8007 実際試験問題と解答 - 模擬練習 - 受験自信を増やす

Question No : 1
Which of the following properties is exhibited by multiplication, but not by addition?

A.associativity
B.commutativity
C.distributivity
D.invertibility

正解:

Question No : 2
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)

正解:

Question No : 3
Every covariance matrix must be positive semi-definite. 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

正解:

Question No : 4
An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101. Approximate the value of the option delta using a first order central finite difference.

A.-4
B.0.25
C.-0.5
D.-0.25

正解:

Question No : 5
Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

A.(i) and (ii)
B.(i) only
C.(i) and (iii)
D.(i), (ii), and (iii)

正解:

Question No : 6
What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?

A.29
B.-25
C.1
D.17

正解:

Question No : 7
If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A.12/29
B.37/45
C.3/4
D.None of these

正解:

Question No : 8
In a multiple linear regression, the significance of R2 can be tested using which distribution?

A.Normal distribution
B.Student's t distribution
C.F-distribution
D.Binomial distribution

正解:

Question No : 9
You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of C 2.89)?

A.The commodity prices are stationary
B.The commodity returns are stationary
C.The commodity returns are integrated of order 1
D.None of the above

正解:

Question No : 10
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)

A.concave, concave, concave
B.concave, convex, convex
C.convex, concave, concave
D.convex, convex, concave

正解:

Question No : 11
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.

正解:

Question No : 12
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%.

正解:

Question No : 13
At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A.-0.666666667
B.0
C.2.66667
D.2

正解:

Question No : 14
Calculate the determinant of the following matrix:

A.4.25
B.-4.25
C.4
D.2

正解:

Question No : 15
Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

A.x = 1, y = 0.5
B.x = -2, y = 2
C.x = 2, y = 0
D.None of the above

正解:

PRMIA 8007 問題練習