### WEDNESDAY: 23 August 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. Discuss THREE criticisms of derivative markets. (6 marks)

2. Distinguish between a “credit default swap (CDS)” and a “credit linked swap (CLS)”. (2 marks)

3. A 250-day futures contract is entered into using a 7% semi-annual pay coupon bond with a spot price of Sh.1,050 (accrued interest inclusive) and will make a coupon payment 182 days later. The annual risk free rate is 6%.

Assume a year has 365 days.

**Required:**

Calculate the price of the 250-day futures contract. (4 marks)

4. An investor is considering a two-period binomial model in which the underlying is at Sh.50 and can go up 4.88% or down 2.53% each period. The risk free rate is 1.25%. The exercise price of the call is Sh.50.

**Required:**

Calculate the payoffs of the call option at expiration. (4 marks)

Calculate the value of the call option expiring in two periods. (4 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Explain the following option spread strategies:

Bull spread. (2 marks)

Bear spread. (2 marks)

Butterfly spread using calls. (2 marks)

2. Lesley Gikenye is an investments practitioner with Wanda Capital and is evaluating the following forward contract positions that affect the company:

1. A 180-day forward contract involving the Mexican Peso (MXN) and the United States Dollar (USD). The risk free rates are 6% in the United States and 8% in Mexico. The current spot exchange rate is $0.0845.

2. The company entered into a four-month forward contract to buy 10 million Euro (€) at a price of USD ($) 1.112 per Euro. A month later, the three-month forward price is $1.109 per Euro. The USD interest rate is 0.30% and the Euro interest rate is 0.40%.

**Required:**

Calculate the forward exchange rate for a 180-day forward contract that Wanda Capital should engage in. (3 marks)

Calculate the value of Wanda Capital’s forward position in the four-month forward contract. (3 marks)

3. Wastaafu Pension Fund owns a Sh.100 million large-Cap position for which the fund manager expects a poor market performance over the next three months. Fund managers have decided to create synthetic cash equal to Sh.100 million exposure.

**Additional information:**

1. Three-month forward contracts are currently at 1,400 with a multiplier of Sh.250.

2. Three-month Treasury rates are estimated at 2.8%.

**Required:**

The appropriate number of forward contracts to meet the fund manager’s desire to create the synthetic cash. (3 marks)

Justify why the fund manager’s decision to create synthetic cash equal to Sh.100 million exposure is

appropriate. (3 marks)

Explain to the fund managers of Wastaafu Pension Fund the relevance of pre-investing in risk management. (2 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Describe THREE types of margin used in the futures market. (6 marks)

2. Samson Ole Kina manages a family investment portfolio which initially consist of Sh.46 million of equities and Sh.32 million of bonds. As a result of a change in family circumstances, the portfolio is rebalanced using the transactions shown below:

Three months after these transactions, the market value of the portfolio’s equities has increased by 3.00% and the market value of its bonds has decreased by 2.40%. The prices of the equity and bond futures are now quoted at Sh.165,000 and Sh.185,250 respectively.

**Required**:

Calculate the profit or loss on the portfolio over the past three months. (6 marks)

3. A portfolio manager expects to purchase a portfolio of stocks in 90 days. In order to hedge against a potential price increase over the next 90 days, he decides to take a long position on a 90 day forward contract on the NSE 20 share index. The index is currently at 1145. The continuously compounded dividend yield is 1.75%. The discrete risk free rate is 4.25%. Twenty eight (28) days after the portfolio has entered the forward contract, the index value is 1225 and at expiration, the index value is 1235. Assume a 365 day year.

**Required:**

Calculate the following:

The no-arbitrage forward price on this contract. (3 marks)

The value of the forward contract 28 days into the contract. (3 marks)

The value of the forward contract at expiration. (2 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Highlight FOUR duties of a Derivatives Exchange in relation to derivative markets. (4 marks)

2. Jacob Imanyara, a derivatives trader has obtained the following information about a call option:

• Time to maturity 3 years

• Continuous risk-free rate 3%

• Continuous dividend yield 2%

• N(d1) 0.7

**Required:**

The delta of the call option. (3 marks)

3. The current price of a share is Sh.25. A call option is available with Sh.20 strike price that expires in three months.

Assume that the underlying stock exhibits an annual standard deviation of 25 and that, the current risk free rate is 4.5%, N(d1) = 0.9737 and N(d2) = 0.9652.

**Required:**

The value of the call option using the Black-Scholes-Merton model. (3 marks)

Suggest three assumptions of the Black-Scholes-Merton model. (3 marks)

4. An Indian company needs to borrow 100 million Kenya Shillings (KES) for one year for its Kenyan subsidiary. The company decides to issue India-denominated bonds in an amount equivalent to KES 100 million. The company then enters into a one year currency swap with a quarterly reset (30/360 day count) and the exchange of notional amounts at initiation and at maturity. At the swaps initiation, the Indian company receives the notional amount in Kenya Shillings and pays the counterparty the notional amount in Indian Rupee. At the swaps expiration, the Indian company pays the notional amount in Kenya Shillings and receives from the counterparty the notional amount in Indian Rupee. Based on interbank rates, the following spot rates are available today, at time 0:

Assume that the counterparties in the currency swap agree to a KES/INR spot exchange rate of 1.140 (expressed as number of Kenya Shilling for 1 INR).

**Required:**

Calculate the fixed swap quarterly payments in the currency swaps in:

Kenya Shilling (KES). (5 marks)

Indian Rupee (INR). (2 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Examine THREE applications of swaps in derivative markets. (6 marks)

2. Gem Holdings Limited purchases a 1 – year cap with annual reset and a strike rate of 5.0% on a notional principal of Sh.25 million. The binomial model below represents a bundle of 1-year option.

3. Mutemi Karuri is considering a three year receiver swaption with an exercise rate of 11.75% in which the underlying swap is a Sh.20 million notional principal four year swap. The underlying rate is secured overnight financing rate (SOFR). At expiration of the swaption, the SOFR rates are as follows:

**Required:**

Calculate the swap fixed rate. (4 marks)

Calculate the payoff value of the swaption. (6 marks)

**(Total: 20 marks)**