### WEDNESDAY: 26 April 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. Outline THREE distinctions between “contingent claims” and “forward commitments” as used in derivatives. (6 marks)

2. On April 15, the spot price of a bushel of corn is Sh.366, the annual storage cost is Sh.35 per bushel, the risk free rate is 3% and the cost of transportation of corn from the destination point specified on the futures contract to a local grain elevator or vice versa is Sh.3.5 per bushel.

**Required:**

Explain the steps to earn a riskless return on futures contract on the July corn given a futures price of

Sh.385 per bushel. (4 marks)

Calculate the riskless return. (1 mark)

3. A share index is at 1,521.75 currently and is the underlying of a futures contract expiring in 73 days. The risk-free rate is 6.1%. The value of the dividends reinvested over the life of the future is Sh.5.26.

Assume a 365-day year.

**Required:**

Calculate the present value of the dividends. (2 marks)

Determine the appropriate futures price. (2 marks)

Assuming a continuously compounded yield of 1.75%, determine the futures price. (5 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Explain THREE changes that have taken place in the regulation of the over the counter market since the 2008 financial crisis. (6 marks)

2. James Kamonya previously bought ABC Ltd. shares at Sh.12 and now buys the November 15 put for Sh.1.46 and simultaneously writes the November 17 covered call for Sh.1.44.

**Required:**

Calculate the following for a collar position created:

The maximum gain. (2 marks)

The minimum gain. (2 marks)

3. Explain the following terms as used in the option markets:

Calendar spread. (2 marks)

Long straddle. (2 marks)

The underlying stock sells for Sh.50 and an investor selects 30 day options with an exercise price of Sh.50.

The call sells for Sh.2.29 and the put for Sh.2.28.

**Required**:

Calculate the breakeven points from the above investment strategy. (2 marks)

4. An investor takes a short position in 1,000 European call options on stock futures. The options mature in 8 months and the futures contract underlying the call options expires in 9 months. The current 9-month futures price is Sh.8 per stock. The exercise price of the options is Sh.8, the risk free rate is 12% per annum and the volatility is 18% per annum.

**Required:**

Calculate the delta of a short position in 1,000 futures options. (4 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Explain the purpose of the following price movement limits in futures contract trading:

Daily price limits. (2 marks)

Position limits. (2 marks)

2. An investor contracts his broker to buy two gold futures contracts. The current futures prices of gold is observed at Sh.1,450 per ounce. The investor contracts to buy 200 ounces and that each contract size is 100 ounces.

**Additional information:**

1. Initial margin requirement is Sh.6,000 per contract.

2. Maintenance margin is Sh.4,500 per contract.

3. The contract is entered into on Day 1 and closed out on Day 7.

4. Daily settlement prices were observed as follows:

**Required:**

Determine the end of the day account balance for a long position in two gold futures contracts for day 2 to day 7. (8 marks)

Determine the variation margin balance amount by end of day 7. (2 marks)

3. A portfolio manager manages a portfolio of Sh.5,000,000 and desires to increase the beta of this portfolio from its current value of 0.8 to 1.1 using futures contracts. The beta of the chosen future contract is 1.05 with a price of Sh.240,000.

**Required:**

The number of futures contracts to achieve a beta of 1.1 for the portfolio. (2 marks)

The unhedged portfolio value increased in value by 5.1% and the futures price increases in value by 5.1%

with one month remaining to the futures contract expiration. The market had a return of 5.2 %.

**Required:**

The realised effective beta (ex-post beta) for the hedged portfolio. (4 marks)

**(Total: 20 marks)**

**QUESTION FOUR**

1. With respect to swap markets and contracts, distinguish between a “plain vanilla interest rate swap” and a “basis swap”. (4 marks)

2. 300 days into a quarterly – pay swap currency contract after initiation, a derivatives analyst gathers the following data:

1. 60-day Dollar ($) interest rate is 5.4%.

2. 60-day Pound (£) interest rate is 6.6%.

3. The exchange rate is £ 0.52 per $.

4. The 90-day $ and £ interest rates on the last settlement date were 5.6% and 6.4% respectively.

5. The fixed £ rate is 6.8%.

**Required:**

The present value in Dollars ($) of a $5,000,000 swap of the $ floating side. (3 marks)

The present value in Pounds (£) of a £ 2,500,000 counter party to the swap in (b) (i) above (£ fixed side). (3 marks)

The value of the receive $ floating pay £ fixed side of the swap. (3 marks)

3. Jackline Mutua, an investment analyst with Cooperative capital is analysing the company’s forward rate agreement (FRA) the company is exposed to and has gathered the following information:

1. The contract is 5.32%, 1 × 4 FRA with a principal amount of Sh.1 million.

2. 10 days have lapsed from initiation of the contract and the 110 days London Interbank Offered Rate

(LIBOR) is 5.9% with 20-day LIBOR quoted at 5.7%.

Assume a 360-day year.

**Required:**

Price of the FRA 10 days into the contract. (3 marks)

Present value of the FRA discounted at the 110-day rate. (4 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Outline SIX functions of the financial futures market. (6 marks)

2. The price of a 1-year put on a stock of KM limited with an exercise price of Sh.70 is Sh.5 and the forward price of the contract expiring in one year is Sh.81. The annual risk free rate is 10%.

**Required**:

Calculate the price of call option on a stock of KM Ltd. with an exercise price of Sh.70 that expires in one year using the put-call forward parity. (3 marks)

3. A bond fund manager purchases a five-year credit default swap (CDS) on BBB rated bond at the 2% spread. One year later the economy becomes weaker, causing credit spreads on four year BBB rated bonds and new CDS spread to increase to 2.5%. The bond fund manager sold his 2% CDS to a swap bank who hedged the CDS by selling a new 2.5% CDS on the four year BBB rated bond. The discount rate is 6% and the national amount is Sh.100 million.

**Required**:

Determine the maximum amount that the swap bank would pay the bond manager for assuming the CDS swap. (4 marks)

4. A firm has entered into a swap agreement for a national principal of Sh.100 million with a bank where bank paid 9% fixed and received secured overnight financing rate (SOFR) semiannually. It has 3 more years to go and has just exchanged the cash flow. The 6 month SOFR for the next payment of interest was reset at 8%. Next day, the market exhibited a fall and the 6 month SOFR fell to 7% leading the firm to believe that it is overpaying. It wants to cancel the swap arrangement.

**Required**:

Determine how much the firm should ask the bank to pay to cancel the swap deal. (7 marks)

**(Total: 20 marks)**