Chapter 6

  • 1
     Simple long or short positions expose the trader to considerable risk. This is spesially true for short positions. By taking an opposite position in another option, ie., executing a spread, the trader is able to keep the risk to a more manageable level. Combined positions of options and stocks do the same thing the option serves as a hedge for the stock or the stock serves as a hedge for the option. However, a position in both options and stocks is harder to execute since the options and stock trade in different markets. This results in time delays in getting the trades executed. On the other hand, a spread can be executed much faster, with both transactions done almost simultaneously in the same market.

  • 2
     Since the stock price is closer to higher exercise price than to the lower exercise price, the short call at the higher exercise price has the greater value. Therfore, holding the position longer could result in greater time value decay on the short call than on the long call. This will occur only, however, if the stock price doesn't move down. The cross-river point indicated in Figure 6.2 in the chapter is a critical stock price below which the shorter holding period is preferred. If it appears as if the stock price will fall below the cross-over stock price, the position should be closed as soon as possible, but only if the stock price is not expected to turn back around before the options expire.

  • 3
     Both a straddle and a time spread can be used in this situation. A straddle consisting of the purchase of a put and a call with identical exercise prices and expirations would profit if the stock price moved substantially in either direction. A time spread consisting of the sale of a longer-term option would also profit if the stock price moved significantly in either direction. This is because a large stock price move will allow repurchase of the longer term option when it has little time value remaining. Note that this example is the opposite of the one discussed in the text. Also, a butterfly spread that is short the high and low exercise prices and long two of the middle exercise price could be used in this situation, but it would have limited gains if the stock price moved substantially.

  • 4
     A put bear spread could offer two advantages over a call bear spred. First, it is possible that the puts could be mispriced while the calls are correctly priced. Second, a call bear spread runs the risk of early exercise. The short call can be in-the-money without the long call also being in-the-money. For the put bear spread, however, the short put will not be in-the-money unless the long put is also. Then if the short put is exercised, the long put can be exercised for a net gain of -(E1-St)+(E2-St)=E2-E1 which is the maximum value that could be expected by holding the position to expiration.

  • 5
     pi=Max(0,E1-St)-P1-Max(0,E2-St)+P2

    if St pi=E1-E2-(P1-P2)

    if E1 pi=-P1-E2+St+P2

    if E1 pi=-P1+P2

  • 6
     First note that the graph for a short sraddle held to expiration is an inverted V. If closed out prior to expiration, a short straddle (which involves the sale of both a put and a call) will require the repurchase of options. This means that prior to expiration, there will be time values on both the put and the call that will have to be repurchased. These time values are highest if the stock price is close to the exercise price. So the profit if the stock price is near the exercise price is lower the shorter the holding period. The longer the investor can hold the position, the less time value that remains on the options. However, this also gives the stock more time to move substantially and potentially generate a large loss.

  • 7
     If an investor feels that the market is as likely to go down as up, a straddle would be appropriate srategy bacause the profit graph is symmetric. If the investor feels slightly more bullish than bearish, then the addition of a second call enables the investor to capitalize if the market does go up. However, the cost of the second call must be recovered, and in a strong bear market or one in which the stock price does not move much in either direction, the cost of the second call cuts significantly into the profit. A strap is like placing more money on the line that the market will go up. Unless you are right and the market goes up enuogh to enable you ti exercise or sell the calls and recover the premiums paid, then your profit will be lower.

  • 8
     In internal rate of return (IRR) problems, the return from the investment is compared to the opportunity cost of capital. The investment is acceptable if the IRR exceeds the opportunity cost. In the box spread problem, the investment pays E2-E1. The initial outlay is C1-C2-P1+P2. The IRR is the value of i that solves

    (E2-E1)(1+i)exp(-T)=C1-C2-P1+P2

    The oppotunity cost is the risk-free rate, r. If i>r, then the box spread is acceptable. If i

  • 9
     Buy the October 170 at 6.

    Sell the October 165 at 8.125

    Breakeven: 167.125

    Maximum profit: 212.50

    Minimum profit: -287.50

  • 10
     Time to expiration: 26/365=0.0712

    r=0.0571

    165 call

    C1=0.4703

    170 call

    C2=0.1148

    spred value=-0.3555

    pi=176.95

  • 11
     Sell October 160 at 11.125.

    Buy two October 165's at 8.125 each

    Sell October 170 at 6.

    Breakevens: 160.875 and 169.125

    Maximum profit: 87.50

    Minimum profit: -412.50

  • 12
     Buy August 170 at 3.25. Sell October 170 at 6.

    August 170: T=20/365=0,0548 r=0.0535

    October 170: T=0.2082 r=0.0571

    By hand with St=155

    August 170 : C1=0.1119

    October 170: C2=1.9301

    spread value= -1.8182

    pi=93.18

    Maximum profit: 275 [if St=0, profit = -100(3.25-6)=275]

    Minimum profit: -117.53

    Approximate breakevens: 161 and 181

  • 13
     C= 8.5106

    intrinsic value= 0.125

    Time value: 8.3856

  • 14
     August 160

    S=165.125 E=160 r=0.0535 T=0.1260 the Delta=0.7091

    October 160

    S=165.125 E=160 r=0.0571 T=0.2795 the Delta=1.0344

    If we buy the August 160 and write the October 160, the hedge ratio is the delta of the August call divided by the delta of the October call.

  • 15
     Buy the October 165 call at 8.125

    Buy the October 165 put at 6.75.

    Breakevens: 179.875 and 150.125.

    Minimum profit: -1487.50

  • 16
     r=0.0571 T=0.0712 By hand with St=155 C=0.1423 P=9.8008

    Approximate breakevens: 177 and 155

  • 17
     Buy two October calls at 8.125 each. Buy one October put at 6.75.

    Breakevens: 176.50 and 142. Minimum profit: -2300

  • 18
     Sell two August 170 puts at 7.5.

    Sell one August 170 call at 3.25.

    Breakevans: 188.25 and 160.875.

    Minimum profit: -31.175.

  • 19
     if r=0.0535 then the discrete rate is 0.055

    Buy August 160 call at 8.125. Sell August 170 call at 3.25. Buy August 170 put at 7.5 Sell August 160 put at 2.75.

    The net premium is: 9.625 The present value of the future payoff is 9.933. The net present value is 0.308.

    This spread is underpriced so buy it. That is buy the August 160 call and 170 put and sell the August 170 call and put. This will generatea nagative cash flow up front of (.625. At expiration you will receive 10, but the present value of 10 is more than the initial cash flow.

  • 20
     Buy August 165 put at 4.75. Buy August 170 call at 3.25.

    Breakevens: 178 and 157.

  • 21
     Buy October 165 call at 8.125. Sell August 170 call at 3.25.

    Value of diagonal spread = 2.9890

    pi= -188.60

    Approximate breakeven: 161.9