Question

Problem 5

Ralph Lauren is a portfolio manager with Point72 Investments, a U.S.-based asset management firm. Lauren is considering using options to enhance portfolio returns and control risk. He asks his junior analyst, Tommy Hilfiger, to help him.

Hilfiger collected and summarize the relationship between a European call option and various factors that might impact the call option value in Table 1. He also collected the current market prices and data of selected instruments related to Lotus stock in Table 2.  

Table 1

Impact of Increasing the Variables on call option value
Variables	Impact on call option value
Stock price	Increase
Strike Price	Decrease
Maturity	Increase
Volatility	Increase
Interest rate	Increase
Dividend	Increase

Table 2

European call option on Lotus equity	$3
European put option on Lotus equity	$4
Lotus equity price	$50
Time to expiration of options	4 months
Exercise price of options	$50
Risk-free rate	10%
Dividend to be paid in 3 months	$0

a.         Which of the relationships shown in Table 1 above is incorrect?

i Volatility and Stock Price

ii. Risk-free rate and Volatility

iii. Exercise price and stock price

iv. Maturity and Dividend        

v. Stock Price and Interest Rate

b.         According to Table 2, Lauren’s arbitrage strategy should include the following:

short the put option, short the stock, long the call option, and long bond (lending money)

short the put option, long the stock, long the call option, and long bond (lending money)

short the put option, short the stock, short call option, and long bond (lending money)

long the put option, short the stock, long the call option, and long bond (lending money)

c.         What will be the arbitrage profit per share without considering the transaction cost?

Answer 1

A1. None of the options are correct.

In table 1, just the dividend effect on call option is incorrect as an increase in the dividend leads to a decrease in the call option. All of the other relationships are correct.

A2. A. Short the put option, short the stock, long the call option and long bond.

A3. Arbitrage profit per share= money gained from shorting put option- money lost on longing the call option= $4-$3 = $1.

Since the exercise price is$50, there would be no gain from any position in the stock.