Question

Consider a sequential trade model in which a security has an uncertain value. The value V of the security can either be $150 or $250 with equal probability. The proportion of informed traders is 60%, whereas the proportion of liquidity traders is 40%. As usual, liquidity traders buy or sell with equal probability, whereas informed traders only buy when they know the security price is high, and sell when they know the security price is low. The probability that V = $150, conditional that the first trade is a buy, is:

a. P[V = 150 | Buy] = 0.2

b. P[V = 150 | Buy] = 0.3

c. P[V = 150 | Buy] = 0.5

d. P[V = 150 | Buy] = 0.7

e. P[V = 150 | Buy] = 0.8

f. None of the above.

2. Consider a sequential trade model in which a security has an uncertain value. The value V of the security can either be $170 or $250 with equal probability. The proportion of informed traders is 50%, whereas the proportion of liquidity traders is 50%. As usual, liquidity traders buy or sell with equalprobability, whereas informed traders only buy when they know the security price is high, and sell when they know the security price is low.

The probability that V = $170, conditional that the first trade is a buy, is:

a.

P[V = 170 | Buy] = 0.25

b.

P[V = 170 | Buy] = 0.35

c.

P[V = 170 | Buy] = 0.50

d.

P[V = 170 | Buy] = 0.65

e.

P[V = 170 | Buy] = 0.75

f.

None of the above.

Consider a sequential trade model in which a security has an uncertain value. The value V of the security can either be $150 or $250 with equal probability. The proportion of informed traders is 40%, whereas the proportion of liquidity traders is 60%. As usual, liquidity traders buy or sell with equalprobability, whereas informed traders only buy when they know the security price is high, and sell when they know the security price is low.

The dealer will set his bid at:

	a.	Bid = 170
	b.	Bid = 180
	c.	Bid = 200
	d.	Bid = 220
	e.	Bid = 230
	f.	None of the above.

Answer 1

1. Probability of price being 150 = 0.5

Probability of a buy at 150 = .6*0+.4*.5 = 0.2.

Hence, P[V=150Ibuy] = P(150 and buy)/P(buy) = 0.2/0.5 = 0.4

Ans – None of the above.

2. Probability of price being 170 = 0.5

Probability of a buy at 170 = .5*0+.5*.5 = 0.25.

Hence, P[V=150Ibuy] = P(150 and buy)/P(buy) = 0.25/0.5 = 0.5

Ans – C.

3. Expected price at which liquidity trader will purchase = .5*150+.5*250 = 200

    Price at which informed trader will purchase                 = 250

    Expected price at which the security will be sold           = .6*200+.4*250 = 220.

Ans = d.