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FINM3405 Assignment Questions
“Big Game: Goldman Sachs' Elephant Hunt in Libya”
Assignment weight 25% +5% (total marks 100)
As a starting point, carefully read “Big Game: Goldman Sachs’ Elephant Hunt in Libya” (see
URL on Blackboard under “Assessment\Team Report”). Please use this case as a background,
together with your reading and understanding of the lecture/textbook and other
publications from academic journals, to carefully develop your answers to the questions listed in
each section. Your report should basically follow the following format.
Introduction (10 marks)
Write an executive summary with no more than 400 words. (10 marks)
Trade Mechanics (10 marks)
1. Based on your own estimates, what do you think of the scenario analysis Goldman
provided to the LIA (Exhibit 4)? (10 marks)
Trade Rationale (6 marks)
1. What might be the LIA’s motivation to enter a trade specifically on Citigroup’s stock?
(3 marks)
2. What might be Goldman Sachs’ motivation(s) for organizing that trade? (3 marks)
Trade Valuation: Value Bounds (10 marks)
The trade being equivalent to a call, it can be valued as such. As valuing options is model-
dependent, it is useful to first derive model-independent value bounds based on the absence
of riskless arbitrage opportunities. Bounds can be inferred from listed options and Put-Call
Parity.
1. Listed American options on Citigroup’s stock were traded on the day of the first Citigroup
trade (Exhibit 5). Explain briefly the following (no calculations needed): (5 marks)
a. All else equal, are call options with higher strike prices more or less valuable?
b. All else equal, are call options with a longer time to maturity more or less valuable?
c. All else equal, is an American call option worth more or less than a European call option?
d. Do listed options entail more or less counterparty risk than over-the-counter options?
e. Simply based on the options’ parameters (strike, maturity, American vs. European), are any
of these call options clearly worth more, or worth less, than the trade itself?
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2. Put-Call Parity (PCP) gives value bounds too. Ignoring any dividends Citigroup might pay
until the trade’s maturity, PCP writes C = S + P – PV(K), where C and P are the values of a
European call and put, S is the price of the underlying asset, and PV(K) is the present value of
a risk-free payment of the strike price K at maturity (i.e., discounted at a 2.28% risk-free rate).
(5 marks)
a. Explain why a put’s value cannot exceed its strike price’s present value (i.e., P ≤ PV(K)).
What is an upper bound for the call’s value C? Explain briefly.
b. Explain why a put’s value cannot be negative (i.e., P ≥ 0). What is a lower bound for the
call’s value C? Explain briefly.
c. Based on the above, estimate an upper and a lower bound for the trade’s value.
d. Where does the $100m price the LIA paid lie relative to the upper and lower bounds? Given
this, did Goldman or the LIA make a riskless arbitrage profit on the trade? If yes, explain how.
If not, does this mean the trade was done at a fair price?
e. Check whether PCP holds for the listed options. If it doesn’t, why might that be?
Volatility (5 marks)
1. Does higher volatility for Citigroup’s stock imply a higher or lower value for the trade?
Explain briefly (no calculations needed). (2 marks)
2. Estimate the volatility of Citigroup’s stock return using stock price history as follows:
a. Using Citigroup’s stock prices S in the Volatility spreadsheet in the BIG GAME (Data +
Templates) Excel file, compute daily stock returns R. The data covers the one-year period
before the trade. The one-day return is Rt = ln(St /St-1) with continuous compounding or Rt
= (St−St-1)/St-1 with simple compounding. With daily data, the compounding frequency has
little impact. (1 mark)
b. Estimate the standard deviation of daily returns (using Excel’s STDEV function). (1 mark)
c. Annualize the standard deviation of daily returns by multiplying it by the square root of
254, the approximate number of trading days in a year. (1 mark)
Binomial Tree (12 marks)
1. Value the trade (i.e., the equivalent call) at inception with a binomial tree (ignore dividends).
Build a 3-step tree (1 step = 1 year), using the template in the Binomial Tree spreadsheet in
the BIG GAME (Data + Templates) Excel file. The up and down factors are u = √∆ and d = 1/
u with =37% Citigroup’s annual return volatility and T a step-in years (e.g., T=1 if 1 step = 1
year).
a. Build a tree for Citigroup’s stock, and another for the call. What is the call’s value? (3
marks)
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b. Value the trade at the time of the case (07/23/08). Citigroup’s price was $21.12 and
assume no change to volatility and interest rates. Use the same tree, reducing the length of
a step. (3 marks)
2. Value the listed call and put options, again ignoring dividends.
a. Use the same tree to value the 1- and 2-year listed options. To do so, cut the length of a
step (e.g., for 1-year options, 1 step = 4 months = 1/3 year). The risk neutral probability,
discount factor and up and down factors will adjust automatically in the sheet. The options
being American, the option tree should be adapted to allow early exercise (i.e., before
maturity). Might these options be exercised early? (3 marks)
b. How well do your models match actual market prices? What might be missing? (3 marks)
The Black-Scholes Formula (11 marks)
1. List and justify briefly the values you set for the Black-Scholes formula’s different inputs,
and value the trade (i.e., the equivalent European call option) using the formula. You can use
the Black-Scholes spreadsheet in the BIG GAME (Data + Templates) Excel file. (11 marks)
Conclusion (10 marks)
1. Do you think Goldman Sachs exploited the LIA? Explain briefly with no more than 400
words. (10 marks)
References and Formatting (10 marks)