bkmsol_ch20 - CHAPTER 20 OPTIONS MARKETS INTRODUCTION 1 a b...

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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION 1. Cost Payoff Profit a. Call option, X = $80.00 $4.40 $5.00 $0.60 b. Put option, X = $80.00 $0.75 $0.00 -$0.75 c. Call option, X = $85.00 $1.35 $0.00 -$1.35 d. Put option, X = $85.00 $2.90 $0.00 -$2.90 e. Call option, X = $90.00 $0.25 $0.00 -$0.25 f. Put option, X = $90.00 $6.80 $5.00 -$1.80 2. In terms of dollar returns, based on a $10,000 investment: Price of Stock 6 Months from Now Stock Price $80 $100 $110 $120 All stocks (100 shares) $8,000 $10,000 $11,000 $12,000 All options (1,000 options) $0 $0 $10,000 $20,000 Bills + 100 options $9,360 $9,360 $10,360 $11,360 In terms of rate of return, based on a $10,000 investment: Price of Stock 6 Months from Now Stock Price $80 $100 $110 $120 All stocks (100 shares) -20% 0% 10% 20% All options (1,000 options) -100% -100% 0% 100% Bills + 100 options -6.4% -6.4% 3.6% 13.6% All options All stocks Bills plus options S T 100 –100 0 – 6.4 Rate of return (%) 100 110 20-1
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3. a. From put-call parity: P = C – S 0 + [X/(1 + r f ) T ] = 10 – 100 + [100/(1.10) 1/4 ] = $7.65 b. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the straddle is: $10 + $7.65 = $17.65 This is the amount by which the stock would have to move in either direction for the profit on the call or put to cover the investment cost (not including time value of money considerations). Accounting for time value, the stock price would have to move in either direction by: $17.65 × 1.10 1/4 = $18.08 4. a. From put-call parity: C = P + S 0 – [X/(l + r f ) T ] = 4 + 50 – [50/(1.10) 1/4 ] = $5.18 b. Sell a straddle, i.e., sell a call and a put to realize premium income of: $5.18 + $4 = $9.18 If the stock ends up at $50, both of the options will be worthless and your profit will be $9.18. This is your maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put. The stock price can move by $9.18 in either direction before your profits become negative. c. Buy the call, sell (write) the put, lend: $50/(1.10) 1/4 The payoff is as follows: Position Immediate CF CF in 3 months S T X S T > X Call (long) C = 5.18 0 S T – 50 Put (short) –P = 4.00 – (50 – S T ) 0 Lending position 82 . 48 10 . 1 50 4 / 1 = 50 50 Total C – P + 00 . 50 10 . 1 50 4 / 1 = S T S T By the put-call parity theorem, the initial outlay equals the stock price: S 0 = $50 In either scenario, you end up with the same payoff as you would if you bought the stock itself. 20-2
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5. a. Outcome S T X S T > X Stock S T + D S T + D Put X – S T 0 Total X + D S T + D b. Outcome S T X S T > X Call 0 S T – X Zeros X + D X + D Total X + D S T + D The total payoffs for the two strategies are equal regardless of whether S T exceeds X. c. The cost of establishing the stock-plus-put portfolio is: S 0 + P The cost of establishing the call-plus-zero portfolio is: C + PV(X + D) Therefore: S 0 + P = C + PV(X + D) This result is identical to equation 20.2. 6. a. Position S T < X 1 X 1 S T X 2 X 2 < S T X 3 X 3 < S T Long call (X 1 ) 0 S T – X 1 S T – X 1 S T – X 1 Short 2 calls (X 2 ) 0 0 –2(S T – X 2 ) –2(S T – X 2 ) Long call (X 3 ) 0 0 0 S T – X 3 Total 0 S T – X 1 2X 2 – X 1 – S T (X 2 –X 1 ) – (X 3 –X 2 ) = 0 X 2 – X 1 S T X 1 X 2 Payoff X 3 20-3
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b.
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