Deck 18: The Lognormal Distribution

Question 1

What is the probability that a number drawn from the standard normal distribution will NOT be between -1 and 1?

A) 0.22
B) 0.32
C) 0.42
D) 0.52

Answer 1

B

Question 2

In a lognormal model of stock price movement,describe the mean and variance of the continuously compounded returns.

Answer 2

The return is normally distributed while both the return and variance grow proportionally with time.

Question 3

Why do we assume a lognormal distribution in option pricing? Ask the class to explain the pluses and minuses to this assumption.Once the downfalls are established,probe students to find out if a better alternative exists.

Answer 3

Not Answer

Question 4

A stock is valued at $28.00.The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%.If the stock is lognormally distributed,what is the expected median stock price after 4 years?

A) $28.00
B) $32.33
C) $40.13
D) $54.60

Question 5

Given a mean of -4.3 and a standard deviation of 26,what is the equivalent draw from a normal distribution for a standard normal sample variable of 0.67?

A) -13.12
B) 03.12
C) 13.12
D) 23.12

Question 6

A stock is valued at $55.00.The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%.If the stock is lognormally distributed,what is the price of the stock given a one standard deviation move up after 3 years?

A) $64.41
B) $74.41
C) $84.41
D) $94.41

Question 7

What is the area under the standard normal distribution curve and is less than 0.654?

A) 0.5115
B) 0.6215
C) 0.7434
D) 0.8283

Question 8

Given a mean of 45 and a standard deviation of 32 from a normally distributed sample,what is the probability of an observation being between 35 and 75?

A) 0.35
B) 0.45
C) 0.55
D) 0.65

Question 9

Given a mean of -7.8 and a standard deviation of 16 from a normally distributed sample,what is the probability of an observation being below 12.0?

A) 0.51
B) 0.61
C) 0.71
D) 0.81

Question 10

Given a mean of 4.5 and a standard deviation of 12 from a sample of variables,what is the equivalent draw from a standard normal distribution for 6.0?

A) 0.065
B) 0.075
C) 0.095
D) 0.125

Question 11

A stock is valued at $55.00.The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%.If the stock is lognormally distributed,what is the expected price after 3 years?

A) $78.83
B) $88.83
C) $98.83
D) $108.83

Question 12

A stock is valued at $28.00.The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%.If the stock is lognormally distributed,what is the expected price after 4 years?

A) $28.00
B) $32.33
C) $40.13
D) $54.60

Question 13

What is the probability that a number drawn from the standard normal distribution will be between -0.60 and 0.45?

A) 0.40
B) 0.50
C) 0.60
D) 0.70

Question 14

A stock is valued at $28.00.The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%.If the stock is lognormally distributed,what is the price of the stock given a one standard deviation move up after 4 years?

A) $28.00
B) $32.33
C) $40.13
D) $54.60

Question 15

Why might normally distributed returns appear non-normal?

Question 16

For a stock price that was initially $55.00,what is the price after 4 years if the continuously compounded returns for these 4 years are 4.5%,6.2%,8.9%,-3.2%?

A) $64.80
B) $74.80
C) $84.80
D) $94.80

Question 17

Give a very brief definition of conditional expected stock price.

Question 18

A stock is valued at $55.00.The annual expected return is 12.0% and the standard deviation of annualized returns is 22.0%.If the stock is lognormally distributed,what is the expected median stock price after 3 years?

A) $57.67
B) $67.67
C) $77.67
D) $87.67

Question 19

What assumption is made in the Black-Scholes model concerning volatility?

Question 20

How are partial expectation prices converted to conditional expectation prices?