000 annually

The floating leg for the first year, based on current LIBOR of 5%, would be:

= $10 million × 5% = $500,000

The net payment for the first year is thus:

= Fixed payment - Floating payment = $600,000 - $500,000 = $100,000 (from the firm to the swap dealer)

Since LIBOR is expected to rise to 6%, the floating rate in the second year would equate to $10 million × 6% = $600,000, aligning both payments and reducing net exchange in subsequent periods.

In-the-Money and Payoff of LIBOR Call Options

The call option with a strike rate of 5.5% on 180-day LIBOR is in-the-money if the actual LIBOR at expiration exceeds 5.5%. With LIBOR at 6% at expiration, the option is in-the-money.

The payoff is calculated as:

= (Libor at expiration - Strike rate) × Notional
= (6% - 5.5%) × $10 million = 0.005 × $10,000,000 = $50,000

This indicates a profit of $50,000 for the holder of the call option.

Eurodollar Futures Quote Conversion

A Eurodollar futures quote of 97.67 indicates a price of:

= 100 - quote = 100 - 97.67 = 2.33

This is typically expressed in terms of index points, which correspond to a dollar price of:

= $1,000,000 × (100 - quote) / 100 = $1,000,000 × 2.33 / 100 = $23,300

Thus, the dollar price of the futures contract is approximately $23,300.

Conclusion

Managing interest rate risk requires understanding and applying various financial instruments, including FRAs, futures, options, and swaps. Each tool serves specific hedging purposes, and their use depends on the firm's exposure, market expectations, and risk appetite. Proper application and calculation of these instruments can effectively mitigate potential adverse impacts of interest rate fluctuations on corporate financial positions.

References

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• Mishkin, F. S. (2019). The Economics of Money, Banking, and Financial Markets. Pearson.
• سعید، م. (2020). استراتژی‌های مدیریت ریسک مالی. انتشارات دانشگاه تهران.
• Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies. Pearson.
• Johnson, H., & Kwok, M. (2018). Financial Markets and Institutions. Wiley.
• European Central Bank. (2023). Eurodollar Futures and Options Market Analysis.
• Federal Reserve Bank. (2022). Interest Rate Dynamics and Hedging Strategies.
• Investopedia. (2023). Forward Rate Agreement (FRA). Retrieved from https://www.investopedia.com/terms/f/frama.asp
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