Taskin: This Assignment On Solving Hedging Problems

Taskin This Assignment You Will Solve Problems On Hedging With Future

In this assignment, you will solve problems on hedging with futures and forwards, specifically from Chapter 5: Exercise 13 and 14. You are to use your textbook for reference, and the solutions should be presented in an Excel file, utilizing the full computing power of Excel for calculations.

For Exercise 13, a US-based corporation intends to invest in Sweden and requires 100 million SEK in three months. The company seeks to hedge against USD/SEK exchange rate fluctuations using forward contracts on either EUR or CHF, based on given statistical estimates:

  • Standard deviation of quarterly changes in USD/SEK spot rate: 0.007
  • Standard deviation of quarterly changes in USD/EUR forward rate: 0.018
  • Correlation between USD/SEK and USD/EUR forward rate changes: 0.90
  • Standard deviation of quarterly changes in USD/CHF forward rate: 0.023
  • Correlation between USD/SEK and USD/CHF forward rate changes: 0.85

Additional data includes current USD/SEK spot rate (0.104), USD/EUR forward rate (0.471), and USD/CHF forward rate (0.602). The assignment asks:

  1. Which currency should the corporation use for hedging—the EUR or the CHF?
  2. What is the minimum-variance hedge position, and should this be a long or short position?

For Exercise 14, you are manufacturing using silver wire and need to purchase 100,000 oz of silver in three months. The task is to hedge silver price fluctuations over this period. Each COMEX silver futures contract covers 5,000 oz. You have conducted a regression of daily silver spot price changes on futures price changes, finding that δs = 0.03 + 0.89δF + ε. Given this, you are to determine:

  1. The optimal number of futures contracts to hedge the silver purchase.
  2. Whether to take a long or short futures position.

Paper For Above instruction

The following comprehensive analysis addresses the complex issues of currency hedging using forward contracts and commodity hedging via futures, as posed in Exercises 13 and 14. We will systematically evaluate the data and apply financial theories, particularly risk minimization principles, to determine optimal hedging strategies. The approach integrates quantitative analysis with practical considerations, culminating in specific recommendations for each scenario to assist decision-makers in managing financial risks efficiently.

Part 1: Hedging Currency Exposure in International Investment

The first scenario involves a US company aiming to hedge against currency risk associated with an impending Swedish Krona (SEK) requirement. The critical decision revolves around selecting the most effective currency—EUR or CHF—for hedging using forward contracts. To make an informed choice, we analyze the variance-covariance structure of the USD/SEK exchange rate and the forward rates of EUR and CHF.

The core concept here is the minimum-variance hedge ratio, which seeks to minimize the variance of the hedged position. It is determined by:

h = ρ (σ_S / σ_F)

where ρ is the correlation between the spot and forward rate changes or, more precisely, the covariance divided by the product of their standard deviations, and σ_S and σ_F are the standard deviations of the spot and forward changes, respectively.

For the EUR hedge, the parameters are: σ_S = 0.007, σ_F = 0.018, and ρ = 0.90. The hedge ratio (h*EUR) is calculated as:

hEUR = 0.90 (0.007 / 0.018) ≈ 0.35

Similarly, for CHF, with σ_F = 0.023 and ρ = 0.85, the hedge ratio (h*CHF) is:

hCHF = 0.85 (0.007 / 0.023) ≈ 0.259

The hedge ratio indicates the proportion of the exposure to be hedged with each currency. The smaller hedge ratio with CHF suggests a less aggressive hedge but also implies potentially lower risk if the variance reduction is considered alongside transaction costs and market factors.

The expected costs or gains are also influenced by the forward rates. Given the current rates, the corporation should choose the hedge that minimizes the residual variance and aligns with its risk appetite. Therefore, the EUR hedge provides a higher hedge ratio, implying a more significant hedge position, but also potentially better risk reduction, assuming the correlations and variances hold true.

The choice between EUR and CHF hinges on the variance analysis and the associated costs. Given the higher correlation and lower variance in the EUR hedging approach, the company should prefer EUR forwards for hedging its SEK exposure. The hedge that minimizes the variance will better stabilize the company's cash flows.

Part 2: Optimal Hedge Position Calculation

The minimum-variance hedge ratio indicates the optimal proportion of the total exposure to be hedged. Using the derived hedge ratios, the actual hedging position is computed by multiplying the ratio with the total exposure of 100 million SEK (or converted into USD at the current rate). For simplicity, assuming the USD/SEK rate of 0.104, the USD exposure is approximately:

USD Amount = 100,000,000 SEK * 0.104 ≈ 10,400,000 USD

Applying the hedge ratio for EUR:

Hedge amount in USD = 10,400,000 * 0.35 ≈ 3,640,000 USD

This suggests a forward contract position to hedge approximately 3.64 million USD worth of SEK exposure, indicating a short position in EUR forwards if the hedging is done directly in EUR.

Part 3: Silver Futures Hedging

The second scenario involves hedging silver price risks with futures contracts. The regression coefficient δs = 0.03 + 0.89δF implies a strong relationship between futures and spot price changes, with a beta of approximately 0.89. Given this, the optimal hedge size is derived from the formula:

Number of contracts = (β * Spot exposure) / Contract size

Here, Spot exposure = 100,000 oz, contract size = 5,000 oz, and β = 0.89. Calculating the number of contracts:

Number of contracts = (0.89 * 100,000) / 5,000 = 17.8

Since you are aiming to hedge against rising prices to avoid increased costs, the position should be short to profit from downward movements or to offset upward movements in silver prices.

Therefore, the optimal hedge involves shorting approximately 18 futures contracts, aligning with risk mitigation objectives.

Conclusion

Effective risk management in international finance and commodity markets necessitates precise quantitative analysis. The currency hedging using EUR forwards is preferred over CHF based on variance reductions, leading to a hedge ratio of approximately 0.35, indicating a substantial hedge position. In silver futures, the approximate requirement is 18 contracts, with a short position to hedge against rising prices. These strategies enable the firm to stabilize cash flows and mitigate market risks effectively, leveraging the foundational principles of hedging theory and regression analysis.

References

  • Fabozzi, F. J., & Modigliani, F. (2009). Financial Markets and Institutions. Pearson.
  • Henry, T. (2011). Hedge Fund Strategies. McGraw-Hill Education.
  • Hull, J. C. (2018). Risk Management and Financial Institutions. Wiley.
  • Levy, H. (2005). International Financial Management. Springer.
  • Madura, J. (2018). International Financial Management. Cengage Learning.
  • Shapiro, A. C. (2013). Multinational Financial Management. Wiley.
  • McDonald, R. (2013). Derivatives Markets. Pearson.
  • Sengupta, R. (2010). Practical Guide to Currency Options and Hedging Strategies. Wiley.
  • Cuthbertson, K., Nitzsche, K., & Riordan, R. (2012). Quantitative Financial Economics. John Wiley & Sons.
  • Choudhry, M. (2010). An Introduction to Hedge Funds. Wiley.

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