At the yearly annual investment meeting, asset allocation across all classes is reviewed and revised. Currently, the size of the fund is 500m and funds allocation is as follows:

10% forex (US and Euros dollar)

20% bonds

30% equity

20% alternate Investments (Real estate and commodities)

20% Private equity

Inflation forecasts have recently been upgraded due to supply and demand mismatch in the fuel and energy sector. This has impacted cost of living index around the world and most central banks now increasing key interest rates for this first time after the Covid-19 pandemic. Due to the uncertain forecast of the UK economy, the investment committee has decided to synthetically reduce bond and equity exposure by 10% each and redirect the funds to Real Estate through REITs (Real Estate Investment Trusts) and commodities.

• Beta of stocks in the fund is 1.2
• Beta of equity index futures is 1
• Price of equity index futures is 150,000

• Modified duration of bond portfolio is 6.2

• Price of bond futures is 30,500
• Duration of treasury futures is 5.0

• Beta of REITs in the fund is 1.2

I) Calculate the number of bond index futures contract and equity index futures that should be bought or sold to reduce to achieve the new allocation. (5 marks)

II) Calculate the number of REITs index futures the fund should buy or sell to increase the allocation to alternate investment by 15% of the fund value that is, 75m. REIT index future beta is 1 and price of REIT index future is 99,000. (3 marks)

III) As the risk manager, you are required to advise the investment committee on whether additional 5% exposure to commodities be gained through forwards and futures. Outline the main similarities and differences between these two. (6 marks)

IV) Assume, the firm decides to enter a forward contract with settlement in 3 months. Determine the price of the forward contract assuming discrete cash flows when the risk-free rate is 3.5%, spot price is 1509.04/ounce, carry cost is 3.86 and benefit is 6.76/ per ounce. Briefly explain how this works and expected gain or loss at settlement date. (3 marks)

V)You are also asked to explain the committee how a futures contract works. The clearing house that the hedge fund uses requires a 25% initial margin and 18% maintenance margin of the contract price. The expected spot price of the future over the next month is: Price end of Day 10 = 1520

Day 20 = 1535

Day 30 = 1400

Assume both parties agree to close out their position. Determine the expected payoff to long and short party. (4 marks)

Given the bleak economic outlook, the firm would also like to hedge its equity portfolio against unexpected price movements. Based on historical data, the equity portfolio manager expects some volatility but is convinced that extreme outcomes are unlikely. He is considering several hedging strategies but is faced with severe cash shortages. Mr. Smith; one of the portfolio managers, suggested to the investment committee that it would be cheaper to acquire increased equity exposure synthetically through options rather than futures.

(V) Do you agree that options are cheaper than futures contracts? Consider overall gain and losses from these 2 positions in explanation your answer? (3 marks)

VI) Mr. Smith also suggested either a collar or a straddle should be used to benefit from the uncertainty. Explain with the aid of diagram, how a collar and straddle work and which strategy would cost lesser to employ. Consider for both: maximum profit, maximum loss and break-even.