Trading Interview Questions

Brainteaser 1
There are N dice, each having x faces. What is the number of combination that give at least one 1 or x?
Ans: (x - 2)^N

Brainteaser 2
What is the longest diagonal within a k-dimensional hypercube?
Ans: sqrt(k)

Finance 1
You purchase a 5yr pure discount bond at 5% yield. One month later you sell it at 4% yield. What is the IRR of this investment?
Ans: ~60%

Finance 2
You enter into a pair trade consisting of CDS_A of 5yr tenor and 100bps, and CDS_B of 5yr tenor and 300bps. Suppose the spread narrows down to 100bps (from 200 bps) after 1 year and you are to unwind it. Describe the strategy and estimate the profit of this trade.
Ans: Sell protection with CDS_B and buy protection with CDS_A. Profit = 600bps (why?)

Finance 3
Part I
You, an American investor, are holding a 10yr convertible bond that is convertible over the first 5 years. Explain what risks you are exposed to and how they can be hedged away.
Ans:
a) Price risk (wrt the underlying equity). Can be hedged by shorting vanilla call.
b) IR risk. Can be hedged by shorting one (or more) zero coupon bonds, or entering into a fixed EUR for floating EUR swap.
c) FX risk. Can be hedged by entering into a floating EUR for floating USD swap.
NOTE: or we can enter into a fixed EUR for floating USD swap to hedge both IR and FX risks.
d) Credit risk. Can be hedged using CDS.
Part II
Suppose this is the only bond issued by the company. How do you calculate/estimate the price of a non-convertible 5yr bond issued by the same company?
Ans:
1. Strip away the embedded option to find the price of non-convertible 10yr
2. Find the spread of non-convertible 10yr over treasury curve/LIBOR swap curve
3. Here we have to make some sort of assumption regarding the term structure of the spread: constant, or usually slowing increasing
4. Using the spread term structure, find the spread of non-convertible 5yr over treasury curve/LIBOR swap curve
5. Using the spread of non-convertible 5yr over treasury curve/LIBOR swap curve, find the yield and hence the bond price

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