Sovereign bonds

E- Options and other derivatives

Derivatives are used for two very different (and theoretically opposite) purposes: hedging or speculation. Hedging is intended to reduce risk. For instance, if an investor fears that a given stock in a portfolio may go down, a put option for that stock can be bought. If the stock does go down, the gain from the option (i.e. from being able to sell the stock at a strike price above the lowered market price) will offset the loss on the underlying stock. Speculation is the willingness to take on risk in order to earn income. For instance, the writer of the put option takes a risk that the stock will go down (i.e. having to buy a stock at a strike price that is higher than the market price), but if the stock does not go down, the writer will keep the premium received when the option was sold. The distinction between hedgers and speculators is really only theoretical. Once our investor in the first example learns how to gain from put options, what prevents him/her from buying a few extra put options to earn an extra profit? Take the case of an investor who hedges a short position (i.e. a contract to sell shares in the future) by buying a call option: is that a hedger or a speculator?

Call options, or a right to buy a stock at a predetermined strike price, are bought with the anticipation that the price of the underlying stock will go up. Writers (or sellers) of call options hope that the price of the stock will go down or remain the same, that the options will not be exercised, and that they will keep the premium. Profit and loss of writer and buyer of call options depending on the pattern of stock price change can be derived from options pricing presented in Chapter 3 Section 3E-1. Graphs G-4.1 and G-4.2 below show these profits or losses of both writer and buyer of a call option with a strike price of $35 and a premium of $5.

Graph G-4.1 and Graph G-4.2

Graph G-4.1 shows that as long as the price stays below $35, the profit of the writer is equal to the premium of $5. If price rises above $40, the writer must absorb losses. Graph G-4.2 shows the position of the call option buyer who has paid the $5 premium in order to be able to buy the stock at $35 no matter how high the price rises, and who hopes for a profit if the price is above $40.

Put options, or options giving a right to sell a stock, are bought with the anticipation that the price of the underlying stock will go down (as can be deduced from Chapter 3 Section 3E-1). Sellers of put options hope that the price will go up and that they will keep the premium. Graphs G-4.3 and G-4.4 show the profits and losses of writer and buyer of a put option with a strike price of $45 and a premium of $5.

Graph G-4.3 and Graph G-4.4

Graph G-4.3 shows that the writer of the put option retains a profit equal to the premium of $5 as long as the price remains above $45. Graph G-4.4 shows that the buyer earns a profit by being able to sell the underlying stock for $45 when that stock trades at a price lower than $40, i.e. when the stock price drop is greater than the premium the buyer paid.

A straddle is a combination of put and call. The buyer of a straddle expects that the stock will drastically change in price (e.g. because of a restructuring, introduction of new product line or merger), and earn a profit from both rise or drop in price shown in Graph G-4.6. The writer of a straddle anticipates that the stock will not change much, that neither option will be exercised and that he/she will retain the premium as his/her profit. Graph G-4.5 shows the profit or loss of a straddle writer with call and put options of $35 and premiums of $5 for each. Graph G-4.6 shows the profit and loss of a straddle buyer with call and put options of $40 and premiums of $5 for each.

Graph G-4.5 and Graph G-4.6

The writer stands to have large losses; the buyer could earn large gains at the risk of losing the premium paid on put and call options. Certainly, the buyer can no longer be considered as a hedger, but a speculator. There are numerous other strategies with options. We need not go any deeper into details of these strategies which are described in most investment textbooks.

It should be clear that, in the case of options, both writers and holders of options must constantly keep a close watch on the current market price of the stock, compare that to the strike price, pay attention to the past and anticipate changes in stock prices, and the time remaining to exercise the option. Options give an opportunity for a high return because the funds involved are but a fraction of the value of the underlying stock. But options can also be source of losses if an investor misjudges trends or fails to act quickly after observing a change in option value. The action is in most cases to offset an open position with an opposite position rather than exercising the option.

As for any financial asset, options should not be looked upon in isolation, but as part of a portfolio. If so, different options strategies can achieve the same outcome. For instance, to protect from loss of value but take advantage of potential gain, one can buy a stock and a put option:
- if the market stock price goes down the combination cannot be worth less than the strike price of the put option, and
- if the market stock price goes up, the put option is worthless, but ownership of the stock provides unlimited gain.
The same can be accomplished with a call option with a strike price exactly equal to the strike price of the put option, and a purchase of a highly secure security, such as a treasury bill, that will mature at the same time as the expiration of the option and generate proceeds equal to the strike price:
- if the market stock price goes down, the call option is worthless, but the combination of the the two assets is worth no less than than the treasury bill, and
- if the market stock price goes up, the call option allows a purchase of the stock at the strike price with the proceeds from the treasury bill for an unlimited gain.
The fact these two strategies are equivalent implies that the values of call and put options are linked to one another. This is called the put-call parity which can be written as

PV(Pr) + Call = P + Put

where Pr = initial sum invested at time zero in a treasury bill: PV() = present value operator; Call = purchase price of call option with a strike price of Pr; P = purchase price of stock at time zero; Put = purchase price of put option with a strike price of Pr

The put-call parity can be rewritten as

Call - Put = P - PV(Pr)

or Put = Call - P + PV(Pr)

Note that the parity equation above omits dividends that the ownership of the stock provides. With the present value of dividends PV(D) the parity becomes

Call - Put = P - PV(Pr) - PV(D)

or Put = Call - P + PV(Pr) + PV(D)

As an example of the put-call parity, let us take May options on IBM stock found in the financial press on April 18, 2001. On that day IBM traded at $99.70 and an interest rate of 5% is used to calculate the present value of Pr. Table T-4.2 below presents prices of call and put options, differences (Call-Put), present values of strike prices received at the end of May (PV(PR)), and excesses of present values of strike prices over current stock price (P-P(Pr)).

Table T-4.2

IBM stock option prices on April 18, 2001 P = $99.70

.

Strike price

(=Pr)
.

Call
.

Put
.

Call-Put
.

PV(Pr)
.

P-PV(Pr)

70 70.3 29.7

75 2.4 75.4 24.6

80 3.2 80.4 19.6

85 4.3 85.4 14.6

90 15.3 5.8 9.5 90.4 9.6

95 12.1 7.4 4.7 95.4 4.6

100 9.7 9.6 0.1 100.5 -0.5

105 7.1 12.6 -5.5 105.5 -5.5

110 5.3 15.6 -10.3 110.5 -10.5

115 3.6 115.5 -15.5

120 2.8 120.6 -20.6

Table T-4.2 shows clear evidence of the put-call parity. Values in the Call-Put column are practically equal to P-PV(Pr) for each strike price. Any difference is less than transaction costs.

The analytical work ought to combine an assessment of company history, an understanding of underlying stock price behavior, a feel for stock market trends and moods, and an up-to-date forecast of economic conditions and industry patterns. Actually, keeping abreast of stock and options markets (in order to price time value of options correctly, as explained in Chapter 3 Section 3E-1) takes usually all the time, and no time is left for fundamental analysis. Once again, the task of the analyst is mostly directed at economic forecasting that affect all capital markets, all stocks and all options.

Strategies with other derivatives are less involved than those with options. Futures, for instance, are just a form of call options. Warrants and rights are also forms of call options. How firms use these financial assets to meet investors' strategies is approached in Chapter 12 Section 12C and Section 12D.

See review questions Q-4E.1 through Q-4E.12.

See research assignments R-4.13, R-4.14, R-4.15, R-4.16, R-4.17 and R-4.18.

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Last modified: Jun/01/01 Next: Shareholders