Question 1

Which of the following statements is are true?
A)A risk-preferring individual always prefers the riskier of two gambles that involve different expected value.
B)A risk neutral individual is indifferent between receiving with certainty the expected value of a gamble and the uncertainty of the gamble itself.
C)A risk neutral individual has a utility function which is linear in wealth.
D)Both a and b.
E)Both b and c.

Accepted Answer

Option B correctly characterizes a risk-neutral individual. Option C is also true because a linear utility function means that the individual gains equal utility from each additional unit of wealth, regardless of the level of wealth already possessed. Option A is false because a risk-preferring individual may prefer the less risky gamble if it has a higher expected utility, not just a higher expected value.

Question 2

If the role of financial intermediaries is to produce and process information, then they are least needed when
A)the capital market is weak-form efficient.
B)the capital market is semi strong-form efficient.
C)the capital market is strong-form efficient.
D)information is costly for individuals to obtain and process.
E)none of the above.

Accepted Answer

Financial intermediaries are least needed when the capital market is strong-form efficient because in such a market, all available information is already reflected in the security prices, leaving little room for financial intermediaries to produce and process additional information. In a weak-form or semi-strong-form efficient market, financial intermediaries can still play a role in producing and processing information that may not be fully reflected in security prices. Information cost is also not a factor in the role of financial intermediaries in producing and processing information.

Question 3

In order for a signal to be informative,
A)it has to be costly for the sender
B)the cost of signal should be positively related to quality
C)the first-best outcome must be attainable
D)all of the above
E)none of the above

Accepted Answer

E

Question 4

Use the following information for questions 
There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $30, a B car is worth $15, and a U car is worth $0.A buyer cannot distinguish the quality of cars offered for sale, but the seller does.If there is equal probability of a car being G, B, or U,
-Suppose the type G seller offers a warranty of $g and the type B seller offers $b.If the probability of failure is 0.1, 0.5, and 1 for types G, B, and U, respectively, what is the warranty offered by type G and B sellers to ensure incentive compatibility?
A)$20, $15
B)$25, $15
C)$30, $30
D)$37.5, $30
E)$37.5, $37.5

Accepted Answer

For a G seller, the expected value of a non-failed car is $27 ($30-$3). To ensure incentive compatibility, they would offer a warranty of $g such that:

$27(1-0.1)+g*0.1=$30-3

Solving for g, we get g=$37.5

For a B seller, the expected value of a non-failed car is $7.5 ($15-$7.5). To ensure incentive compatibility, they would offer a warranty of $b such that:

$7.5(1-0.5)+b*0.5=$15-7.5

Solving for b, we get b=$30.

Therefore, the best choice is D.

Question 5

In a market with asymmetric information,
A)market failure may occur and therefore regulation may be needed
B)individuals are unable to prevent market failure
C)first-best outcome can always be achieved
D)both a and c
E)both b and c

Accepted Answer

In a market with asymmetric information, market failure can occur due to the information advantage of some market participants. This can lead to adverse selection, moral hazard, and other forms of market inefficiencies. Therefore, regulation may be necessary to correct these market failures and improve social welfare. Choice B is incorrect because individuals can still take actions to prevent market failure through mechanisms such as signaling, reputation, and contractual agreements. Choice C is incorrect because the first-best outcome (where all market participants have perfect information) may not be achievable in reality.

Question 6

There are two assets, A and B, with a standard deviation of 10 and 15, respectively.If the correlation coefficient between the two assets is 0.5, then a portfolio that consists of 0.4 of A and 0.6 of B has a standard deviation of
A)11.53
B)13.00
C)15.00
D)18.02
E)20.00

Accepted Answer

The standard deviation of a portfolio consisting of two assets can be calculated using the formula: $\sigma_p = \sqrt{w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\sigma_A\sigma_B\rho}$, where $w_A$ and $w_B$ are the weights of assets A and B in the portfolio, $\sigma_A$ and $\sigma_B$ are the standard deviations of assets A and B, and $\rho$ is the correlation coefficient between the two assets. Plugging in the given values: $\sigma_p = \sqrt{0.4^2 \times 10^2 + 0.6^2 \times 15^2 + 2 \times 0.4 \times 0.6 \times 10 \times 15 \times 0.5}$ = 11.53.

Question 7

Which of the following statements is are false?
A)A risk-averse individual demands a premium for bearing risk.
B)A risk-averse individual prefers a certain amount to a gamble with the same expected value.
C)A risk-averse individual has a convex utility function.
D)All of the above.
E)None of the above.

Accepted Answer

A risk-averse individual actually has a concave utility function, not a convex one. This concavity reflects the diminishing marginal utility of wealth and explains why a risk-averse person demands a premium for bearing risk.

Question 8

Use the following information for questions .
There are two possible states of nature, s = 1, and s = 2, over the next period.There are two securities i and j) whose current prices are $10 and $15, respectively.Security i has a payoff of $10 in state s = 1, and $16 in state s = 2, while security j provides $25 in state s = 1 and $8 in state s = 2.
-What are the prices of the Arrow-Debreu securities in the two states?
A)0.25 in state s = 1 and 0.675 in state s = 2.
B)0.3 in state s = 1 and 0.6 in state s = 2.
C)0.4 in state s = 1 and 0.75 in state s = 2.
D)0.5 in state s = 1 and 0.3125 in state s = 2.
E)insufficient information.

Accepted Answer

The Arrow-Debreu security prices can be found by solving the system of equations derived from the payoffs and current prices of the securities. Solving the equations: 10 = 10p1 + 16p2 and 15 = 25p1 + 8p2, we get p1 = 0.5 and p2 = 0.3125.

Question 9

Suppose there are two risky assets, X and Y, and a riskless bond, B.There are two possible states H and L of the economy over the next period.X provides a payoff of $0 in state H and $50 in state L, while Y provides a payoff of $50 in state H and $0 in state L.B provides a payoff of $50 regardless of the states.X, Y, and B are currently selling for $30, $30, and $25, respectively.A possible riskless arbitrage opportunity is to...
A)buy one unit each of X and Y and sell one unit of B to get a riskless profit of $35
B)buy one unit of B and sell one unit each of X and Y to get a riskless profit of $35
C)buy one unit each of X and B and sell one unit of Y to get a riskless profit of $25
D)buy one unit each of Y and B and sell one unit of X to get a riskless profit of $25
E)there is no riskless arbitrage opportunity.

Accepted Answer

To find if there is any arbitrage opportunity, we need to check if there is a portfolio of assets that can produce a riskless profit. To do this, we need to find portfolio weights that sum up to 1 such that the payoff of the portfolio is the same in both states of the economy. 
Let's assume we buy one unit of X, Y, and B. The cost of this portfolio would be $30+$30+$25 = $85. If the economy is in state H, the payoff of the portfolio would be $0+$50+$50 = $100. If the economy is in state L, the payoff of the portfolio would be $50+$0+$50 = $100. Therefore, the payoff of the portfolio is the same in both states of the economy. 
As the cost of the portfolio is $85, we can borrow $85 from the riskless bond and buy the portfolio. At the end of the period, we will have to return the borrowed amount of $85, but we will receive a payoff of $100 from the portfolio, leaving us with a riskless profit of $15. 
Therefore, we can buy one unit of B and sell one unit each of X and Y to get a riskless profit of $15. We can repeat this transaction to get a riskless profit of $35.

Question 10

An incentive compatibility condition is one where
A)an agent must be offered at least his reservation utility in order to agree to a contract with the principal
B)an agent must offer the principal at least her reservation utility in order to induce her to write a mutually beneficial contract
C)an agent with a certain type does not have an incentive to mimic the action of another agent of different type
D)both a and b
E)both a and c

Accepted Answer

Incentive compatibility ensures that agents reveal their true types or preferences, meaning they do not benefit from pretending to be another type.

Question 11

Use the following information for questions .
There are two possible states of nature, s = 1, and s = 2, over the next period.There are two securities i and j) whose current prices are $10 and $15, respectively.Security i has a payoff of $10 in state s = 1, and $16 in state s = 2, while security j provides $25 in state s = 1 and $8 in state s = 2.
-A third security is introduced.It generates a payoff of $16 in state s = 1 and $24 in state s = 2.How many units of this new security can you buy if your initial wealth is $3,100?
A)200 units
B)162 units
C)154 units
D)127 units
E)More information is needed

Accepted Answer

To determine the number of units of the new security that can be purchased, we need to calculate the price of the security in each state.

In state s = 1, the total payoff from the three securities would be $57 (10 from security i, 25 from security j, and 16 from the new security). In state s = 2, the total payoff would be $48 (16 from security i, 8 from security j, and 24 from the new security).

To find the price of the new security, we need to find the expected payoff in each state and discount it by the risk-free rate of return. Assuming the risk-free rate is 5%, we have:

Expected payoff in state s = 1: (0.5)(16) = 8
Expected payoff in state s = 2: (0.5)(24) = 12
Price of new security = (8/(1+0.05)) + (12/(1+0.05)^2) = $21.36

Therefore, the number of units of the new security that can be purchased with $3,100 is:
3100/21.36 = 145.15

Rounding down, we get 145 units. However, if we purchase 200 units of the security, the total cost would be $4,272, which is greater than the initial wealth of $3,100. Therefore, option A, 200 units, is not feasible. Therefore, the best choice is not to purchase any units of the new security.

Question 12

Use the following information for questions .
There are two possible states of nature, s = 1, and s = 2, over the next period.There are two securities i and j) whose current prices are $10 and $15, respectively.Security i has a payoff of $10 in state s = 1, and $16 in state s = 2, while security j provides $25 in state s = 1 and $8 in state s = 2.
-If you want to get a payoff of $16 in state s = 1 and $12.8 in state s = 2, how would you allocate your wealth between the two securities i and j?
A)10% in I and 80% in J
B)10% in J and 90% in J
C)80% in I and 20% in J
D)70% in I and 20% in J
E)60% in I and 40% in J

Accepted Answer

The answer of Use the following information for questions .
There...

Question 13

With diversification, an investor can
A)reduce risk and increase his return from holding risky assets.
B)reduce risk due to imperfect correlation of returns among risky assets in his portfolio.
C)reduce the market risk associated with holding a portfolio of risky assets.
D)Both a and c.
E)Both b and c.

Accepted Answer

Diversification reduces risk by taking advantage of the imperfect correlation of returns among different assets, which helps to lower the overall risk of the portfolio. However, it does not eliminate market risk, which affects all assets.

Question 14

Which of the following statements is are false about options?
A)A call option is more valuable when the value of the underlying security is more volatile.
B)An American option can never be worth less than a European option.
C)An option buyer has the right, not the obligation, to buy or sell an asset at a predetermined price over a fixed time interval.
D)A put option is more valuable when the value of the underlying security is less volatile.
E)All of the above is false.

Accepted Answer

A put option increases in value when the underlying security's price decreases, and volatility generally increases the value of options because it raises the potential for the option to end up in the money. Therefore, a put option is actually more valuable when the underlying security is more volatile, not less.

Question 15

The efficient market hypothesis implies that
A)investors have perfect forecasting ability.
B)prices do not fluctuate.
C)the market is irrational.
D)competition among investors is such that one can earn only a normal return.
E)all of the above.

Accepted Answer

The efficient market hypothesis suggests that competition among investors is so high that no single investor can consistently outperform the market or earn abnormal returns, known as beating the market. This implies that investors cannot have perfect forecasting ability and that prices are always fluctuating based on new information. The efficient market hypothesis does not suggest that the market is irrational, as it implies that prices always reflect all available information. Therefore, option D is the best choice.

Question 16

When a market is incomplete,
A)subject to his budget constraint, an individual can achieve any desired distribution of income 
B)an individual has a limited ability to manage uncertainty
C)the introduction of new securities generally make individuals better off
D)both a and c
E)both b and c.

Accepted Answer

In an incomplete market, individuals have limited ability to manage uncertainty because not all risks can be traded or hedged due to the absence of certain financial instruments. The introduction of new securities can make individuals better off by allowing them more options to hedge against risks or to invest, thus partially completing the market.

Question 17

In problem 4, if the correlation coefficient is -1 and you want to completely eliminate the risk of the portfolio, then you will invest
A)0.3 in A and 0.7 in B
B)0.4 in A and 0.6 in B
C)0.6 in A and 0.4 in B
D)0.8 in A and 0.2 in B
E)any combination will eliminate the risk completely since the correlation coefficient is -1

Accepted Answer

The answer of In problem 4, if the correlation coefficient...

Question 18

Adverse selection is a situation where
A)a party of a transaction undertakes an unobservable action at the detriment of the second party after contracting takes place
B)a party of a transaction possesses an unobservable attribute which is unknown to the second party prior to contracting
C)the informed party must send a costless signal to prevent market break down
D)both a and c
E)both b and c

Accepted Answer

Adverse selection occurs when one party in a transaction has more or better information than the other party, typically before a contract is made, leading to an imbalance.

Question 19

Use the following information for questions 
There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $30, a B car is worth $15, and a U car is worth $0.A buyer cannot distinguish the quality of cars offered for sale, but the seller does.If there is equal probability of a car being G, B, or U,
-which car is offered for sale in equilibrium and at what price?
A)B and U, at a price = $15.
B)U only, at a price = $15.
C)U only, at a price = $0.
D)All cars will be offered for sale, at a price = $30.
E)No cars will be offered for sale.

Accepted Answer

In equilibrium, sellers will only offer U cars for sale at a price of $0. This is because if they offer a G or B car for sale, the buyer cannot distinguish between them, and will only be willing to pay the expected value of the car, which is $15 (($30 + $15 + $0)/3). Thus, the seller would receive no extra profit for offering a G or B car, and would only incur the cost of giving up their higher-valued car. On the other hand, by offering a U car for sale, the seller will receive the full expected value of $15 as profit, since this is the only car the buyer is willing to pay for at a price of $0. Therefore, in equilibrium, only U cars will be offered for sale at a price of $0.

Question 20

A market is considered complete if
A)there are more number of states of nature than there are securities
B)there are fewer number of states of nature than there are securities
C)there are as many securities as there are states of nature
D)it is frictionless
E)both b and d.

Accepted Answer

A complete market is one in which there are as many securities as there are states of nature. This means that investors can construct a portfolio that perfectly hedges against any possible outcome, and there are no opportunities for arbitrage. The number of states of nature being less than the number of securities (option B) or a frictionless market (option D) do not necessarily determine completeness. Option A is incorrect because having more states of nature than securities would mean that there are some outcomes that cannot be hedged, while option E is a combination of incorrect choices.

Quiz 1: Basic Concepts

Which of the following statements is are true?

If the role of financial intermediaries is to produce and process information, then they are least needed when

In order for a signal to be informative,

In a market with asymmetric information,

There are two assets, A and B, with a standard deviation of 10 and 15, respectively.If the correlation coefficient between the two assets is 0.5, then a portfolio that consists of 0.4 of A and 0.6 of B has a standard deviation of

Which of the following statements is are false?

An incentive compatibility condition is one where

With diversification, an investor can

Which of the following statements is are false about options?

The efficient market hypothesis implies that

When a market is incomplete,

In problem 4, if the correlation coefficient is -1 and you want to completely eliminate the risk of the portfolio, then you will invest

Adverse selection is a situation where

A market is considered complete if