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In statistical hypothesis tests, 'Type I error' refers to the situation in which…

A.

The null hypothesis is accepted when in fact it should have been rejected

B.

The null hypothesis is rejected when in fact it should have been accepted

C.

Both null hypothesis and alternative hypothesis are rejected

D.

Both null hypothesis and alternative hypothesis are accepted

Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A.

arithmetic sequence, common difference 2

B.

arithmetic sequence, common ratio 2

C.

geometric sequence, common ratio 2

D.

geometric sequence, common ratio 3

The natural logarithm of x is:

A.

the inverse function of exp(x)

B.

log(e)

C.

always greater than x, for x>0

D.

46

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A.

2.362

B.

1.623

C.

1.638

D.

0.377

Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%, +3%, -3%, +9%, -9% .

What can you say about the annual geometric and arithmetic mean returns of this investment fund?

A.

The arithmetic mean return is zero and the geometric mean return is negative

B.

The arithmetic mean return is negative and the geometric mean return is zero

C.

The arithmetic mean return is equal to the geometric mean return

D.

None of the above

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

The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

A.

1.50%

B.

6%

C.

6.14%

D.

None of the above

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

Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A.

Changing the volatilities to be greater than 100%

B.

Changing all the correlations to be unity

C.

Changing all the correlations to be zero

D.

All of the above

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A.

a lump-sum payment of $22 500 on maturity (in five years)

B.

an annually compounded rate of 4.15%

C.

a quarterly-compounded rate of 4.1%

D.

a continuously-compounded rate of 4%