Advanced Financial Theory Assessment questions.
Multiple choice questions
Choose the correct answer and give the explanation.
QUESTION 1
Consider a company with a production opportunity set given by the equation C1=7-(C0)3. The preferences for consumption of the owner in the present and the future are given by the utility function U(C0,C1)=C0(C1)2. The optimal consumption and investment plan of the investor in a world without financial markets is (Y0,Y1)=
| A) (2,3) | ||
| B) (1,6) | ||
| C) (sqrt(2),5) | ||
| D) (sqrt(3),4) |
1 points
QUESTION 2
Assume now that the investor can borrow and lend on a capital market with an interest rate of r. The optimal production decision (Y0,Y1) is
| A) 3+[(1+r)/3]1/2 , 4- [(1+r)/3]1/2 | ||
| B) 3-[(1+r)/3]1/2 , 4+ [(1+r)/3]1/2 | ||
| C) 6-[(1+r)/3]1/2 , 1+ [(1+r)/3]1/2 | ||
| D) [(1+r)/3]1/2 , 7- [(1+r)/3]3/2 |
1 points
QUESTION 3
The Fisher separation theorem claims that
| A) Managers should maximize the profit of their companies | ||
| B) There is an agency problem between managers and shareholders which can be resolved by incentive schemes and/or monitoring | ||
| C) The optimal production decision of companies is independent of the consumption preferences of shareholders if all economic agents can borrow and lend at the same interest rate | ||
| D) The ownership and control of corporations should be separated in order to improve efficiency and increase corporate profits |
QUESTION 4
You have a logarithmic function U(W)=ln(W) and your current level of wealth is $5000. Suppose that you are exposed to a situation that results in a 50/50 chance of winning or losing $1000. If you can buy insurance that completely removes the risk for a fee of $125, will you buy it or take the gamble?
| A) Purchase insurance | ||
| B) Not purchase insuranc |
QUESTION 5
A car owner with a utility function U(W)= considers insuring a car of value $10,000. Assume that the probability for an accident is 10% in which case the owner suffers a total loss of value (i.e. the car is worth $0 following an accident). The expected value of the loss is
| A) $100 | ||
| B) $1000 | ||
| C) $2000 |
QUESTION 6The expected utility of the car owner in a situation of uninsured car is
| A) 70 utils | ||
| B) 80 utils | ||
| C)90 utils |
QUESTION 7
The Markowitz risk premium associated with the gamble (the uninsured car) is
| A) $800 | ||
| B) $900 | ||
| C) $1000 |
QUESTION 8
Would the car owner be willing to insure the car if the insurance policy costs $1500?
| A) Yes | ||
| B) No |
QUESTION 9
Would the car owner be willing to insure the car if the insurance policy costs $2000?
| A) Yes | ||
| B) No |
QUESTION 10
Consider the following three gambles:
- X=(1,1/3; 3,1/3; 5,1/3)
- Y=(1,1/3; 2,1/3; 6,1/3)
- Z=(2,1/2; 5,1/2)
Which of the following nine statements is true?
Y dominates X first degree
| Yes | ||
| No |
QUESTION 11
Z dominates Y first degree
| A) Yes | ||
| B) No |
QUESTION 12
Z dominates X first degree
| A) Yes | ||
| B) No |
QUESTION 13
There is no first degree dominance between the three bets
| A) True | ||
| B) False |
QUESTION 14
X dominates Y second degree
| A) Yes | ||
| B) No |
QUESTION 15
Z dominates X second degree
| A) Yes | ||
| B) No |
1 points
QUESTION 16
Z dominates Y second degree
| A) Yes | ||
| B) No |
1 points
QUESTION 17
Y dominates X second degree
| A) Yes | ||
| B) No |
1 points
QUESTION 18
There is no second degree stochastic dominance between the bets
| A) True | ||
| B) False |
1 points
QUESTION 19
Consider a capital market with two securities. The payoffs of these securities in the two possible states of the world in the future are given in the table below. Currently the two securities are traded at the prices PA=1 and PB=2. The probability that State 1 will occur is 50% and the probability that State 2 will occur is 50%.
Security State 1 State 2
A 2 1
B 2 4
The price of pure security one and pure security two are:
| A) 1, 1/2 | ||
| B) 1,1 | ||
| C) 1/2, 1/3 | ||
| D) 1/3, 1/3 |
1 points
QUESTION 20
Determine the price of a European call option on the stock A with a strike price of $1
| A) 1/3 | ||
| B) 2/3 | ||
| C) 1 | ||
| D) 4/3 |
1 points
QUESTION 21
Determine the price of a European put option on the stock B with a strike price of $5
| A) 1/3 | ||
| B) 2/3 | ||
| C) 1 | ||
| D) 4/3 |
1 points
QUESTION 22
Assume that the investor has a utility function given by U(W)=(W)1/2 and the investor has $10 to invest in the stock market. How many stocks A and how many stocks B will the investor hold?
| A) 2, 3 | ||
| B) 1, 2 | ||
| C) 5, 2.5 | ||
| D) 6, 4 |
1 points
QUESTION 23
The securities A and B have the following joint distribution of returns
| Security B | |||
| Outcomes | 0 | 2 | |
| Security A | 0 | 0 | 0.20 |
| 4 | 0.20 | 0.60 | |
The variance of A is _______ and the variance of B is ____________
| A) 2.02 1.35 | ||
| B) 3.05 0.13 | ||
| C) 2.56 0.64 | ||
| D) 2.18 0.78 |
1 points
QUESTION 24
- The covariance between A and B is
| A) -1.00 | ||
| B) -0.32 | ||
| C) -0.06 | ||
| D) 0.28 |
1 points
QUESTION 25
Assume that the investor invests only in A and B. In order to minimize the variance of her portfolio, the investor should invest _______ of her wealth in stock A.
| A) 10% | ||
| B) 25% | ||
| C) 30% | ||
| D) 35% |
1 points
QUESTION 26
Assume now that a risk-free asset exists which offers an interest rate of Rf=0.5. The tangency portfolio is a portfolio which consists of approximately ____ of the wealth invested in asset A and ____ of the wealth invested in asset B.
| A) 18% and 82% | ||
| B) 22% and 78% | ||
| C) 36% and 64% | ||
| D) 46% and 64% |
1 points
QUESTION 27
The Sharpe ratio of the tangency portfolio is approximately
| A) 1.31 | ||
| B) 2.16 | ||
| C) 2.51 | ||
| D) 3.12 |
QUESTION 28
The following data have been developed for the company i:
| State | Probability | Market return, Rm | Return for the Firm i, Ri |
| 1 | 0.20 | -0.10 | -0.20 |
| 2 | 0.40 | 0.10 | 0.30 |
| 3 | 0.40 | 0.20 | 0.40 |
The risk free rate of return is Rf=5%.
The Beta of Firm i is:
| A) 1 | ||
| B) 2 | ||
| C) 2.4 | ||
| D) 2.75 |
1 points
QUESTION 29
According to the CAPM model, the stock of Firm i should offer an expected return of
| A) 10% | ||
| B) 15% | ||
| C) 20% | ||
| D) 22% |
1 points
QUESTION 30
If we believe in the CAPM model, we expect that the price of stock i will ____________ in the future.
| A) increase | ||
| B) decrease | ||
| C) remain unchanged |
