PRMIA 8002 Exam Questions Free Practice Test

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Questions # 11:

Let f(x) = c for x in [0,4] and 0 for other values of x.

What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?

Options:

1/4 and 1/7

1/7 and 1/9

1/4 and 1/6

None of the above

Expert Solution

Questions # 12:

Every covariance matrix must be positive semi-definite. If it were not then:

Options:

Some portfolios could have a negative variance

It could not be used to simulate correlated asset paths

The associated correlation matrix would not be positive semi-definite

All the above statements are true

Expert Solution

Questions # 13:

Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

Options:

64%

75%

98%

Cannot be determined without estimates of the volatilities of the individual returns

Expert Solution

Questions # 14:

Every covariance matrix must be positive semi-definite. If it were not then:

Options:

Some portfolios could have a negative variance

One or more of its eigenvalues would be negative

There would be no Cholesky decomposition matrix

All the above statements are true

Expert Solution

Questions # 15:

What is a Hessian?

Options:

Correlation matrix of market indices

The vector of partial derivatives of a contingent claim

A matrix of second derivatives of a function

The point at which a minimum of a multidimensional function is achieved

Expert Solution

Questions # 16:

Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

Options:

x = 1, y = 0.5

x = -2, y = 2

x = 2, y = 0

None of the above

Expert Solution

Questions # 17:

Which of the following statements is true for symmetric positive definite matrices?

Options:

Its eigenvalues are all positive

One of its eigenvalues equals 0

If a is its eigenvalue, then -a is also its eigenvalue

If a is its eigenvalue, then is also its eigenvalue

Expert Solution

Questions # 18:

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

Options:

(0, 2, 1)

(0, 0, 0)

(1, 1, 1)

(0, 1, -1)

Expert Solution

Questions # 19:

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:

Options:

f has necessarily a minimum at this point

f has necessarily a maximum at this point

f has necessarily neither a minimum nor a maximum at this point

f might have either a minimum or a maximum or neither of them at this point

Expert Solution

Questions # 20:

Calculate the determinant of the following matrix:

Options:

4.25

-4.25

Expert Solution

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