### TUESDAY: 25 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. In the commodities market, some possible forward market term structures are observed, according to the relationship between the expected future spot price and the current forward price and also by the relationship between the current spot price and the current forward price.

In relation to the above statement, explain the following possible forward market term structures:

Backwardation. (1 mark)

Normal backwardation. (2 marks)

Contango. (1 mark)

Normal contango. (2 marks)

2. Fanishi Fund is a hedge fund with a committed capital of Sh.500 million and carried interest of 25%. An investment of Sh.200 million is made. Later in the year, the firm exits the investment and earns a profit of Sh.110 million.

**Required:**

Determine whether the general partner receives any interest using the following waterfall distribution methods:

Deal by deal method. (2 marks)

Total return method 1. (2 marks)

Total return method 2. (2 marks)

3. The table below shows data from a sequential pay Collateralised Mortgage Obligation (CMO) tranches of Hakika Limited:

**Additional information:**

Tranche C had been split to create a floater with a principal of Sh.80,416,667 and an inverse floater with a principal of Sh.16,083,333.

**Required:**

Compute:

The capitalisation rate for the inverse floater assuming the coupon rate for the floater is 1 month LIBOR plus 1%. (6 marks)

The capitalisation rate on the floater assuming that the coupon formula for the floater is 1 month LIBOR

plus 1% and a floor is imposed on the inverse floater of zero. (2 marks)

**(Total: 20 marks)**

**QUESTION TWO**

1. Analyse FOUR benefits of incorporating alternative investments in a portfolio. (4 marks)

2. Describe FOUR legal documents used in establishing alternative investments partnerships. (4 marks)

3. The following is the mortgage pool held by Nyumba Bora Finance Corporation in the year 2022:

Loan Outstanding mortgage balances Mortgage rate (%) Months remaining

**Required:**

The weighted average coupon (WAC) rate for Nyumba Bora Finance Corporation mortgage pool.

(2 marks)

The weighted average maturity (WAM) for Nyumba Bora Finance Corporation mortgage pool. (2 marks)

The spot price of gold is Sh.228,600 per ounce. The current continuously compounded interest rate is 4%.

A 6-month forward contract on gold currently trades at Sh.230,560 per ounce.

**Required:**

Determine whether the contract is fairly priced. (2 marks)

Explain the steps to undertake the arbitrage opportunity in (d) (i) above, if any. (4 marks)

Calculate the arbitrage profit. (2 marks)

**(Total: 20 marks)**

**QUESTION THREE**

1. Explain the following types of mortgage structures:

Ballon payment loan. (1 mark)

Interest-only mortgage loans. (1 mark)

Fixed amortised mortgage. (1 mark)

Variable rate mortgage. (1 mark)

2. Pendo and company are real estate developers who invest in undeveloped land. Recently, they discovered a piece of underdeveloped land which they wish to invest in. The developers would like to estimate the value of the option to develop the land using binomial option pricing model approach. They intend to use a single-period binomial model. The risk free rate of return is 0%. They forecast that if the economy weakens, the cost of construction will be Sh.2,000,000, but the value of finished project will be Sh.1,750,000. If the economy strengthens, the cost of construction will increase to Sh.2,500,000, but the value of the completed project will be Sh.3,400,000. The developers have found out that comparable finished projects in the region are selling for Sh.2,080,000.

**Required:**

The value of the call option to develop the land. (4 marks)

The value of the call option assuming the construction cost are not positively correlated with improved

property, but fixed to Sh.2,100,000 with original expected value. (1 mark)

The value of the call option assuming the economy strengthens and the property is worth Sh.4,000,000

with the original construction cost. (1 mark)

3. A recently finished 50-unit estate in Nairobi rents at Sh.100,000 per unit per month for a five-bedroom house with a servant quarter. The estate currently has 45 units rented. Operating expenses, including income taxes, insurance, maintenance and advertising are 40% of effective gross income. The property manager is paid 10% of effective gross income. Other incomes from parking and laundry is expected to average Sh.500,000 per rented unit per year.

Capitalisation rate on comparable properties around the area is 5%.

**Required:**

The estimated net operating income (NOI) in the first year. (4 marks)

The estimated value of the estate. (1 mark)

4. Mwazo Ltd. is a startup company specialising in mobile applications. The company’s founders believe that they can sell the company for Sh.100,000,000 in four years time. Mwazo Ltd. requires Sh.14,000,000 in capital now, and from their projections after 4 years, they will want to hold 2,000,000 shares in the company. Azilisha Venture, a capitalist investor firm, decides that given the high risk of Mwazo Ltd., a discount rate of 45% is appropriate.

**Required:**

Calculate for Mwazo Ltd.:

The post-money valuation. (1 mark)

The pre-money valuation. (1 mark)

The ownership fraction for the venture. (1 mark)

The number of shares for the venture capital. (1 mark)

The stock price per share. (1 mark)

**(Total: 20 marks)**

**QUESTION FOUR**

1. Summarise FIVE stages associated with life cycle of a venture capital fund. (5 marks)

2. Highlight THREE advantages and THREE disadvantages of reward-based crowdfunding. (6 marks)

3. Tutor Private Equity (PE) Fund invest in private credit and distressed debt investments has invested Sh.20 million.

The Fund expects to earn an average return of 18% per year over a holding period of three years. The Fund charges a management fee of 2% of committed capital per year and a carried interest of 20% on profits above a hurdle rate of 12%. At the end of the holding period, the portfolio was sold for Sh.35 million.

**Additional information**

1. Management fees are calculated on committed capital. For Tutor Private Equity Fund, committed capital is equal to invested capital.

2. The hurdle rate is applied on a deal-by-deal basis, not on the overall portfolio.

**Required:**

Calculate:

The total management fees charged by the Fund over the holding period. (2 marks)

The total carried interest earned by the fund at the time of sale. (3 marks)

The net internal rate of return (IRR) earned by the Fund investors. (4 marks)

**(Total: 20 marks)**

**QUESTION FIVE**

1. Distinguish between “zero volatility spread (Z-Spread)” and “option adjusted spread (OAS)” in relation to mortgage backed and asset backed securities. (4 marks)

2. In relation to hedge funds:

Identify THREE primary elements of hedge funds. (3 marks)

Evaluate THREE reasons responsible for the growth of the hedge fund industry. (6 marks)

3. The following information relates to the coupon curve of prices for a pass through security for some months:

**Required:**

Compute the coupon curve duration for the 8% coupon pass through security. (3 marks)

4. A pension fund has been pursuing an investment strategy that tracks the stock market index that had a return of 8.6% with a standard deviation of 12%. The pension fund is considering an investment in a hedge fund with a standard deviation of 5.5% and expected return of 6.7%. The correlation between the stock market index and the hedge fund is 0.62 and the risk free return is 2.8%.

**Required:**

Calculate the hurdle rate on the hedge fund. (3 marks)

Advise the pension fund whether it should add hedge fund to its portfolio. (1 mark)

**(Total: 20 marks)**