Solution of Derivative

# Solution of Derivative - Chapter 1 Introduction to...

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1 Chapter 1 Introduction to Derivatives Question 1.2. A variety of counter-parties are imaginable. For one, we could think about speculators who have differences in opinion and who do not believe that we will have excessive temperature variations during the life of the futures contracts. Thus, they are willing to take the opposing side, receiving a payoff if the weather is stable. Alternatively, there may be opposing hedging needs: Compare the ski-resort operator and the soft-drink manufacturer. The cooling degree-day futures contract will pay off if it the weather is relatively mild, and we saw that the resort operator will buy the futures contract. The buyer of the cooling degree-day futures will make a loss if the weather is cold (which means that the seller of the contract will make a gain). Since the soft drink manufacturer wants additional money if it is cold, she may be interested in taking the opposite side of the cooling degree-day futures. Question 1.4. In this problem, the brokerage fee is variable, and depends on the actual dollar amount of the sale/purchase of the shares. The concept of the transaction cost remains the same: If you buy the shares, the commission is added to the amount you owe, and if you sell the shares, the commission is deducted from the proceeds of the sale. a) 32 . 117 , 4 \$ 315 . 117 , 4 \$ 003 . 0 ) 100 05 . 41 (\$ ) 100 05 . 41 (\$ = = × × + × b) 72 . 082 , 4 \$ 715 . 082 , 4 \$ 003 . 0 ) 100 95 . 40 (\$ ) 100 95 . 40 (\$ = = × × × c) 6 . 34 \$ 72 . 082 , 4 \$ 32 . 117 , 4 \$ = The variable (or proportional) brokerage fee is advantageous to us. Our round-trip transaction fees are reduced by \$15.40. Question 1.6. A short sale of XYZ entails borrowing shares of XYZ and then selling them, receiving cash. Therefore, initially, we will receive the proceeds from the sale of the asset, less the proportional commission charge:

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2 72 . 011 , 9 \$ 995 . 0 057 , 9 \$ 005 . 0 ) 19 . 30 (\$ 300 ) 19 . 30 (\$ 300 = × = × × × When we close out the position, we will again incur the commission charge, which is added to the purchasing cost: 31 . 007 , 9 \$ 005 . 1 5 . 962 , 8 \$ 005 . 0 ) 875 . 29 (\$ 300 ) 875 . 29 (\$ 300 = × = × × + × Finally, we subtract the cost of covering the short position from our initial proceeds to receive total profits: 41 . 4 \$ 31 . 007 , 9 \$ 72 . 011 , 9 \$ = . We can see that the commission charge that we have to pay twice significantly reduces the profits we can make. Question 1.8. We learned from the main text that short selling is equivalent to borrowing money, and that a short seller will often have to deposit the proceeds of the short sale with the lender as collateral. A short seller is entitled to earn interest on his collateral, and the interest rate he earns is called the short rebate in the stock market. Usually, the short rebate is close to the prevailing market interest rate. Sometimes, though, a particular stock is scarce and difficult to borrow. In this case, the short rebate is substantially less than the current market interest rate, and an equity lender can earn a nice profit in the form of the difference between the current market interest rate and the short rebate.
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