**WEDNESDAY: 6 December 2023. Morning Paper. Time Allowed: 3 hours.**

**Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings. Do NOT write anything on this paper.**

**QUESTION ONE**

1. Explain the following terms as used in derivatives markets:

Forward commitments. (2 marks)

Contingent claims. (2 marks)

Exotic derivatives. (2 marks)

2. Describe THREE market participants in derivatives markets. (6 marks)

3. Peter Mwangangi owns Taifa Limited shares currently trading at Sh.150 at the securities exchange. Peter plans to sell the shares in 250 days from now. The risk free rate is 5.25%. Taifa Limited plans to pay dividends to its common shareholders according to the following schedule:

There are 365 days in a year.

**Required:**

State the position that Peter Mwangangi should take in the forward markets in order to hedge against a

possible price decline. (1 mark)

Determine the no-arbitrage forward price of a contract established now expiring in 250 days. (3 marks)

At expiration, the price of Taifa Limited’s share is at Sh.130. Determine the value of the forward contract.

(2 marks)

Elaborate whether the value in (c) (iii) above was a gain or loss to Peter Mwangangi. (2 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Assess THREE ways of terminating a futures contract. (6 marks)

2. The following information has been obtained from Zig trading exchange:

**Additional information:**

1. Initial margin requirement is Sh.5 per contract.

2. Maintenance margin requirement is Sh.2 per contract.

3. An investor establishes a long position of 20 contracts, meets all margin calls and does not withdraw any funds.

**Required:**

Determine the ending balance of the long position account from day 1 to day 6. (6 marks)

3. A Kenyan businessman deals with imports from United Kingdom (UK). Due to the recent exchange rate movement, he has been advised that the value of the Pound is likely to increase against the Kenyan Shilling over the next 30 days. The businessman is expected to make payment of imported goods in 30 days’ time and wants to hedge the currency exposure. The applicable Kenyan risk free rate is 5.5% and the UK risk free rate is 4.5%. These rates are expected to remain unchanged over the next month.

The current spot rate is Sh.150/£.

**Required:**

Explain whether the businessman should use a long or short forward contract to hedge the currency risk.

(2 marks)

Calculate the no-arbitrage price at which the businessman should enter into a forward contract that expires in 30 days. (3 marks)

Assume it is 10-days later into the life of the forward contract and the spot rate is Sh.153/£. Interest rates

are unchanged. Calculate the value of the forward contract held by the businessman. (3 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Explain THREE uses of a swaption. (6 marks)

2. Hildah Mwongeli is a financial analyst at Bottomline Bank, a commercial bank based in South Africa. One of the bank’s investments is exposed to movements in the South African Rand and Hildah Mwongeli desires to hedge the currency exposure. He prices a one year fixed for fixed currency swap involving Rand and Kenya Shilling with a quarterly reset. Mwongeli uses the interest rate data presented below to price the currency swap.

**Required:**

Determine the annualised equilibrium fixed swap rate for South African Rand. (4 marks)

3. John Okenangwa manages an investment portfolio consisting of a futures contract on a Treasury bill that expires in 50 days. The treasury bill matures in 140 days. The discount rates on Treasury bill are as follows:

• 50 day treasury bill 5.0%

• 140 day treasury bill 4.6%

**Required:**

The appropriate futures price by using the prices of the 50 day and 140 day Treasury bill. (1 mark)

Determine the futures price in terms of the underlying spot price compounded at the appropriate risk free rate. (2 marks)

Convert the futures price to the implied discount rate on the futures. (2 marks)

4. Washington Omondi gathers the following information from a financial service data terminal on 14 May 2023 relating to TMA Ltd. (option data):

**Additional information:**

1. The current stock price: Sh.125.94.

2. Expirations: 21 May 2023, 18 June 2023, 16 July 2023.

3. The applicable annualised risk free rate is 4.56%.

4. An option contract is for 100 shares of the stock employed.

5. Washington Omondi decides to examine the TMA Ltd. June box spread using the 125 and 130 options.

He undertakes the following transactions:

• Buy the 125 call at Sh.13.50, buy the 130 put at Sh.14.25, write the 130 call at 11.35 and write the

125 put at Sh.11.50. The premiums paid for the 125 call and 130 put minus the premium received

for the 130 call and 125 put net out to Sh.4.90.

**Required:**

Determine the payoff at expiration. (1 mark)

Calculate the net present value (NPV) of the box spread. (4 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Highlight FOUR common characteristics among all forward commitments. (4 marks)

2. The following information relates to put and call options on an asset:

Call price Sh.3.5

Put price Sh.9.0

Exercise price Sh.50

Forward price Sh.45

Days to option expiration 175

Risk free rate 4%

**Required:**

The synthetic call option price. (2 marks)

Price of the synthetic put option. (2 marks)

Price of the synthetic forward contract. (2 marks)

3. Hassan Korir manages the equity portion of the Bold Beverage Pension Fund which is converting its pension plan from defined benefit scheme to defined contribution scheme effective three months from now. Plan participants have three months to elect various investments for the new plan. The trustees inform Hassan that they wish to keep the value of the pension fund stable during these three months.

Accordingly, Hassan wants to eliminate systematic risk in the equity portion of the fund by using futures on the Securities Exchange (SE) 100 index which is the benchmark for the fund’s equity portfolio. He collects the information shown below:

Value of Bold Beverage pension fund equity portfolio Sh.235,400,000.

Level of SE 100 index 4,650

Level of three month SE 100 futures contract 4,667

Futures multiplier Sh.10

Beta of Bold Beverage Pension Fund equity portfolio 1.04

Beta of SE 100 futures contract 0.98

**Additional information:**

1. Three months after Hassan implements the hedge, the SE 100 index is up 3.75%.

2. The equity portion of the Beta Beverage Pension Fund is up 3.5% and the level of the expiring three month

SE 100 futures contract that Hassan sold is 4,824.

3. The trustees ask Hassan to assess the effectiveness of the hedge that has been in place.

**Required:**

State the target beta for Hassan’s hedging strategy. (1 mark)

Determine the number of futures contract that Hassan should sell to achieve the target. (4 marks)

Determine the effective beta of the Bold Beverage Pension Fund equity portfolio, including the futures

assuming that Hassan sold 5,200 futures contract. (5 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Assess THREE trends that will shape the future of derivatives markets globally. (6 marks)

2. The following information relates to a call option on Bendera Limited’s shares trading at a securities exchange:

1. The exercise price is Sh.70.

2. The risk free rate is 6%.

3. The volatility is 0.4.

4. The days to option expiration is 90 days.

5. The current share price is Sh.60.

**Required**:

The price of a call option on Bendera Limited’s shares using the Black-Scholes-Merton (BSM) pricing model. (5 marks)

The formula for BSM is given as follows:

3. A company issues an inverse floating rate note with a face value of Sh.30 million and a coupon rate of 14% minus SOFR (secured overnight financing rate). The company uses the proceeds to buy a bond with a coupon rate of 8%.

**Required:**

Explain how the company would manage the risk of this position using a swap with a fixed rate of 7%.

(2 marks)

Calculate the overall cash flow given that SOFR is less than 14%. (3 marks)

Explain what would happen if SOFR exceeds 14%. (2 marks)

Describe what the company would do to offset this problem if SOFR exceeds 14%. (2 marks)

**(Total: 20 marks)**