1. A trader creates a long butterfly spread from options with strike prices of $90, $100, and $110 per share by trading a total of 20 option contracts (buy 5 contracts at $90, sell 10 contracts at $100 and buy 5 contracts at $110). Each contract is written on 100 shares of stock. The options are worth $15, $18, and $22 per share of stock, respectively.

a) What is the value of the butterfly spread at maturity as a function of the then stock price?

b) What is the profit of the butterfly spread at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.

Suppose a 2 year 5% (annual coupon) bonds are selling at par (that is, for $100 of face value, the price is equal to $100) and 1 year zero coupon bonds has a yield to maturity of 7%.

(a) What are the 1-year and 2-year interest rates, r1 and r2, respectively?
(b) What should be the price of a two year 8% coupon bond with a face value of $100?

(c) What are the Durations of 5% coupon bonds and 8% coupon bonds? Which one has longer duration? What is the implication about interest rate risk?

(Please give the specific numbers of part c.)

Below are some data from the land of milk and honey.

YEAR       PRICE OF MILK        QUANTITY OF MILK    PRICE OF HONEY        QUANTITY OF HONEY

2001                $1                                100 Qts.                     $2                               50 qts.

2002                $1                                200                              $2                                100

2003                $2                                200                              $4                                100

1. Compute for each year the following below using 2001 as the base year.

a) nominal GDP

b) real GDP,and

c) the GDP deflator for each year, using 2001 as the base year.

2. Why do economists use real GDP rather than nominal GDP to gauge economic well being?

Consider an airline trying to sell plane tickets to business travelers and tourists. The airline cannot distinguish between the two at the point of sale, but knows that in general, business travelers have higher willingness to pay for better seats. Let PF and PC be the price of first class and coach tickets respectively. Suppose that business travelers are willing to pay $1000 for a first class seat and $400 for a coach seat, whereas tourists are willing to pay $500 for a first class seat and $300 for a coach seat.

(a) If the airline wants to implement second-degree price discrimination so that business travelers buy first class seats and tourists buy coach seats, what are the incentive compatibility constraints they face?

(b) Using your incentive compatibility constraints, find the price that the airline will charge for a coach seat.

(c) What are the information rents that the airline must leave to business travelers? What is the price of a first class seat?

You buy one Home Depot (HD) call option and one HD put option, both with a $215 strike price and a June expiration date. The call premium is $9.25 and the put premium is $23.70.

1. Your maximum loss from this position could be ________.

2. At expiration, you break even if the stock price is equal to _____.

2)

JPM stock currently sells for $90. A 6-month call option with strike price of $100 sells for $6.00, and the risk free rate is 2%.

1. According to the put-call parity, what should be the price of a 6-month put option with strike price of $100?

2. If the put option is currently priced at $17.00, state an arbitrage strategy to take advantage of this mispricing.

3. If the put option is currently priced at $13.00, state an arbitrage strategy to take advantage of this mispricing.

You are given the following information. Please use it for the following

Stocks W and X had 2 for 1 splits on December 31, 2016. The information in the table

for 2016 is pre-split.

3.4 Calculate the price weighted series for Dec 31, 2016, prior to the splits.

3.5 Calculate the price weighted series for Dec 31, 2016, after the splits.

3.6 Calculate the price weighted series for Dec 31, 2017.

a.

Calculate the value weighted index for Dec 31, 2016, prior to the splits. Assume a base

index value of 100. The base year is Dec 31, 2016.

b.

Calculate the value weighted index for Dec 31, 2016, after the splits. Assume a base index

value of 100. The base year is Dec 31, 2016.

3.8 Calculate the value weighted index for Dec 31, 2017. Assume a base index value of

100. The base year is Dec 31, 2016.

3.9

a.

Calculate the unweighted index for Dec 31, 2016, prior to the splits. Assume a base index

value of 100. The base year is Dec 31, 2016.

b.

Calculate the unweighted index for Dec 31, 2016, after the splits. Assume a base index

value of 100. The base year is Dec 31, 2016.

3.10 Calculate the unweighted index (geometric mean) for Dec 31, 2017. Assume a base

index value of 100. The base year is Dec 31, 2016.

The common stock of Texas Energy Company is selling at $90. A 1-year call option
written on Texas’s stock is selling for $8. The call’s exercise price is $100. The risk-free
interest rate is 1% per year. Suppose that puts on Texas stock are not tradable, but you
want to hold one. How would you do it? Suppose that puts are traded, what should a 1-
year put with an exercise price of $100 sell for?

b. What are stocks? What are their features and how are they traded?

c. How do you calculate an annual rate of return?

d. You buy a share of stock for $100 and it pays no dividend. A year later the market price is $105. What is the rate of return?

e. You buy a share of stock for $100 and a year later the market price is $105 and it pays a dividend of $2. What is the return?

I. Suppose the inverse demand function for a monopolist’s product is given by ? = 150 − 2? and the total cost function is given by ?? = 100 + 30?

1. Determine the profit-maximizing price and quantity

2. Determine the maximum profits

II. Suppose the inverse demand function for a monopolistically competitive firm’s product is given by

? = 100 − 2?
and the cost function is given by ?? = 52 + 4?

1. Determine the profit-maximizing price and quantity

2. Determine the maximum profits.

A portfolio manager wants to exchange one bond in a portfolio for another. The old bond position has a market value of 6.5 million, a price of $81.90 per $100 of par value, and a duration of 4.33. The new bond has a duration of 4.33 and a price of $85.52 per $100 of par value.

What is the total market value of the new bond that the portfolio manager must buy in order to keep the same portfolio duration?

Correct Answer: 6,500,000