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PRMIA 8002 Dumps
Exam: Exam II: Mathematical Foundations of Risk Measurement
PRMIA 8002 Exam Tutorial
Question No : 1
A 2step binomial tree is used to value an American put option with strike 104, given that
the underlying price is currently 100. At each step the underlying price can move up by
20% or down by 20% and the riskneutral probability of an up move is 0.55. There are no
dividends paid on the underlying and the discretely compounded risk free interest rate over
each time step is 2%. What is the value of the option in this model?
A. 11.82
B. 12.33
C. 12.49
D. 12.78
Question No : 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. 0.64
C. 0.96
D. 1.92
Question No : 3
A 2year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay
Duration of the bond?
A. 2
B. 1.95
C. 1.86
D. 1.75
Question No : 4
Simple linear regression involves one dependent variable, one independent variable and
one error variable. In contrast, multiple linear regression uses
A. One dependent variable, many independent variables, one error variable
B. Many dependent variables, one independent variable, one error variable
C. One dependent variable, one independent variable, many error variables
D. Many dependent variables, many independent variables, many error variables
Question No : 5
Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with
respect to y?
A. f'(g(x,y))
B. f(dg/dy)
C. f(g(x,y)) dg/dy
D. f'(g(x,y)) dg/dy
Question No : 6
If the annual volatility of returns is 25% what is the variance of the quarterly returns?
A. 0.1250
B. 0.0156
C. 0.0625
D. None of the above
Question No : 7
Which of the provided answers solves this system of equations?
2y 3x = 3y +x
y2 + x2 = 68
A. x = 1; y = square root of 67
B. x = 2; y = 8
C. x = 2; y = 8
D. x = 2; y = 8
Question No : 8
When the errors in a linear regression show signs of positive autocorrelation, which of the
statements below is true?
A. The regression coefficient will be too high and the standard error of the regression coefficient will be understated
B. The regression coefficient will be too low and the standard error of the regression coefficient will be overstated
C. The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated
D. The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated
Question No : 9
What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by
inequalities x 1, y 2, yx 3 ?
A. 29
B. 25
C. 1
D. 17
Question No : 10
A 95% confidence interval for a parameter estimate can be interpreted as follows:
A. The probability that the real value of the parameter is within this interval is 95%.
B. The probability that the real value of the parameter is outside this interval is 95%.
C. The probability that the estimated value of the parameter is within this interval is 95%.
D. The probability that the estimated value of the parameter is outside this interval is 95%.
Question No : 11
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. 0.00109
C. 0.00087
D. 0.32583
Question No : 12
Which of the following is not a sequence?
A.
B.
C.
D. 30
Question No : 13
Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter
A. (i) and (iv)
B. (i), (ii), and (iii)
C. (i), (iii), and (iv)
D. (i), (ii), (iii), and (iv)
Question No : 14
Every covariance matrix must be positive semidefinite. If it were not then:
A. Some portfolios could have a negative variance
B. One or more of its eigenvalues would be negative
C. There would be no Cholesky decomposition matrix
D. All the above statements are true
Question No : 15
A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and
the correlation between the dependent and explanatory variables is 0.5. What is the
explained sum of squares?
A. 0.75
B. 1.125
C. 0.3333
D. 0.375
Question No : 16
Which statement regarding the matrix below is true?
A. It is not positive definite
B. It is positive semidefinite
C. It is positive definite
D. It is negative definite
Question No : 17
A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the
coefficient of ?
A. [0, 1.5]
B. [1, 2]
C. [0, 3]
D. None of the above
Question No : 18
Let N(.) denote the cumulative distribution function and suppose that X and Y are standard
normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability
that X 0 and Y 1.96 is approximately
A. 0.25%
B. 0.488%
C. 0.49%
D. 0.495%
Question No : 19
Let N(.) denote the cumulative distribution function of the standard normal probability
distribution, and N' its derivative. Which of the following is false?
A. N(0) = 0.5
B. N'(0) 0
C. N(x) 0 as x
D. N'(x) 0 as x
Question No : 20
Suppose I trade an option and I wish to hedge that option for delta and vega. Another
option is available to trade. To complete the hedge I would
A. trade the underlying in such a way as to make the portfolio delta and vega neutral.
B. trade the other option in such a way as to make the portfolio delta and vega neutral.
C. trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.
D. trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.
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