# P1.T3.22.18 Short-selling and financial forward contracts

#### David Harper CFA FRM

##### David Harper CFA FRM
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Learning objectives: Define and describe financial assets. Define short-selling and calculate the net profit of a short sale of a dividend-paying stock. Describe the differences between forward and futures contracts and explain the relationship between forward and spot prices. Calculate the forward price given the underlying asset’s spot price and describe an arbitrage argument between spot and forward prices.

Questions:

22.18.1. In May, the spot price of an asset was $80.00 per share. At that time, Peter believed the asset was significantly overpriced. At that time, he did not own any shares of the stock. He executed a short sale of 100 shares with his broker. Later, in July, the asset paid a dividend of$4.00 per share. Finally, in September, the price had dropped to $50.00 per share (Peter's bearish view was very correct!). If we assume financing and transaction costs are zero, and if we ignore the time value of money, what was Peter's profit on the trade? a.$2,600.00
b. $3,000.00 c.$3,400.00
d. Not applicable (the broker would not have executed the naked short sale)

22.18.2. The spot price of an investment asset is $50.00 while the riskfree rate is 2.0% per annum with continuous compounding. The asset pays a quarterly dividend equal to 4.0% of the asset price at the time of the dividend payment; i.e., the dividend is 12.0% per annum with quarterly compounding. Which is nearest to the two-year forward price, F(2.0)? a.$39.37
b. $41.08 c.$52.60
d. $63.36 22.18.3. The risk-free interest rate term structure is upward-sloping. Specifically, the six-month rate is 2.0% and the one-year rate is 3.0%. Both rates are given per annum with annual compound frequency. An asset has a spot price of$29.00. The asset will pay a cash-flow dividend of $8.50 in six months. The observed one-year forward price of this asset is$25.00; i.e., a trader can enter into this forward contact with a long or short position. What is the arbitrage trade?

a. Long the forward contact and short the spot asset to lend cash for a future profit of $4.20 b. Long the forward contact and borrow cash to buy the spot asset for a future profit of$5.50
c. Short the forward contract and short the spot asset to lend cash for a future profit of $1.75 d. Short the forward contract and borrow cash to buy the spot asset for a future profit of$3.80

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