FIN 7220 Homework 1
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FIN 7220 Homework 1
1. Identify if there is an arbitrage opportunity in the following scenarios. If yes, how do you form your strategy?
(a) In Forex market, 1 USD is traded at 6.344 CNY and 7.851 HKD, and 1 CNY is
traded at 1.229 HKD.
(b) Assets A, B, and C’s prices and payoffs are given below. Construct TWO different
trading strategies if there are arbitrage opportunities.
(c) Assests A, B, C, and D’s prices and payoff are given below Construct TWO different trading strategies if there are arbitrage opportunities.
2. There are three states of the economy. Sufjan is expected to receive a bonus with the following payoffs. There are three assets traded in the market, with year-end cash flows
and their current prices given by:
(a) Using no arbitrage principle, can you determine today’s ”price” of Sufjan’s bonus?
[Hint: note that Sufjan’s bonus is also an asset.]
(b) If Sufjan desires smooth consumption across the three different economic states,
what can he do to achieve this? [Hint: Smooth consumption is an asset with equal payoffs at each state, and the cost to replicate these cashflows should be equal to your answer in 2(a) (self-funded project).]
(c) Suppose the three states represent low, medium, and high economic conditions. Among the three securities A, B, and C, can you identify which one pays off $1 in the high economic state? And which pays off $1 in the low economic state?
3. Consider the gamble in which you draw a random ball from a container of 98 blue balls and 2 red balls. It requires $1M to participate. You earn nothing if you draw a blue ball but you win $200M if you draw a red ball.
(a) If you play this gamble once, what is your average return and what is the proba-
bility of earning nothing?
(b) If you play this gamble 100 times (you have to pay $1M each time you play), what
is your average return and what is the probability of earning nothing at the end? [Hint: The number of times of wining follows Binomial Distribution]
(c) If you play this gamble 100 times, what is the probability that you at least break even?
4. Suppose that the stock market consists of only two stocks: Stock ABC and Stock EFG. Please predict the price change of stock ABC in the following scenarios. (Hint: when analyzing one factor, fix all other factors unchanged. Graphs may help. If you need more conditions, state them clearly.)
(a) Wall Street analysts predict that Company EFG’s next quarterly earnings will be
$10 per share, which is lower than investors’ initial prediction.
(b) Following (a), Company EFG finally announces that their earnings is $12 per
share.
(c) Company EFG restructures their current business by scaling down their most risky business operation.
(d) Analysts’s disagreement on the Company ABC’s next quarterly earnings increases. For example, Analyst A and Analyst B’s forecasts differed by $2 before but now this difference increases to $4.
(e) The Central Bank announces Reverse-Quantitative Easing.
2021-12-16