By Philippe Jorion
I've got used this ebook as a textual content for a graduate point monetary possibility administration path, in guidance for the GARP FRM examination (which I passed), and as a reference professionally. The instruction manual supplies precisely what it says it is going to, and serves as a superb primer ahead of stepping into the heavier, extra particular assigned readings (this isn't an assigned studying for the FRM examination, brain you).
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Horizontal) of weights and X is the vertical vector containing individual asset returns. The appendix for this chapter provides a brief review of matrix multiplication. 31) JWPR017-02 Design-Sample April 16, 2007 17:39 Char Count= 0 43 Fundamentals of Probability which is a weighted average of the expected returns μi = E(Xi ). 32) Using matrix notation, the variance can be written as ⎡ σ11 ⎢ .. 2 σ p = [w1 . . wN] ⎣ . σ12 σ13 ... ⎤⎡ ⎤ w1 σ1N .. ⎥ ⎢ .. ⎥ . ⎦⎣ . ⎦ σ N1 σ N2 σ N3 ... 33) This is a useful expression to describe the risk of the total portfolio.
With semiannual compounding, duration is in semesters. It then has to be divided by two for conversion to years. 17) Modified duration is the appropriate measure of interest rate exposure. The quantity (1 + y) appears in the denominator because we took the derivative of the present value term with discrete compounding. If we use continuous compounding, modified duration is identical to the conventional duration measure. In practice, the difference between Macaulay and modified duration is usually small.
B. c. d. 2: FRM EXAM 2000—QUESTION 81 Which one of the following statements about the correlation coefficient is false? a. It always ranges from −1 to +1. b. A correlation coefficient of zero means that two random variables are independent. c. It is a measure of linear relationship between two random variables. d. It can be calculated by scaling the covariance between two random variables. 3 FUNCTIONS OF RANDOM VARIABLES Risk management is about uncovering the distribution of portfolio values. Consider a security that depends on a unique source of risk, such as a bond.