FINANCE 362 : Risk Management

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Risk Management FINANCE 362 S2 2024

 Assignment

Due Date: 11.59 pm, Friday 16 August 2024

Instructions:

1. Answer all 5 questions in order and show all your workings. Please clearly record down the question numbers.

2. All assignments are to be handed online via Canvas in PDF format. Please visit the link below for the step-by-step help on submission.

https://uoa.custhelp.com/app/answers/detail/a_id/8924/~/guide-on-submitting-assignments-on-canvas

3. Hand-written answers are also acceptable unless it is otherwise stated in the question. Please write your answers neatly and legibly. You will need to scan your hand-written assignments and convert to a PDF file for submission. If using Excel, insert a picture into a word or pdf file.

4. Make sure you submit ONLY ONE file.

5. Late submission will NOT be accepted.

Question 1 (10 Marks)

The West Texas Intermediate (WTI) Light Sweet Crude Oil futures contract, as one of the world’s most liquid energy futures contract, provides market participants with direct exposure to the crude oil market.

On 15 February 2006 a speculator who expects the crude oil price to fall over the short term sells ten June 2006 WTI futures contracts at a price of USD $62.17 per barrel. The speculator closes out the futures position on 1 March 2006 at a price of USD $66.36 per barrel. Each contract is written on 1,000 barrels of crude oil (“contract size”). The initial and maintenance margins are USD $5.00 and USD $3.00 per barrel, respectively.

The daily settlement prices for the June 2006 WTI futures contract during the holding period are shown in the table below. Note futures contracts are traded only on business days.

Required:

(a) At the time the futures position is established on 15 February 2006, what is the minimum price movement on a per barrel basis that would generate a margin call? Report your answer in 2 decimal places (dps).    (2 marks)

(b) Construct a table as below to illustrate the daily marking-to-market (and final settlement) of the speculator’s overall futures position for the ten contracts. Assume no withdrawals of any money deposited to the “Initial and Margin account balance”. If there is a shortfall in the “Initial and Margin account balance” at the end of any trading day, the speculator will receive the margin call soon afterwards (i.e., within the same day), and is able to top up the margin account balance back to initial margin level by the start of the next trading day as instructed.   (6 marks)

Note: the format of the table is identical to Table 2.1 on page 46 of the prescribed textbook.

(c) What is the overall profit/loss of the speculator? Decompose the overall profit/loss into two components: (i) total margin calls, and (ii) the change in the margin account balance.   (2 marks)

Question 2 (10 Marks)

In mid-July, JK Ltd (a US firm) holds a pay-fixed, receive-floating 6x9 FRA contract which was entered into 6 months ago (i.e. in mid-January). The FRA rate is 0.70% per annum and the notional amount is $20,000,000.

The 6x9 FRA reaches expiration now (in mid-July), and the following LIBOR rates are observed from the market:

Note: The FRA contracts follow the standard US FRA settlement terms and adopt the Actual/360 day count convention. All interest rates are measured with a compounding frequency reflecting the length of the period they apply to.

Required:

(a) Based on the information above, explain whether JK Ltd makes a gain or loss by showing the settlement amount for JK Ltd to settle the 6x9 FRA at expiration. Report your answer in 2 decimal places (dps).  (4 marks)

(b) Suppose that JK Ltd plans to take a 20-million 90-day floating-rate loan in mid-October from a local bank. The firm wants to hedge the interest rate risk involved in the floating-rate loan by entering into another FRA contract in mid-July. Based on the LIBOR rate information in mid-July, explain what type of FRA contracts it should use.

Hint: You need to specify what the values of M and N are for such a MxN FRA contract, and whether the firm should buy (long) or sell (short) such a contract. (3 marks)

(c) What should be the FRA rate of the contract specified in part (b). Report your answer in percentage (%) with 4 dps i.e. xx.xxxx%.  (3 marks)

Question 3 (10 Marks)

Rebecca Smith, an analyst in the investment management division of a financial services firm, is developing earnings forecast for a small local dairy company in New Zealand (NZ). The company’s revenues are closely linked to the price of global dairy commodity products, which are set by the global market and priced in US dollars (USD). All expenses of the company are incurred in the local market and denominated in NZ dollars (NZD).

The strength of the NZ economy depends significantly on sales of dairy commodity products denominated in USD. As a result, movements in world dairy commodity products in USD terms and the value of the NZD are strongly positively correlated. That is an increase in the USD price of dairy commodities is strongly correlated with an increase in the value of the NZD against the USD.

An increase in commodity prices would increase the company’s sales in USD terms, all else being equal. On the other hand, the appreciation of the NZD relative to the USD would reduce the company’s sales in terms of the home currency (NZD).

The company’s chief risk officer, has made the following statement:

“The company has rejected hedging the market risk of a decline in global dairy commodity prices by selling commodity futures and hedging the currency risk of a depreciation of the US dollar relative to our home currency (NZD). We have decided that a more effective risk management strategy for our company is to not hedge either market risk of commodity price changes or currency risk.”

Required:

(a) State whether the company’s decision to not hedge commodity market risk is justified. Explain your answer with at least one reason. (Please type your answers, word limit 200). (5 marks)

(b) State whether the company’s decision to not hedge currency risk is justified. Explain your answer with at least one reason. (Please type your answers, word limit 200). (5 marks)

Question 4 (10 Marks)

Suppose you observe the following market data on debt securities:

Note: Data deviates from the current market conditions as it simplifies the calculations.

Required:

(a) What are the continuously compounded zero-coupon yields for 6 months and one year, respectively? Report your answer in percentage (%) with 4 dps. i.e. xx.xxxx% (4 marks)

(b) What is the of the following default-free bond portfolio? (4 dps)

Note: Each bond has a face value of $1.00 and coupons are paid semi-annually. You should assume the zero-coupon rate calculated in part (a) above.

Hint: Use the following formula to measure the duration of the bond portfolio, i.e.,

, where t_i, c_i, and r_i denote for term, cash-flows, and zero-coupon yield for the i^th period. (6 marks)

Question 5 (10 Marks)

Union Pacific Railroads, the largest railroad corporation in the United States, consumes approximately 1,200 million gallons of diesel fuel per annum. Assume the price that Union Pacific pays for its diesel fuel is best approximated by the diesel fuel benchmark Ultra-Low Sulfur No. 2 Diesel Fuel Los Angeles. In the absence of any futures contract on diesel fuel the railroad decides to hedge its fuel price risk using one of the following nearby NYMEX futures contracts: (i) Crude Oil (Light-Sweet, Cushing, Oklahoma), (ii) RBOB Regular Gasoline (New York Harbor), and (iii) No. 2 Heating Oil (New York Harbor). Union Pacific must determine which one of these NYMEX futures contracts is the best for hedging its fuel price risk.

Note: You would need to use the end-of-month prices of diesel fuel and the three NYMEX futures contracts over the five-year period from August 2016 to July 2021 in the Excel data file published on Canvas.

Required:

(a) Provide a single table showing the time series of monthly returns for each price series. Returns are to be calculated using the natural logarithm of the price relative — i.e., . You should be familiar with this method from FINANCE 261. (4 marks)

(b) Use the monthly ‘return’ data in an OLS regression model to obtain estimates of the optimal hedge ratio and hedging effectiveness for each futures contract over the entire period. Provide a copy of the regression output. Indicate clearly the optimal hedge ratio and hedging effectiveness for each contract.  (4 marks)

(c) Which futures contract should Union Pacific use to hedge its diesel fuel price risk? What position of the nearby future contracts will it need to trade to hedge the price risk on an expected monthly diesel consumption of 100 million gallons? Explain your answers (Please type your answers, word limit 100).   (2 marks)