Investment Analysis

Chapter 15

Options Markets

1. Options provide numerous opportunities to modify the risk profile of a portfolio. The simplest example of an option strategy that increases risk is investing in an ‘all options’ portfolio of at-the-money options (as illustrated in the text). The leverage provided by options makes this strategy very risky and potentially very profitable. An example of a risk-reducing options strategy is a protective put strategy. Here, the investor buys a put on an existing stock or portfolio, with exercise price of the put near or somewhat less than the market value of the underlying asset. This strategy protects the value of the portfolio because the minimum value of the stock-plus-put strategy is the exercise price of the put.

1. Options at the money have the highest time premium and thus the highest potential for gain. Since the highest potential gain is at the money, the logical conclusion is that they will have the highest volume. A common phrase used by traders is “avoid the cheaps and the deeps.” Cheap options are those with very little time premium. Deep options are those that are way out of or in the money. None of these provide profit opportunities.

1. Each contract is for 100 shares:  $7.25 × 100 = $725

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1. If the stock price drops to zero, you will make $80 – $5.72 per stock, or $74.28. Given 100 units per contract, the total potential profit is $7,428.

1. The price has to be at least as much as the sum of the exercise price and the premium of the option to breakeven: $40 + $4.50 = $45.50

1. Maximum loss happens when the stock price is the same to the strike price upon expiration. Both the call and the put expire worthless, and the investor’s outlay for the purchase of both options is lost: $7.00 + $8.50  = $15.50

1. Loss: Final value – Original investment

 = (ST – X) – (C + P) = $8 – $15.50 = –$7.50

1. There are two break even prices:

1. ST > X

(ST – X) – (C + P) = (ST – 80) – $15.50 = $0 ⇒ ST = $95.50

1. ST < X

(X – ST) – (C + P) = (80 – ST) – $15.50 = $0 ⇒ ST = $64.50

1. Option c is the only correct statement.

a. The value of the short position in the put is –$4 if the stock price is $76.

b. The value of the long position in the put is $4 if the stock price is $76.  

d. The value of the short position in the put is zero for stock prices equaling or exceeding $80, the exercise price.  

1. i. A long straddle produces gains if prices move up or down and limited losses if prices do not move.  A short straddle produces significant losses if prices move significantly up or down.  A bullish spread produces limited gains if prices move up.

1. i. Long put positions gain when stock prices fall and produce very limited losses if prices instead rise.  Short calls also gain when stock prices fall but create losses if prices instead rise.  The other two positions will not protect the portfolio should prices fall.

1. The initial outlay of this position is $38, the purchase price of the stock, and the payoff of such position will be between two boundaries, $35 and $40.

1. The maximum profit will thus be: $40 – $38 = $2, and the maximum loss will be: $35 – $38 = –$3.

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1. The collar involves purchasing a put for $3 and selling a call for $2. The initial outlay is $1.

1. ST = $30

Value at expiration = Value of call + Value of put + Value of stock

                                      = $0 + ($35 – $30) + $30 = $35

Given 5,000 shares, the total net proceeds will be:

(Final Value – Original Investment) × # of shares

= ($35 – $1) × 5,000 = $170,000

Net proceeds without using collar = ST × # of shares

                                                             = $30 × 5,000 = $150,000

1. ST = $40

Value at expiration = Value of call + Value of put + Value of stock

                                 = 0 + 0 + $40 = $40

Given 5,000 shares, the total net proceeds will be:

(Final value – Original investment) × # of shares

= ($40 – $1) × 5,000 = $195,000

Net proceeds without using collar = ST × # of shares

                                                       = $40 × 5,000 = $200,000

1. ST = $50

Value at expiration = Value of call + Value of put + Value of stock

                                = ($45 – $50) + 0 + $50 =$45

Given 5,000 shares, the total net proceeds will be:

(Final value – Original investment) × # of shares

= ($45 – $1) × 5,000 = $220,000

Net proceeds without using collar = ST × # of shares

                                                       = $50 × 5,000 = $250,000

1. With the initial outlay of $1, the collar locks the net proceeds per share in between the lower bound of $34 and the upper bound of $44. Given 5,000 shares, the total net proceeds will be between $170,000 and $220,000 when the position is closed. If we simply continued to hold the shares without using the collar, the upside potential is not limited but the downside is not protected.

1. In terms of dollar returns:

In terms of rate of return, based on a $10,000 investment:

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1. Purchase a straddle, i.e., both a put and a call on the stock.  The total cost of the straddle would be: $10 + $7 = $17

1. Since the straddle costs $17, this is the amount by which the stock would have to move in either direction for the profit on either the call or the put to cover the investment cost (not including time value of money considerations).

1. Sell a straddle, i.e., sell a call and a put to realize premium income of:

        $4 + $7 = $11

1. If the stock ends up at $50, both of the options will be worthless and the profit will be $11. This is the maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put.

1. The stock price can move by $11 (your initial revenue from writing the two at-the-money options) in either direction before your profits become negative.

1. Buy the call, sell (write) the put, lend the present value of $50. The payoff is as follows: