AP

Question 1

What is the equity premium puzzle?

Answer 1

The equity premium puzzle refers to the empirical fact that the historically observed equity premium is much higher than the one predicted by the CCAPM. Based
on the CCAPM, the observed equity premium can only be explained by assuming agents with an extremely high degree of risk aversion. On the other hand, if we stick to a more reasonable degree of risk aversion, the model predicts only a minuscule premium.

Question 2

In the Grossman-Stiglitz model, the competitive equilibrium (CE) is not a satisfactory equilibrium concept. Why?

Answer 2

In the CE, the price is fully informative about the informed investor’s signal. However, the CE does not require that the uninformed investors use the price
to infer that signal. It only requires that the investors use the price to determine their budget constraint. So, the CE is not a satisfactory equilibrium concept in the sense that it allows such “naive” investors who do not use available information fully.

Question 3

In Kyle’s insider-trading model,” the insider is risk-neutral
and knows the asset’s payoff perfectly. Nevertheless, in equilibrium, he may trade only a small number of shares. Why wouldn’t he trade an infiniitely large number of shares to make an infinitely large profits using
his informational advantage?

Answer 3

It is because the insider tries to reduce the price impact against him. If he submitted a large buy (sell), the market makers would infer that the insider submitted a buy (sell) knowing that the asset’s cash flow was high (low). Then the market makers would competitively increase (decrease) the asset’s price — this would lower the insider’s trading profits. Therefore, in order not to reveal his information about the asset’s cash flow, the insider cuts down the size of his order and tries to “hide” behind the noise traders.

Question 4

The CCAPM predicts that an asset’s expected excess return is high when the covariance between the asset’s return and the agents’ consumption is large and positive. What is the intuition for this relationship?

Answer 4

The fact that the covariance is large and positive means that the asset’s return tends to be high when the consumption is high, and low when the consumption is low. Such an asset is not desirable for the purpose of consumption smoothing: it tends to yield a high return when the agents don’t need it so much (consumption is high anyway) and a low return when they need it most. Since it is not desirable, the agents demand a high expected return to hold it

Question 5

In the Rational Expectations Equilibrium (REE) of the GrossmanStiglitz model (without noisy supply), the uninformed investor’s demand function is price inelastic. What is the economic intuition for this result?

Answer 5

This is because the price has two opposite effects on the uninformed investor’s demand. On the one hand, the price affects his budget constraint: if the price is high, he is discouraged to buy the asset because it’s expensive. On the other hand, the price affects his inference about the informed investors’ information. Since the price is fully informative, if the price is high, he can infer that the informed investors have received positive information about the asset’s cash flow — this encourages him to buy the asset. In equilibrium, these two effects just cancel out, and his demand is price-inelastic

Question 6

Suppose that agents’ consumptions positively covary with asset A’s return but negatively covary with asset B’s return. According to the CCAPM, which asset should have a higher expected return? Explain the intuitions for the result.

Answer 6

The CCAPM predicts that asset A has a higher expected return than asset B.
Intuition: For the purpose of consumption smoothing, asset A is less desirable than asset B because it tends to yield a high return when the agents don’t need it so much (consumption is high anyway) and a low return when they need it most. Since it is less desirable, the agents demand a higher expected return to hold it

Question 7

In the Grossman-Stiglitz model, the competitive equilibrium (CE) is not a satisfactory equilibrium concept. Why?

Answer 7

In the CE, the price is fully informative about the informed investor’s signal. However, the CE does not require that the uninformed investors use the price to infer that signal. It only requires that the investors use the price to determine their budget constraint.
So, the CE is not a satisfactory equilibrium concept in the sense that it allows such “naive” investors who do not use available information fully

Question 8

In the Kyle model, if the noise-trading volatility σu2

increases, how is the insider’s trading aggressiveness affected? Why?

Answer 8

In the Kyle model, if the noise-trading volatility σu
increases then the insider’s trading aggressiveness increases. Intuition: If the noise trading becomes more volatile, the aggregate order flow becomes less informative about the asset’s value. So the market
maker’s pricing becomes less sensitive to the order flow. Thus the insider becomes less worried about his price impact in the market, hence encouraged to trade more aggressively

Question 9

What are the two key predictions of the Sharpe-Lintner CAPM? Do they hold empirically? Explain.

Answer 9

The first prediction is that the cross-sectional variation in average asset returns is solely explained by differences in beta. Empirical studies reject this prediction: for example, small stocks and value stocks (with high book-to-market ratio) tend to have high returns. The second prediction is that assets’ average returns and betas should be located on the Security Market Line (SML). Empirical studies reject it too.
In data, the relation between average returns and betas is much flatter than the SML.

Question 10

Suppose that agents’ consumptions positively covary with asset A’s return but negatively covary with asset B’s return. According to the CCAPM, which asset should have a higher expected return? Explain the intuitions for the result.

Answer 10

The CCAPM predicts that asset A has a higher expected return than asset B. Intuition: For the purpose of consumption smoothing, asset A is less desirable
than asset B because it tends to yield a high return when the agents don’t need it so much (consumption is high anyway) and a low return when they need it most. Since it is less desirable, the agents demand a higher expected return to hold it.

Question 11

In the Rational Expectations Equilibrium (REE) of the
Grossman-Stiglitz model (without noisy supply), the uninformed investor’s demand function is price inelastic. What is the economic intuition for this result?

Answer 11

This is because the price has two opposite effects on the uninformed investor’s demand. On the one hand, the price affects his budget constraint: if the price
is high, he is discouraged to buy the asset because it’s expensive. On the other hand, the price affects his inference about the informed investors’ information. Since the price is fully informative, if the price is high, he can infer that the informed investors have received positive information about the asset’s cash flow—this encourages him to buy the asset. In equilibrium, these two effects just cancel out, and his demand is
price-inelastic.

Question 12

In the Kyle model, if the cash-flow volatility σ

increases, how is the insider’s trading aggressiveness affected? Why?

Answer 12

In the Kyle model, if the cash-flow volatility σ
increases then the insider’strading aggressiveness decreases. Intuition: If the cash flow becomes more volatile, the insider’s informational advantage increases (because the cash flow becomes more uncertain
for the market maker while it is still perfectly known to the insider). So the market maker’s pricing relies more on the order flow. Thus the insider becomes more worried about his price impact in the market, hence trades less aggressively to hide his information.

Question 13

What happens to the bid-ask spread if π increases? Explain the economic intuition for the result.

Answer 13

We have Ask − Bid = 0 for π = 0 and π = 1, but Ask − Bid > 0 for π ∈ (0, 1). That is, the bid-ask spread is inverse-U shaped in π. Intuition: If π is very small (very large), the market makers believe regardless of the order flow that it is very likely that δ = δL (δ = δH), so they set both Ask and Bid very close to δL (δH), leading to a small bid-ask spread. By contrast, if π is close to 1/2, the market makers have large uncertainty about δ. (Note that π = 1/2 corresponds to the case in which they have absolutely no idea about δ, as it’s equivalent to a coin toss.) So they change their estimate of δ significantly depending on the order flow: they update the estimate upward (downward) given a buy order (sell order), leading to a large bid-ask spread.

Question 14

What is the dierence between the Sharpe-Lintner CAPM and the zero-beta CAPM? What is the key result common to both of these models?

Answer 14

The main difference is that the Sharpe-Lintner CAPM assumes the presence of a risk-free asset, whereas the zero-beta CAPM does not. The common result is that the cross-sectional variation in expected asset returns is solely explained by differences in beta.

Question 15

In the Kyle model, if the cash-flow volatility σ2

increases, how is the insider’s trading aggressiveness affected?

Answer 15

In the Kyle model, if the cash-flow volatility σ2
increases then the insider’s trading aggressiveness decreases. (Beta =σu2/σ2) Intuition: If the cash flow becomes more volatile, the insider’s informational advantage increases (because the cash flow becomes more uncertain for the market maker while it is still perfectly known to the insider). So the market maker’s pricing relies more on the order flow. Thus the insider becomes more worried about his price impact in the market, hence trades less aggressively to hide his
information.

Question 16

What are the key assumptions of th CAPM?

Answer 16

1) Investors can borrow and lend at a risk-free rate rf.
2) All inverstors have the same beliefs about the asset’s future returns.

=> These assumptions guarantee that the mean-variance efiicient frontier is linear and is the same for every investor.

Question 17

CCAM intuition

Answer 17

The expected excess return or the “risk premium” is high when cov (u’(ct+1),Rn,t+1) is large and negative, that is , whem the return Rn,t+1 is high (and thus when u’(ct+1 is low), and low when Ct+1 s low. Such an asset is not desirable for the purpose of consumption smoothing. Indeed, it tends to yield a high return when the agent doesn’t need it and low return when he needs it most.

Question 18

CAPM vs CCAPM

Answer 18

CAPM: An asset as a high expected return when it covaries postitively with the market portfolio.

CCAPM: An asset has a high expected return when it covaries positively with consumption.

Question 19

Grossman-Stiglitz Paradox

Answer 19

In REE, informed and uninformed get the same allocation. Thus, they make also the same profit => if info acquisition is costly, why acquire information?

Question 20

Intuition when alpha increases

Answer 20

The order is more likely from informed=> A buy order ( sell order ) more likely implies teta=1 (teta=0) => Ask increases and bid decreases => bid-ask spread increases

Question 21

Intuition when π increases

Answer 21

It is more likely that teta=1 => Ask and bid increases=> The bid-ask spread is inverse-u shaped in π. ( Ask= bid= 0 if π=0 and Ask=bid=1 if π=1 ) but Ask>bid if 0

Question 22

Intuition when C increases

Answer 22

order flow x+u less informative=> Market maker’s pricing less sensitive to the order flow.=> Insider less worried about the price impact, hence encouraged to trade aggressively

Question 23

Intuition when σ2

Answer 23

Insider’s informational advantage increases => Market makers’ pricing relies more on the order flow x+u => Insider more worried about the price impact, hence trades less aggressively

Question 24

ASK = 1 + β/1 + 2β

BID = 1 − β/3 − 2β
What happens to the bid and ask prices if β increases?
Explain the economic intuition for the result.

Answer 24

We have dAsk/dβ < 0 and dBid/dβ < 0. The intuition for dAsk/dβ < 0 is as follows. As β increases, a buy order becomes less informative (i.e., more likelyfrom an uninformed trader). Thus, conditional on a buy order, the market makers set
a price closer to the prior expected payoff, π = 1/2. The intuition for dBid/dβ < 0is as follows. As β increases, a sell order becomes more informative (i.e., more likely
from an informed trader). Thus, conditional on a sell order, the market makers set a price closer to the lower value of the payoff, δ = 0.

Question 25

ASK = 1 + β/1 + 2β

BID = 1 − β/3 − 2β
For what value of β the bid-ask spread is the largest ?
Explain the economic intuition for the result.

Answer 25

If β is very close to 0, almost all uninformed traders would place a sell order. So, given a buy order, the market maker infers that it is very likely from an informed trader. So Ask is very high (i.e., very close to 1), leading to a large bid-ask spread. If β is very close to 1, almost all uninformed traders would place a buy order. So, given a sell order, the market maker infers that it is very likely from an informed trader. So Bid is very low (i.e., very close to 0), leading to a large bid-ask spread.