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Quantitative Finance Analyst interview questions shared by candidates

## Top Interview Questions

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Quantitative Finance Summer Associate was asked...5 August 2010

### At a party everyone shakes hands, 66 hand shakes occur, how many people are at the party?

12

You can suppose there are n people in the room and think of them in a row. The first one has to shake hands with (n-1) people (because he doesn't have to shake hands with himself). The second one has already shaken hands with the first one, so he has (n-2) shakes remaining... and so on. So you have to sum: (n-1)+(n-2)+(n-3)+...+1= (n/2)*(n-1) Then you have to solve (n/2)*(n-1)=66 and you get n=12. Less

n(n-1)/2=66 so n=12

### There are two stocks with the same expected value, with variance 0.3 and 0.2 and correlation 0.5. What proportion of each stock do you invest in to yield a minimum risk portfolio?

17/44 of the stock with variance of .3 and 27/44 from the stock with variance of .2 Less

No, if you can short, the variance could be reduced even further since the stocks are correlated. Less

Above answers used variance in portfolio variance equation, rather than std. Answer is .386 for security with var .3, and .613 for security with var .2 Less

### A use 5 hours finish a job. B use 8 hours finish it. How long A and B take it together?

I mean it is not correct (but probably I do not have got true): 1 hour A can make 20% (1/5) B can make 12.5% (1/8) A+B can make 32.5% (1/5 + 1/8 = 13/40) The work will be finished at 100% (1) 1 hour - 32.5% (13/40) x hour - 100% (1) x = 1*1/(13/40) = 40/13 = 3.077 (hours) tha half of the equation was good, but: 8 = X + 1.6*X = 2.6X; -&gt; x=8/2.6) Please post a comment if I do not have true!!! Less

40/13

http://brainteaserbible.com/interview-brainteaser-andy-and-ben-working-together

### What kind of subjects are you looking to teach?

I detailed my CV and what relevant subjects I could teach. Also went through my demo. Less

I wanted to teach Urdu

To implementing the policies and plans developed by the top managers

### If W is standard Brownian Motion, for what values of n is W^n still a martingale?

By Ito W^n is a martingale for n=0,1

Xt is a martingale you get f(Xt) is a martingale if f is linear otherwise convexity or concavity will increase or decrease the expectation, think of Jensen inequality. Less

Agree, for any n&gt;1 you get a drift term

### In a set of cereals, there are 4 kinds of coupons. A child wants to collect all the 4 kinds of coupons. How many boxes in average should he buy?

25/3

sorry, should be 25/3

169/16

### Evaluate the integral from 0 to pi/6 of sec(x) dx.

ln(root 3)

ln(3)/2

Reaching back to high school, I'd say -.5

### Each timestep an Amoeba can produce 0,1,2 offspring or it can die with equal probability for each event (1/4 each). What is the probability that the population can survive indefinitely?

sqrt(2)-1

0: it is an undercritical process.

### Say you have one bacterium now. In any minute, each living one has a quarter chance of dieing, a quarter of staying still, a quarter of splitting into 2, and a quarter of splitting into 3. What is the probability of this species dieing out finally.

(1+p+p^2+p^3)/4 = p So p = sqrt(2) - 1.

P(dying out)= \sqrt(2)-1