Brain Teaser | Quant Stipend

Source: Google

Question: 

Eight interns hired from IIM Bangalore in different quant profiles are getting together for drinks. They are all interested in knowing the average stipend of the group. Nevertheless, being cautious and humble individuals, everyone prefers not to disclose his or her own stipend to the group.  

Can you come up with a strategy for the interns to calculate the average stipend without knowing other people's stipends?  

 

Solution: 

There can be more than one answer.  

One approach is for the first intern to choose a random number, adds it to his/her stipend and gives it to the second intern. The second intern will add his/her own stipend to the result and give it to the third intern; the eighth intern will add his/her own stipend to the result and give it back to the first intern. Then the first intern will deduct the "random" number from the total and divide the "real" total by 8 to yield the average stipend.  

 

You may be wondering whether this strategy has any use except being a good brain teaser to test interviewees. It does have applications in practice.  


For example, a third-party data provider collects fund holding position data (securities owned by a fund and the number of shares) from all participating firms and then distribute the information back to participants. Surely most participants do not want others to figure out what they are holding. If each position in the fund has the same fund ID every day, it is easy to reverse-engineer the fund from the holdings and replicate the strategy. So different random numbers (or more exactly pseudo-random numbers since the provider knows what number is added to the fund ID of each position and the complicated algorithm is involved to make the mapping one to one) are added to the fund ID of each position in the funds before distribution. As a result, the positions in the same fund appear to have different fund IDs. That prevents participants from re-constructing other funds. Using this approach, the participants can share market information and remain anonymous at the same time.  

 

For more visit - Medium


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