Interview Questions at JPMorgan Sales and Trading

[Andy Nguyen]

The following questions are said to be asked during an internship interview for a sales and trading role at London JPMorgan bank

1) I can pay you twice your money every two years, three times your money every three years or four times your money every four years. Which option do you choose and why?

2) I flip a coin. If it's heads you pay me £100. What should I pay you to play this game? What about if I only have to get 1 heads in two tosses, what is the new price?

3) What is the smaller angle between the two hands of the clock when it’s five minutes past nine?

4) What happens to pension liabilities when interest rates go up?

5) What will you do if you don't get an offer at JP Morgan?

6) Do you have any remunerated work experience? Did you get on well with your manager?

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[euroazn]

For two, do you just mention that your utility function is offset by volatility/risk? (So a minimum rather greater than 50 [75 for part two] but less than 100 - example: 66 and 90)?

Also, how much time do you essentially get per question, and is it all in your head (e.g number 3)?

 

[Andy Nguyen]

The interviewers will want you to "think out loud" so time per question is not that important. You don't want to take one hour to think out loud one question. That would be ridiculous.

For question 3, it's not that difficult to talk your logic through it.

The angle between any two consecutive number on the clock is 30 degree. At 9 o'clock, the smaller angle is 90 degree. At 9:05, the minute hand is at number 1.
In 5 minutes, the hour hand moves 2.5 degree clockwise.

So the answer is 90 (angle at 9 o'clock) + 30 (additional angle of minute hand) - 2.5 (angle of hour hand) =117.5 degree

 

[Stuart Truax]

If my logic is correct on the first one, it requires that the interviewee know that 3^(1/3) > 2^(1/2) = 4^(1/4). Does anyone know any quick manual methods for estimating cubed roots?

 

[euroazn]

@Stuart
To compare 2 and 3, just take the ending amount of money after 6 years.

 

[Stuart Truax]

@Stuart
To compare 2 and 3, just take the ending amount of money after 6 years.

LOL. Precision can be a time killer. Thanks.

 

[TBeas]

Isn't the first one saying 2*salary not salary^2? So it is linear. That is how I read it. Saying you have twice as much as something just means double.

 

[Andy Nguyen]

Question 1 needs to be generalized, that is your solution needs to be flexible enough to solve "your salary will grow by a factor of X in X years", how do you maximize the equation to find best X.

Then, let t be the time you are expected to work there, let fix X and try to find the best t.

Your thought process is more interesting than the answer. A lot of questions has no correct answer.

 

[Ezra]

Isn't the first one saying 2*salary not salary^2? So it is linear. That is how I read it. Saying you have twice as much as something just means double.

You definitely wouldn't choose 4x every 4 years, because 2x every 2 years is equivalent to a payment of 4x every four years with an extra payment in between each 4 year period.

So its between 2x and 3x. This should depend on how long the stream of payments are. If it is only 6 years, then 2x is better (x +2x+4x+8x = 15x vs x + 3x +9x = 13x). However, eventually 3x every 3 years should overtake 2x every 2 years in total pay, but Im not sure the best way to figure out (w/o pen/paper/calculator) when that happens.

But if we go out another 6 years, the total payout from 2x every 2 years should be 15*8x +2x +1 = 127x , and similarly for 3x it should be 13*9x +3x +x = 121x. So for a 12 year period, 2x is still better. However by the 12th year our payout should be 64x (just for that year, not total payout) for 2x E2Y and 91X for 3x E3Y, taking it out another 6 years we see the 3x option overtakes in total pay (13*91x > 15*64x). So if the stream is for longer than 18 years 3x is better, and 2x is better for anything 13 years or less. Would have to think a bit more about length in between 13 yrs and 18 yrs.

Edit: just realized its not enough to just say 13*91x > 15*64x to conclude total pay for 3x overtakes 2x. You would have to say (13*91x + 30x) > (15*64x + 63x). since 13*91x and 15*64x represent only the total pay over the 6 year period between year 6 and 12, and doest account for the differences in earlier payments.

And theres no way I can see myself getting this far in the heat of an interview without taking an awkwardly long time. I guess thats where practicing these kinds of questions thoroughly before an interview can really pay dividends.

 

[euroazn]

So its between 2x and 3x. This should depend on how long the stream of payments are. If it is only 6 years, then 2x is better (x +2x+4x+8x = 15x vs x + 3x +9x = 13x). However, eventually 3x every 3 years should overtake 2x every 2 years in total pay, but Im not sure the best way to figure out (w/o pen/paper/calculator) when that happens.

Correct me if my logic is off.

I might be completely dumb, but that would never happen.
After 6 years, set that year to zero. If the starting sums were even equal, then 2 would overcome, correct? However, the starting sum for 2 is even higher, so 2x is consistently higher. Does that make sense?

 

[tobias elbert]

In regards to the salary question, what does the forward (rate) curve look like?

 

[euroazn]

Ezra, I think your streams are wrong since you are not compounding...?
I.e it should be
Money Stream
1 2
3 6
9 18
27 54

For 2x, assets are in the form of 3^(t/2).

For 3x it is similar
Money Stream
1 3
4 12
16 48
64 192

As you can see, assets are in the form of 4^(t/3) for 3x

Thus it is a comparison between 3^1/2 > 4^1/3

 

[Ezra]

Ezra, I think your streams are wrong since you are not compounding...?
I.e it should be
Money Stream
1 2
3 6
9 18
27 54

For 2x, assets are in the form of 3^(t/2).

For 3x it is similar
Money Stream
1 3
4 12
16 48
64 192

As you can see, assets are in the form of 4^(t/3) for 3x

Thus it is a comparison between 3^1/2 > 4^1/3

What we're comparing are the areas under different step functions.

A spreadsheet will show u 3x overtakes 2x on and after 15 years.

Another way to look at it is comparing annualized "growth" rates. 2^1/2 = 4^1/4 < 3^1/3. But since we are really comparing the areas under two step functions, not continuous functions, 2x is optimal for t<15 years and 3x is optimal for t>=15 years. A basic spreadsheet should make it clear.

And it is important to note that I'm ignoring interest rates for simplicity =)

 

[pramau]

choose option 3 times in 3 years

1) I can pay you twice your money every two years, three times your money every three years or four times your money every four years. Which option do you choose and why?

answer..

can we take lcm of 2,3,4= 12

and then @ 2x multiples in 2 years implies 2^6= 64x in 12 years
@3x mltp in 3 years implies= 3^4= 81x in 12 years
@4x mltp in 4 years implies= 4^3=64x in 12 years

so it looks like you get highest returns by choosing second option @3x in 3 years. rest of the options give equal returns but not highest!!

let me know if the logic is correct.

Pramau

 

[AlexandreH]

For question 2:
you would pay anything that will give you positive Expectation.
so, for the first part, prob of H = prob of T = 1/2.

RV x= x0? 100
f(x) 1/2 1/2

the maximum you are willing to pay is 100 (or x0= -100), at which E[x]=100 x 0.5 - 100 x 0.5 = 0


for the second part
Prob H in two tosses = 1/2 + 1/2 x 1/2 = 3/4

RV x= x0? 100
f(x) 1/4 3/4

Maximum you are willing to pay is x0=100 * 3/4 / 1/4 = 300 (or x0=-300)
What do you think?

 

[pramau]

Phd Math entrance test question :

Q:suppose 3 coins with 1st coin both sides white,second coin (black & white) and 3rd coin both are black sides then what is the P(white side/white) = ?

 

[Ezra]

1) I can pay you twice your money every two years, three times your money every three years or four times your money every four years. Which option do you choose and why?

answer..

can we take lcm of 2,3,4= 12

and then @ 2x multiples in 2 years implies 2^6= 64x in 12 years
@3x mltp in 3 years implies= 3^4= 81x in 12 years
@4x mltp in 4 years implies= 4^3=64x in 12 years

so it looks like you get highest returns by choosing second option @3x in 3 years. rest of the options give equal returns but not highest!!

let me know if the logic is correct.

Pramau

I think the question is a little vague. If it is to be understood as a salary than triples/doubles/quadruples then you need to take into account income over the total period. If it is understood to be an investment whose proceeds you can continually reinvest, your approach is valid.

There is also a third way to interpret the question, and that is of 3 different sets of CONSTANT cash flows: 2x every two years, 3x every 3 years, or 4x every four years (where x is constant). In this case, they all return the same amount over any 12 year period, but since u can reinvest the cash flows elsewhere at the risk free rate, 2x every 2 years would be optimal.

 

[mwaqqas]

Phd Math entrance test question :

Q:suppose 3 coins with 1st coin both sides white,second coin (black & white) and 3rd coin both are black sides then what is the P(white side/white) = ?

What is the meaning of 'white' in P(white side/white). Is white = {1st coin, 2nd coin} or just that white = {1st coin}?

 

[pruse]

1) "X times your money in X years" seems to mean in general (X^{\frac{t}{X}}) times your money in (t) years. (X^{\frac{1}{X}) is increasing for (X<e), decreasing for (X>e), so the optimal choice would be (e) times your money in (e) years.*

2) what should you pay means what is the fair price of the game, i.e., your expected winnings.

under the first scenario, your expected winnings are 50, so 50 is the fair price of that game.

under the second scenario, the outcomes under which you get 100 are H and TH, with total probability 0.75. so the fair price for this game is 75.

 

[Ezra]

1) "X times your money in X years" seems to mean in general (X^{\frac{t}{X}}) times your money in (t) years. (X^{\frac{1}{X}) is increasing for (X<e), decreasing for (X>e), so the optimal choice would be (e) times your money in (e) years.*

2) what should you pay means what is the fair price of the game, i.e., your expected winnings.

under the first scenario, your expected winnings are 50, so 50 is the fair price of that game.

under the second scenario, the outcomes under which you get 100 are H and TH, with total probability 0.75. so the fair price for this game is 75.

e isn't one of the choices.

"1) I can pay you twice your money every two years, three times your money every three years or four times your money every four years. Which option do you choose and why?"

Remember, this is an S&T interview, not a quant position (correct me if I'm wrong), and the question as asked can be answered with basic arithmetic. And the question as posted can reasonably be interpreted in a few ways. I'm sure the original phrasing was more clear, and if not, it was probably an opportunity for the interviewee to ask for more clarity.