Mini Quiz Competition Island Shangri La Hotel Hong Kong May 26, CFE School Risk Latte Company Limited

Transcription

1 Mini Quiz Competition Island Shangri La Hotel Hong Kong May 26, 2011 CFE School Risk Latte Company Limited

2 Are You Better than a Goldman Sachs Trader? (This is a mini-quiz and not a full Quiz) The objective of this mini-quiz is to test whether a person has the potential to become as good as a Goldman Sachs trader. There are three metrics on which a person is tested in this mini-quiz: (1) Basic level of knowledge of Quantitative Finance (2) Intuitive understanding of concepts of Quantitative Finance (3) Thinking about concepts in Quantitative Finance Quiz Questions:» All questions are developed and compiled with the help and under the advice of market professionals working in top tier global banks and financial institutions. Risk Latte Company and CFE School owns the copyright to his quiz and all the questions contained therein.

3 Question #1 You are an options trader and a client approaches you to buy a call option on this building (where we are now sitting). You d be very reluctant to sell a call on this building primarily because: (a)it s not possible to estimate the volatility of this asset (b)the property market (of which this asset is a part) is not complete. (c)transaction costs for this trade would be too high (d)no closed form solution / model (Black-Scholes type) exists for such an option This question carries 5 points.

4 Question #2 In the Black-Scholes option pricing formula we see two terms N(d1) and N(d2). Call = S*N(d1) K*exp(-rT)*N(d2) Mathematically speaking, which one of these is a probability measure? (a) N(d1) measures the probability (b) N(d2) measures the probability (c) Both N(d1) and N(d2) represent probabilities under different measures (d) N(-d2) measures the probability This question carries 5 points.

5 Question #3 You are trading an asset that is capped at 100 (like the Eurodollar futures Contract which is capped at 100 and cannot go above this value. Implying an interest rate of zero). The asset is currently trading at 100. What is the value of a 100 strike call and a 100 strike put? (a)the call will be valued at zero and the put value will be infinite (very large) (b)both the call and the put will be valued at zero (c)the call will be valued slightly more than zero and the put value will be extremely difficult to determine (as the put-call parity will break down at 100). (d) The call and put will both be valued at infinity (very large) This question carries 5 points.

6 Question #4 Dollar-Yen (USD/JPY) follows a lognormal distribution and a Geometric Brownian motion. USD/JPY has a volatility of 20% and a drift (foreign interest rate minus domestic interest rate) of 3%. If you are pricing an option on Yen-Dollar (JPY/USD) the values of volatility and drift that you d input in your option pricing model would be: (a)volatility of 20% and drift of 3% (same as USD/JPY) (b)volatility of 20% and drift of 1% (c)volatility of 18% and drift of 3% (d)volatility 17.5% and drift of 2.5% This question carries 5 points.

7 Question #5 They say that traders have GARCH in their heads. GARCH has the most resemblance with: (a)stochastic Volatility models (b)exponentially Weighted Moving Average (EWMA) models (c)dupiere Volatility Surface model (d)implied Volatility tree This question carries 5 points.

8 Question #6 A trader dynamically hedges a sold binary (digital) option with a call spread. He finds that the call spread always trades a bit higher than the binary and as the spread narrows the difference begins to vanish but the prices of the binary and the call spread never becomes exactly equal (even ignoring the transaction costs). The main reason for this is (a)the dynamic hedging makes the binary option path dependent (b)the binary has a substantial pin risk (c)the mathematical approximation of a binary using call spread is not exact. (d)none of the above. This questions carries 5 points.

9 Question #7 Black-Scholes option pricing model is an equilibrium model. Equilibrium is a concept borrowed from physics. In the context of quantitative finance, equilibrium means: (a)the price of a security reflects all available information in the market (b)a security can infinitely divided into component securities (c)there are no arbitrage opportunities in the market (d)the price of a security can be in a particular state for a long period of time. This questions carries 5 points.

10 Question #8 EUR/USD volatility is 10% and is represented by a vector of length 10 from the origin (USD). GBP/USD volatility is 8% and is represented by a vector of length 8 from the origin (USD). If the correlation between EUR/USD and GBP/USD is zero then the angle between the two vectors will be: (a)90 degrees (b)45 degrees (c)25 degrees (d)zero degree This questions carries 5 points.

11 Question #9 Ito s Lemma is used in Stochastic Calculus, which is the bedrock of quant finance models for valuation of financial derivatives. Simply put, in a trader s language (English), Ito s lemma states that: (a)both the stock price equation (SDE) and the option price equation (PDE) are non-differentiable and not smooth; (b)the stock price equation (SDE) is a random walk and non-differentiable but the function of the stock price, the option price equation is smooth and differentiable; (c)no matter how small a slice we make, the stock price always remains non-differentiable; (d)any variable multiplied by an infinitesimal increment of time (delta t) vanishes. This questions carries 5 points.

12 Question #10 For a particular asset, the volatility on an hourly sampled basis turns out to be higher than the volatility on a daily sampled basis. You would then conclude that the asset is mostly like in a: (a) mean reverting mode (b) Trending mode (c) In a sideways model (d) Nothing can be said based on this information This questions carries 5 points.

13 Question #11 Stock A is 100% correlated with stock B. Over a particular period, stock A went up by 2%. A trader expected stock B to also go up by 2%. However, she observed that stock B actually went up by 4%. Why is that? (a)this is because correlation is a linear measure and cannot capture non-linearity; (b)the volatility of stock B must have been double the volatility of stock A; (c)correlation gets distorted by noise (randomness) in the market (d)none of the above This questions carries 5 points.

14 Question #12 A stock is trading at $100 and the volatility of stock is 10%. If risk free rates in the economy are extremely low, then a one year at the money (ATM), i.e. spot equal to the strike, will approximately cost (assuming no transaction costs and vol skew): (a)$2 (b)$3 (c)$4 (d)$5 This questions carries 5 points.

15 Question #13 A one year at the money (ATM) call option on a stock costs $1. Assuming low interest rates and no transaction costs and volatility skew, a two year ATM option on the same stock will cost: (a)$1.15 (b)$1.41 (c)$2.00 (d)$2.15 This question carries 5 points

16 Question #14 If Google = 8, Yahoo = 8, facebook = 8 then Hotmail is equal to (a)2 (b)4 (c)6 (d)8 This question carries 5 points

17 Question #15 A proprietary trader at a hedge fund trades a basket of derivatives. With regard to the trader s P&L, his boss should, on an average, expect it: (a)to remain six months in profits (black) and six months in loss (red); (b)to remain 11 months in black and one month in red or 11 months in red and one month in black; (c) to remain all the 12 months in black or all the 12 months in red; (d) to remain 4 months in black and 8 months in red or 8 months in black and 4 months in red; This question carries 5 points

18 Question #16 Volatility of volatility (or what the traders call vvol ) is the: (a)second moment of the Normal distribution (b)third moment of the Normal distribution (c)fourth moment of the Normal distribution (d)fifth moment of the Normal distribution This question carries 5 points

19 Question #17 An asset, S, say, USD/JPY, is assumed to follow a Geometric Brownian motion (GBM), which is the most conventional way of looking at assets like equity and FX on the trading floor of banks. The asset has a certain drift and a volatility. If we now consider the process for the inverse of the asset, 1/S, i.e. JPY/USD then: (a)the volatility of (1/S) will change from that of S. (b)the drift of (1/S) will change from that of S. (c)both the drift and the volatility of (1/S) will change from that of S. (d)both the drift and the volatility of (1/S) will remain the same as that of S. This question carries 5 points

20 Question #18 The head trader of the swaps desk of a bank recently remarked that 3 month USD LIBOR (short term interest rate) is itself a call option. Your reaction would be that: (a)the head trader actually means a call option on the USD LIBOR, i.e. a cap; (b)the head trader is alluding to the fact that some structured products tied to 3 month USD LIBOR may display convexity in their payoff and hence resemble the payoff of a call option (c)the head trader is absolutely correct and a short term interest rate can be itself thought of as a call option; (d)the head trader usually hides the fact that he s sometimes drunk during the office hours. This question carries 5 points

21 Question #19 Bank A with a capital of $1 million enters into a game of coin tossing with Bank B with a capital of $10,000. Bank A wins $1 every time a head shows up and loses $1 every time a tail shows up. It s a very cruel world and the game (the show) must go on until one of them goes bankrupt. The probability of Bank B going bankrupt is: (a)0.99% (b)10% (c)50% (d)99.01% This question carries 5 points

22 Question #20 Which of the following options (financial products) is the odd one out? (a)israeli option (b)parisian option (c)napoleon option (d)himalayan option This question carries 5 points

23 Answers 1.(b) 2.(c) 3.(c) 4.(b) 5.(b) 6.(a) 7.(c) 8.(d) 9.(b) 10.(a) 11.(b) 12.(c) 13.(b) 14.(b) 15.(b) 16. (c) 17. (b) 18. (c) 19. (d) 20. (c)

24 Winners 1 st Prize: Girish Kumarguru Equity Derivatives Trader Royal Bank of Scotland Hong Kong 2 nd Prize: Lynn Raebsamen and Brian Chau Commodity Analytics Market Risk Management Bloomberg Wing Lung Bank Hong Kong Hong Kong 3 rd Prize: Catherine Mak Middle Office UBS Hong Kong