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Baruch MFE Baruch MFE Facebook Contest

dstefan

dstefan

Baruch MFE Director
Joined
5/19/06
Messages
1,336
Points
93
Baruch MFE Facebook Contest ​

The Baruch MFE Program will hold a one week Facebook contest beginning on Monday, April 18. One question will be posted every day at 12noon New York time (EST) on the Baruch MFE Facebook page, beginning on Monday 04/18 through Saturday 04/23. The contest is open to people all over the world.

The questions will be similar to phone interview type questions, requiring short answers. Sample question:

By how much would the price of a five year zero-coupon bond change if the yield increases by ten basis points?

Answers will be posted as Comments on the Facebook Page.

Prizes:
1st Prize: Signed copy of A Primer for the Mathematics of Financial Engineering, Second Edition and its Solutions Manual, by Dan Stefanica, the Director of the Baruch MFE Program, and a meeting with the author (or phone conversation, if not located in the NY area)
2nd Prize: Signed copy of "A Primer for the Mathematics of Financial Engineering, Second Edition" and its "Solutions Manual"
3rd Prize: Signed copy of "A Primer for the Mathematics of Financial Engineering, Second Edition"

Scoring:
2 points - every correct answer submitted in the first 5 minutes after the question is posted
(suggestion: post your answer as close to the 5 minute mark as possible :))
1 point - every correct answer submitted in the first 30 minutes after the question is posted,
but later than the first 5 minutes
3 points - the best answer submitted within one hour of the question being posted

Good luck, and looking forward to it!
 
The contest will start a week later, on Monday, April 18, to allo more people to participate. Good luck to everyone!
 
To better gauge the kind of questions that will be asked, a possible one would have been as follows:

A six months butterfly is made of long positions in a $40 strike call and a $50 strike call and short two $45 calls.
(i) For what values of the underlying asset at maturity would the butterfly spread have a positive payoff?
(ii) If the butterfly spread was set today, by purchasing the $40 strike call for $6, the $50 strike call for $1, and be selling the $45 strike calls was sold for $3 each, for what values of the underlying asset at maturity would the butterfly spread be a profitable investment?
 
Would anybody attempt a solution? We will point out correct answers and what would constitute a 3 points answer.
 
I'll try.

(i) The value at maturity of the butterfly spread is (V(T) = \max(0,S(T)-40)+\max(0,S(T)-50)-2 \max(0,S(T)-45)). Consider the following ranges of the underlying asset at maturity: ( S(T) < 40, 40 \leq S(T) < 45, 45 \leq S(T) \leq 50, 50 < S(T)).
Then

(
V(T) = \left\{
\begin{array}{rl}
0 & \text{if } S(T) < 40, \\S(T)-40 & \text{if } 40 \leq S(T) < 45,\\50-S(T) & \text{if } 45 \leq S(T) \leq 50,\\0 & \text{if } 40 < S(T).
\end{array} \right.
)

Therefore V(T) is positive for (40 < S(T) < 50).

(ii) To be profitable, we need the following to be positive: V(T) minus the future value at maturity of the cost of the investment. Today the cost of butterfly spread is $6 + $1 - 2*$3 = $1, and the future value at maturity is (\$e^{rT}), where (r) is the constant risk-free rate. Therefore we have the profit

(

\text{Profit}(T) = \left\{
\begin{array}{rl}
-e^{rT} & \text{if } S(T) < 40, \\S(T)-40-e^{rT} & \text{if } 40 \leq S(T) < 45,\\50-S(T)-e^{rT} & \text{if } 45 \leq S(T) \leq 50,\\-e^{rT} & \text{if } 40 < S(T).
\end{array} \right.
)

Profit is positive for (40+e^{rT} < S(T) < 50-e^{rT}).
 
I'll have you know that I've been dreaming of a conversation with Dan all my life. Why shatter my dreams like that? :(
 
In three hours, the first question will be asked on the Baruch MFE Facebook page. They will be typical phone interview questions, with a correct brief answer and a more involved answer showing a deeper understanding. Looking forward to it!

A reminder about the rules:

Scoring:
2 points - every correct answer submitted in the first 5 minutes after the question is posted
(suggestion: post your answer as close to the 5 minute mark as possible :))
1 point - every correct answer submitted in the first 30 minutes after the question is posted, but later than the first 5 minutes
3 points - the best answer submitted within one hour of the question being posted
 
We can disclose the first question is not a probability brainteaser. 33 minutes left to posting the first question. Post answers as responses on Facebook.
 
post the answer here, since it was a technology problem.
 
All correct answers posted by 12:30pm will receive one point each. the best answer received by 1pm will receive three points.
 
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