Individual Project: Cyberdyne Systems

Report format: MS Word

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You work as an analyst for Cyberdyne Systems in Los Angeles, CA.

Yoshiyuki Sankai, the CEO, has ordered a pair of advanced supercomputers from the UK for

an artificial intelligence based neural network system called Skynet.

The equipment will cost £ 150 million and is due in Pounds, one year from now. Sankai is

concerned about the foreign exchange exposure of this upcoming payment. Especially

during the last 12 months, currency market volatility has been high, fueled mostly by

uncertainty about the potential weakness of the US dollar.

State Street Bank in Boston offers the following spot rate and 12 months forward points1 (see footnote):

Spot ($/£) 1.3140/ 1.3145

12 months ($/£) 72 / 67 (.0072 / .0067)

You look at Bloomberg for interest rates to calculate a money market forward alternative:

USD 12-month interest rate 0.96 % / 0.98 %

UK 12-month interest rate 1.51 % / 1.55 %

You call the Bank of New York Mellon (BNYM) and ask for one year 1.3150 $/£ strike call option to buy £ 150 million.

BNYM quotes the following one year offer price for you to buy the option.

One year call option on Pounds (exercise price) 1.3150 $/£

Percentage of $ amount at exercise price 4.38 %

Assignment: Analyze each of the alternatives below, and then choose one as your suggested hedging strategy. The

possible hedging choices are:

a) Remain unhedged.

Evaluate the risks and results of this strategy ($ cost) if the $/ £ turns out to be 1.20, 1.25, 1.30, 1.35, 1.40, 1.45, 1.50.

b) State Street forward hedge. Explain the implementation of this hedge and the cash flows at maturity. (A. What is the

exchange rate that Cyberdyne would have to pay if they used this alternative? B. What is the $ cost of the

machinery?)

1In the interbank market, dealers quote forward points as pips (1 pip is equal to 0.0001). To derive the outright forward rate, you need to add or subtract the

appropriate forward points to or from the spot rate. If the forward bid points < forward ask points (forward premium), add the forward points to the spot. If
the forward bid points > forward ask points (forward discount), subtract the forward points from the spot.

c) Money market hedge. Explain the implementation of this hedge (all the transactions needed) and the cash flows at spot and

at maturity. (C. What is the effective exchange rate that Cyberdyne would have to pay if they used this alternative?

D. What is the $ cost of the machinery?)

d) Cyberdyne Systems does not use futures contracts to hedge, but to make your report complete, you want to include a section

on British pound currency futures and the steps Cyberdyne would take to hedge the exposure. Describe how futures could be

used to hedge this risk. Assume the currency futures market for the pounds is fairly priced. Explain in detail the

implementation of this hedge and the cash flows / transactions you would have to make on day one and at the time of the

account payable if you were to use a futures hedge. (E. Which contract month? F. How many contracts would you buy

or sell? G. When would you remove the hedge?)

e) BNYM option hedge.

i. Use the option model to see the implied volatility of the BNYM option premium using only the data in the case. In

other words, what combinations of the given strike price, maturity, volatility, spot, and the US 12m interest rate,

UK 12m interest rate would generate the call option price from BNYM. Include a screenshot of the option model

results. (H. What is the implied volatility you calculated?)

ii. Evaluate historical volatility using actual spot $/£ prices (not from the case) over the past three months, six

months, and past year starting from the actual day you download the data. (Use Bloomberg or an online source.)

http://www.investopedia.com/ask/answers/021015/how-can-you-calculate-volatility-excel.asp

(Include screenshots of your final calculations – not all the data – but save your data in case I ask for it later.)

(I. What is the three month volatility you found? J. Six month volatility? K. One year volatility?)

iii. Based upon what you found out about historical and market quoted volatility (above in ii and iii), compare it to the

implied volatility you found (above in i) to see if the BNYM call option is fairly priced.

(L. Yes/No/Maybe.) Discuss your choice.

iv. Evaluate the overall hedged results of this strategy ($ cost) if the $/£ turns out to be 1.20, 1.25, 1.30, 1.35, 1.40,

1.45, 1.50 noting in what cases the option is exercised or not, and (M. Which exchange rate scenario of the

above works out best for Cyberdyne – list only the exchange rate that works out best) if they hedged with

the call option. (Be careful on this.)

Deliverable: The deliverable should be formatted as if you work in the corporate finance department at Cyberdyne and

are submitting this to the CEO. Please use only your own words. The following section headings are suggested:

Introduction of the problem

Analysis of each hedging alternative with valuations/risks/rewards answering all the questions for each section

Recommendation

At the end, list just the answers (without explanation) to questions A-M, labeled very clearly in a column.

The case is due on Sunday, April 10th at 2pm via TURNITIN as a single MS Word document. (Embed screenshots

of Excel calculations as needed. Do not submit a separate Excel file. You are strongly advised to start work on this

soon, as it is a very complex case. Use the option model I post on Blackboard (under Course Documents) for all

option calculations. Late cases will be penalized 10% per day with no exceptions, as you have more than enough time

to complete this case well ahead of the deadline.

You have all the information you need above to complete the case, which you should consider a take-home test. You

should work on it alone, not in groups, and you should not seek help from the LEAF or any other source. I will post

a video explanation of the case which you should use alongside the course materials on forwards, futures, and options.

0.20%

1.0000

0.20% 0.20%

1.000%

0.0020

0.0020 0.0020

80.1425

0.0000

-0.0012 0.0012

0.3989

0.4990

0.5010

Black-Scholes Worksheet for Foreign Currency Options | ||||||||||||||||||||||||||||

The user must change the yellow inputs | ||||||||||||||||||||||||||||

Inputs | % of $ Amount | % of £ Amount | ||||||||||||||||||||||||||

Spot Rate ($/£) | 1.0000 | Call Price = | 0.20% | |||||||||||||||||||||||||

Strike price ($/£) | ||||||||||||||||||||||||||||

volatility (annualized) | 1.00% | Put Price = | ||||||||||||||||||||||||||

US interest rate (annualized) | 1.000% | |||||||||||||||||||||||||||

Sterling interest rate (annualized) | ||||||||||||||||||||||||||||

time to maturity in days (365 day year) | 90 | |||||||||||||||||||||||||||

time to maturity in years | 0.25 | |||||||||||||||||||||||||||

Call Option | Put Option | |||||||||||||||||||||||||||

Option Prices | 0.0020 | The units are the same as the exchange rate | ||||||||||||||||||||||||||

Delta | 0.4998 | -0.4978 | Derivative of price wrt spot rate | |||||||||||||||||||||||||

Vega | Derivative of price wrt volatility | |||||||||||||||||||||||||||

Gamma | 80.1425 | Derivative of delta wrt spot rate | ||||||||||||||||||||||||||

Theta | 0.0000 | Derivative of price wrt time measured in days | ||||||||||||||||||||||||||

Rho domestic | 0.0012 | -0.0012 | Derivative of price wrt to the domestic interest rate | |||||||||||||||||||||||||

Rho foreign | Derivativeof price wrt to the foreign interest rate | |||||||||||||||||||||||||||

Required Expressions | ||||||||||||||||||||||||||||

Black-Scholes D1 | 0.0025 | |||||||||||||||||||||||||||

Black-Scholes D2 | -0.0025 | |||||||||||||||||||||||||||

Cumulative Normal(D1) | 0.5010 | |||||||||||||||||||||||||||

Cumulative Normal(D2) | 0.4990 | |||||||||||||||||||||||||||

Normal PDF(D1) | 0.3989 | |||||||||||||||||||||||||||

Normal PDF(D2) | ||||||||||||||||||||||||||||

Cumulative Normal(-D1) | ||||||||||||||||||||||||||||

Cumulative Normal(-D2) |

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