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| Section | Weight | Objectives |
|---|---|---|
| Probability Theory | 25% | - Basic probability concepts
|
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Calculus and Functions | 20% | - Multivariable calculus
|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Numerical Methods & Financial Mathematics | 15% | - Time value of money - Basics of risk modeling - Root finding and approximation |
1. Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:
A) 0.40729
B) 0.00087
C) 0.00109
D) 0.32583
2. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?
A) 0.32
B) 1.92
C) 0.96
D) 0.64
3. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:
A) f might have either a minimum or a maximum or neither of them at this point
B) f has necessarily neither a minimum nor a maximum at this point
C) f has necessarily a maximum at this point
D) f has necessarily a minimum at this point
4. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:
A) 0.5292
B) 0.5288
C) 0.5290
D) 0.5286
5. Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?
A) 9/16
B) 7/8
C) None of these
D) 11/16
Solutions:
| Question # 1 Answer: C | Question # 2 Answer: D | Question # 3 Answer: A | Question # 4 Answer: B | Question # 5 Answer: D |
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