Tutorial 1 Answer – Chapter 1 & 2
Short sale entails borrowing shares and then selling them, receiving cash. Therefore, initially, we will receive the proceeds from the sale of the asset, less the proportional commission charge:
300 ($30.19) 300 ($30.19) 0.005 $9,057 0.995 $9,011.72
When we close out the position, we will again incur the commission charge, which is added to the purchasing cost:
300 ($29.87) 300 ($29.87) 0.005 $8,961 1.005 $9,005.81
Finally, we subtract the cost of covering the short position from our initial proceeds to receive total profits: $9,011.72 $9,005.81 $5.91. We can see that the commission charge that we have to pay twice significantly reduces the profits we can make.
RHS of the Forward pricing formula: S0 e rT 1100e5%6 /12 1127.85 (a)
If F0T 1120 we would buy low and sell high (i.e. Long Forward; Short-sell stock and lend out the short-selling proceed).
T = 6 months
ST – 1120
If F0T 1130 we would buy low and sell high (i.e. Short Forward; Long stock and borrow to finance our long stock position).
T = 6 months
-1100e5%×6/12 = -1127.85
1130 – ST
The payoff to a short forward at expiration is equal to:
Payoff to short forward = Forward price – Spot price at expiration
Therefore, we can construct the following table:
Price of Asset in 6
Agreed Forward Price
Payoff to Short
(b) The payoff
to a purchased put option at expiration is:
Payoff to long put option = max [0, Strike price - Spot price at expiration]
The strike is $50. Therefore, we can construct the following table: Price of Asset in 6
Payoff to the
Long Put Option
If we compare the two contracts, we see that the put option holder is protected from increases in the price of the asset.
If the spot price is above $50, the buyer of the put option is able to walk away and does not incur a loss; whereas, the holder of the short forward position incurs a loss since he is obligated to sell the asset for $50.
If the spot price is above $50, the holder of the put option and the holder of the short forward position have identical payoffs. Therefore, the put option should be more expensive due to this walk away feature.
Since we sold the stock initially, our payoff at expiration from being short the stock is negative.
order to obtain the profit diagram at expiration, we have to lend out the money
we received from the short sale of the stock. We do so by buying a bond for $50. After one year we receive from the investment in the bond: $50 × (1 + 0.1) = $55. This figure shows the graph of the sold stock, of the money we receive from the investment in the bond, and of the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. 3
35-strike call: $9.12 (1 0.08) $9.8496
40-strike call: $6.22 (1 0.08) $6.7176
45-strike call: $4.08 (1 0.08) $4.4064
Call’s strike price is the price at which you have the option to buy. The lower the buying price, the more valuable the call option (all else equal). As to the payoff diagram, the 35-strike call’s payoff is equal to the other two’s payoffs when the stock price (b)
expires below 35, and strictly above the others when the stock price is above 35. Since its payoff is greater than or...
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