1. Positions

What is the difference between a long forward position and a short forward position?

With a long forward position, you are obligated to buy in the future at a pre-determined price.

With a short forward position, you are obligated to to sell.

2. Forwards and Calls

What is the difference between (a)entering into a long forward contract when the forward price is

$50 and (b) taking a long position in a call option with a strike price of$50?

The payoffs at expiration will be very different.

With the long forward position there is potential for a loss in the future if ST < 50.

With a long call option position there is no downside risk.

3. Investment Strategies

You would like to speculate on the rise in the price of a certain stock. The current stock price is $29

and a 3-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two alter-

native strategies, one involving investment in the stock and the other involving investment in the

option. What are the potential gains and losses from each?

Strategy 1 - Invest all of your money in the stock.

⇒ Buy $5,800

$29 = 200 shares of the stock.

Total profit in 3 months:200(S3 − $29) = 200S3 − F V (5800)

Total payoff in 3 months:200S3

Strategy 2 - Invest all of your money in call options.

⇒ Buy $5,800

$2.9 = 2000 call options.

Total profit in 3 months:2000 ∗ max(0, S3 − 30) − F V (5800)

Total payoff in 3 months:2000 ∗ max(0, S3 − 30)

4. Combining Positions

Describe the payoff from the following portfolio: a long forward contract on an asset and a long

European put option on the asset with the same maturity as the forward contract and a strike price

that is equal to the forward price of the asset at the time the portfolio is set up.

Long a forward contract:

→ P ayof f = St − X

P ayof f

X

ST

Long a European put:

→ P ayof f = max(0, X − ST )

2

P ayof f

❅

❅

❅

❅

❅

❅

ST

❅

❅

X

Combine the two:

→ P ayof f = max(0, ST − X)

P ayof f

X

ST

5. Combining Positions

”A long forward contract is equivalent to a long position in a European call and a short position in

a European put.” Explain this