Problem #1

If and do not differ from each other greatly in value then which of the following identities is true?

( Hint : You can apply the Taylor series expansion on and see what happens or take numerical values and see which of the identities fit. The above expression has applications in return calculations of financial assets, as well as used in many financial economics applications.)

Problem #2

Matrix A is given by and it is transformed as: where is an identity matrix and is a constant. If the determinant of the left hand side in the above transformation should be zero, i.e. for getting a non-trivial solution of the equation then will have a unique value as:

1. 0
2. 1
3. 2
4. 3

( Hint : is the eigenvalue of the matrix A. Simply expand the determinant and solve for lambda. The applications of eigenvalues and eigenvectors are in market risk management of assets, interest rate modeling, quantitative portfolio modeling, etc.)

Problem #3

A famous economist made the following statement: " It is not possible for 50% of the population to have above average wealth. "

1. the above statement is universally true;
2. the above statement is universally false;
3. the above statement can be false in many circumstances;
4. the above statement is only 50% of the times true;

( Hint: The above statement relates to the inequality of mean and median in a probability distribution. If the mean and median values are different, such as in asymmetric distributions, then the above statement could become false.)

Problem #4

There is a 99% probability that a stock will go up and a 1% probability that it will go down. If it goes up you make $1 and if it goes down you lose $1,000. Given the above payoff you:

1. will go long (buy) the stock;
2. will go short (sell) the stock;
3. it is not possible to make informed trading decision based on the above information;
4. you¡¦ll be indifferent between going long (buying) or shorting (selling) the stock;

( Hint : This is perhaps one of the most profound areas of mathematical finance, i.e. the application of probability and distribution to make trading decisions. What should matter is the expected payoff from a trade and not the respective probabilities of the up move and the down move

Problem #5

If you observe the output #NAME? in an Excel spreadsheet cell, when you enter a function, then it means:

1. the function is not defined (either in the VBA module or Excel library);
2. the function has a circular reference with other functions;
3. the function is returning a value that cannot be computed (such as square root of minus one);
4. None of the above;

Answers:

1. c
2. b
3. c
4. b
5. a

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