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Interview Questions to share

Joined
5/6/06
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Hi, just screwed a phone interview (I think :)) for a quant position. Anyway, just want to share with you guys...for fun ;)

....

(1) What is Ito's Lemma? What is d(LnS(t)) ?
---sounds familiar, eh ? so, work harder in Stochastic calculus, ladies and gentlemen :) (happend to look at the formula last night before went to bed, and gave the right answer for the second part in 40 seconds (thanks to Mona)

(2)How is Gamma change, or what is the sign of Gamma when interest rate is very high?
---finally, my thinking process came to a downward concave, which I mumbered in the phone...but somehow got the wrong sign:wall(Gamma for long call is always positive!!)

(3) How would you model to price a barrier with stochastic vol,while the underlying is a two year S&P future price...
--- :cry::cry:


Good luck for those who are undergoing the torture of interview.:dance:
 
Maggie,

Thank you for sharing interview questions.
I also would like to share classical questions I was asked interviewing at Goldman's Securities Division. I think we should answer this kind of question without thinking.

Could you tell me a little about your trading experience?
What did you do last summer? (There is a gap in my resume)
What are your greatest strengths?
What do you think you should work on? (weaknesses)
Why Goldman Sachs?
How are looking for an internship?
In particular, what fields are you interested in?
What do you do when you have free time?
Why should we hire you?
Give an example when you can apply your leadership skills.
 
Hi, more to share:

This is the first round on site for a Fixed Income Derivative Portfolio group, role is trading support. Head of group is a French, who interviewed me. Mostly simple concept questions, and what we learnt from Baruch MFE is enough for this part, and the only one has to do calculate is to get dS(t) from Ito's process :) :)) so, folks, do Stochastic homeworks, and no more whining ...)

(This one seems like very popular interview question, I've been asked twice within 24 hours :) not a hard one, but we should be able to do it right away, since this is the basic to derive BS models)

Good luck !
 
From interview with an ib structured product sales & trading group:

How do you price swap rate?
How do you price swaption?
How do you calculate the amortization schedule of amortizing security?
What is Macaulay, modified, effective, dollar duration?
Which bond has higher duration? the 5-year coupon bond or 5-year zero-coupon bond?
If the cost of the money (prevailing interest rate) rises from 4% to 5%, does that affect a 5-year zero coupon bond's duration? (trick question)
What are the differences between a straight bond and a CMBS's convexity?
Do you know how to perform a financial statement analysis?
How did you find out about this opening?
 
From interview with an ib structured product sales & trading group:

How do you price swap rate?
How do you price swaption?
How do you calculate the amortization schedule of amortizing security?
What is Macaulay, modified, effective, dollar duration?
Which bond has higher duration? the 5-year coupon bond or 5-year zero-coupon bond?
If the cost of the money (prevailing interest rate) rises from 4% to 5%, does that affect a 5-year zero coupon bond's duration? (trick question)
What are the differences between a straight bond and a CMBS's convexity?
Do you know how to perform a financial statement analysis?
How did you find out about this opening?


John, thank you so much to share with the questions.

Just for the pricing of Swaptions. is Black (1976) enough for the valuation?:)
 
Here are some of my favorites

1. Lets consider a IR swap: Notional=$10million, 10 years duration, half yearly payments. Suppose the swap rate for the same today is 4% and you decide to pay floating. Tomorrow the yield curve goes up (assume parallel shift) by 10 bps, what's your PnL?

2. I randomly pick 2 stocks out of the SnP 500. What do you think is the historical 3m correlation between them. Justify your answer.

3. I will give you $10million today. Where would you invest it ? (the right answer to this question, is a question)

4. What is the expected value of W^6 W being brownian motion.

5. What is the value of an ATM European call with time to maturity as infinity? what's the value of american ATM with time to maturity infinity?

6. (I really like this puzzle -- neat one). the three trader dilema. 3 traders have initial indications A, B,C for their bonus this year. You need to design a set of arguments so that each one of them knows the mean (A+B+C)/3, but no one is able to back trace the individual indications for the other 2.

7. consider the following option: you have an option to buy (maximum) M units of gas at a fixed price K for over any N days (you can exercise the option on at max N days) over the next T days. However if you choose to exercise on day i, you cannot buy more than C units. (obviously M <= C*N) how would you value this option. (I still don't know the answer to this one :( )

8. Your view is that tomorrow the 6 months skew (defined as the implied vol difference btw 25 delta put and 25 delta call) will reduce by 25% tomorrow. What positions would you take? What if your view is that it will reduce by 50% over the next 2 months. What positions would you take?

9) You have to fill numbers on the faces of 3 die (18 numbers in all). The property they should have is that no matter what die I choose you should be able to pick a die from the remaining 2 such that you always win in expectation. That is if B beats A, C should be such that C beats B but C loses to A (in expectation)

10) There are 60 blue ribbons in a box such that all 120 ends are hanging out and you cannot see which ends belong to which ribbons. You randomly join all 120 ends together into pretty bows and dump out the box. Depending on chance you will form anywhere from 1 to 60 loops. How many loops would you expect?

11) Which has a higher ATM implied vol (a portfolio of puts on single stocks) or (a put option on an index with the same portfolio weights as the single stocks portfolio).

12) Continuing q11, if the argument of diversification is true, why has been ATM for SP500 been consistently higher than Dow (Dow has 30 names whereas SP500, 500 names. For e.g. recently 3mATM put on Dow traded at 22%, whereas for SP500 it traded at 24%)

13) consider a one period binomial tree with r=0, u=10 d = 5. Write the equations you would write to get a risk neutral world. calculate the price of the option. what's wrong with the price you get.

14) An American call option is about to pay a large dividend tomorrow. Give me an algorithm to decide whether or not it is optimal to exercise the option today.

15) I will sell my house in an year from now. I want to buy a put option where the payoff would be (K-S(1yr)+ where S(1yr) is the price I receive from selling my house 1 yr from now. Assume that house prices are log normally distributed. Is the Black Scholes formula valid for this situation? How would price such an option ? How would hedge this option ?

16) Assume you are Toyota. Lists all the potential risks you are exposed to, and how do you plan to hedge yourself against them.

17) there are 100 statements on a wall. Statement 0 says that atmost 0 statements can be true. Statement 1 says that atmost 1 statement can be true. Statement i says atmost i statements can be true. How many true statements are there and which ones.

18) How does d(delta)/dvol vary with the spot?

19) Consider an infinite big chess board floor with individual squares of side 5 each. A coin of radius 2cm is tossed with its center initially at one of the confluence points of 4 small squares. What is the probability that the coin lands exactly inside one of the squares.

20) Draw me the basic efficient portfolio line. Where do you think your house is on this graph. Where do you think is your own investment on this graph?
 
And here is something I heard today (great introduction to risk aversion!):

There are 2 sealed envelopes, one has 50$, and another has 100$. You get to choose one at random, and keep the money.... How much would you be willing to pay for this?

Assume now that you have $50mil, and $100mil, how much would you be willing to pay this time?
 
And here is something I heard today (great introduction to risk aversion!):

There are 2 sealed envelopes, one has 50$, and another has 100$. You get to choose one at random, and keep the money.... How much would you be willing to pay for this?

Assume now that you have $50mil, and $100mil, how much would you be willing to pay this time?

great question on risk aversion.

Think of this from a slightly different angle. If you are running an prop desk, and you are allocated certain amount of risk (VaR or other risk measures), question of how much to risk (exposure) might override the question of how probable it is to turning a profit (dispersion), if the exposure is large enough (in term of % VaR used up)
 
John, thank you so much to share with the questions.

Just for the pricing of Swaptions. is Black (1976) enough for the valuation?:)

yes, I think the Black model is the standard one used by traders AFAIK.
 
great question on risk aversion.

Think of this from a slightly different angle.

And from yet another view, it does really help one understand what's happening right now.... With risk aversion being the theme of the markets, people are shunning all but the safest bets -- look at the treasury yields vs corporate bond spreads... and obviously the story for asset backed bonds is even strongly related to this innocent question !!!
 
Suppose that one starts with $0 has a fair coin. Each time you get a head, you win $1 and loose $1 otherwise. What is the probability of getting $2 without getting below $0 at any time.
 
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