FIN7050: Derivatives Investments B - Accounting and Finance Assignment Help

Assignment Task

Learning outcomes and pass attainment level:

1. Assess derivative contracts and their appropriateness and suitability for investment and management of different risks.

2. Construct derivative contracts to get exposure to investments in different markets & asset classes.

3. Evaluate different risks associated with investments & financing and use derivative contracts to hedge the relevant risks.

 

Answer all part of all 3 questions.

Question 1

Assume you are the risk manager of a hedge fund at Arcku Asset Management Plc, a UK based firm. The hedge fund is heavily invested in stocks and alternate investments due to its aggressive return targets. Strategic Investment targets and allocations are reviewed and revised by the Investment Committee on a quarterly basis on March 16th, Jun 16th, Sep 16th and Dec 16th. Hence, for the sake of simplicity, assume all derivative strategies have settlement/exercise date in line with these 4 dates or the nearest expiration dates available.

The equity portfolio is divided into 2 sub-portfolios: short-term and long-term capital gain targets. The Short to medium term return target sub-portfolio comprises mainly of value stocks. The managers pursue active trading based on style and benchmark deviations. As the main purpose of this portfolio is to provide liquidity and to meet short to medium term liabilities, trading is allowed as and when needed. On the other hand, the long-term return based strategic portfolio aims at significant capital gains to enhance the fund’s long-term net asset value, mostly comprising of growth stocks and physical assets. Strategic re-allocations are only allowed at quarter ends.

Mr. Peter Rogers, equity portfolio manager approaches you to consult on the use of Financial Derivatives using Options to hedge the equity portfolio. Mr. Peter Rogers has recently bought £20 million worth of Tesla stocks (£10 m is allocated to long-term and £10m allocated to short-term sub-portfolio) based on the company’s growth potential and current positive market outlook. However, he is aware that short term return expectations may not materialise and would like to hedge his position using covered calls and protective put.

In order to execute the 2 Option strategies for both types of stock sub-portfolios, you are considering 2 different methods of option valuation:

1. Year ended strategic re-adjustment using Calls and Puts on £10 m worth of Tesla stock in the Long-term portfolio, using 2 period Binomial Pricing model.

2. Use Black Scholes Mertin for short-term sub-portfolio.

You can choose exercises prices, expirations, risk free rate and measure of volatility to use as inputs in pricing the options1.

                             

Requirement:

I) Estimate the prices of European calls and puts for both strategies using the two-period binomial pricing model. Determine the hedge ratio, appropriate strategy and whether the strategy provided a perfect or imperfect hedge for each strategy.

 

II) How would the Call and Put prices differ if the options were American style.

 

III) Estimate prices of European puts and calls for both strategies with two different expiration dates and two different exercise prices of your choice using the BSM model.

 

IV) Do you agree with using Binomial pricing model for option pricing for stocks in long term return portfolio and BSM for short term? Hint: consider when trading is allowed. Also, discuss the main similarities and differences between these models and when should these be used?

 

Question 2:

At the yearly annual investment meeting, asset allocation across all classes is reviewed and revised. Currently, the size of the fund is £500m and fund’s 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?ch 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.

 

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.

 

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.

 

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.

 

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.

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.

 

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

 

VII) 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.

 

Question 3

Bond Portfolio:

Your colleague Nina Peter is also a risk manager at Arcku Asset management Plc and specialises in swaps. She has been temporarily assigned to your hedge fund to assist you.

Arcku Plc has outstanding bonds worth £200m, 5 year semi-annual pay, floating rate bonds with coupons rate equal to 180 day LIBOR + 50 basis points with an embedded call option. Arcku Plc is worried that interest rates may rise over the rest of tenor of the issue. This would increase the cost of debt financing and Arcku would like to hedge against this risk.

 

Nina Peter offers two solutions:

1. Arcku can call the bonds early, if LIBOR rises above 5% or,

2. Take a long position in a swaption with strike rate of 5% for the remaining 3 years.

The expected term structure of interest for the remaining tenor of the issue is as follows:

180 day LIBOR 4.5%

360 day LIBOR 5%

540 day LIBOR 5%

720 day LIBOR 5.6%

900 day LIBOR 6%

1080 day LIBOR 4.8%

 

Equity Portfolios:

The dividends received from stock holdings were previously re-invested into trending stocks in short-term sub-portfolio until the end of the financial year. Due to recent bleak outlook of the UK economy, Arcku Plc’s hedge fund has decided to re-invest the dividend income into foreign currency (Euros) instead, as the UK Pound has been and is expected to continue to lose value against the Euro. If the Pound depreciation against the Euro continues, Arcku expects earn positive returns from this strategy that would help ease up its cash shortages. Dividend income amounts to approximately 2.5% of size of equity portfolio, that is, £2.5 m every quarter.

Nina suggests that Arcku Plc should enter into currency swap for next 5 year to exchange the dividend income with another EU based hedge firm whose annual dividend income is the same as Arcku, when converted into Pounds. Given today’s exchange rate of £1 = € 0.85 any firm with dividend income of €/ £ (0. 85 x £2.5 m= € 2,125,000) should qualify.

If not swaps, Arcku’s may enter into a forward contract or a future contract or go long in currency option. Any method chosen must consider Arcku’s current cash shortage and require a minimum cash outflow over the next 2 to 3 months.

 

Currency portfolio:

In order to execute a currency hedge, Nina suggests it is important to determine what would be the correct spot price of the currency 3 months from now. Nina thinks that the Pound is likely to depreciate against the Euro, as the UK is expected to have a higher inflation rate compared to mainland Europe. The UK inflation expectation is at 4.5%, while the cost-of-living index for EU is expected to increase by 3% over the next 3 months. The spot exchange today is €0.85 = £1

 

Required:

Bonds:

(I) Discuss the possible benefits, costs and limitation of the 2 options presented by Nina.

 

(II) Determine the net settlement of Arcku from swaption?

(III) Comment on last swap settlement? Can this be avoided?

(IV) Derive the equation to show how can Arcku eliminate the uncertainty regarding FRN interest payments by using the swaption?

 

Equity:

(V) Critically valuate Nina’s statement regarding currency swap on equity dividends.

Consider all elements of the suggestion you may or may not agree with? (8 marks)

(VI) Assuming a currency swap is not feasible, is a long position in forward or future contract better, considering the cash shortage?

(VII) Determine the expected spot exchange 3 months from now. Are Nina expectations of currency movements, correct?

 

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