CFA Level 1 (2009) - 5

The following is a review of the Detivative Investments principles designed to address the learning outcome- statements set forth by CFA Institute(~. This topic is also covered in:

RISK MANAGEMENT ApPLICATIONS OF

OPTION STRATEGIES

Srudy Session 17

EXAM Focus

LOS 72.a: Determinc the value at expiration, profit, maximum pralll, maximum loss, breakeven underlying price at cxpiration, and general shape of the graph of the str;l[cgies of buying and selling calls and Plll~;, and indiclle the

market outlook of investors Ilsin'nT these stratcvlcs.

L'

Call option profits and losses. Consider a call option with a premium of $5 and a srrike price of $50. This means the buyer pays $5 to rhe writer. At expiration, if the price of the srock is less than or equal to the $50 strike price (the option has zero value), rhe buyer of the option is our $5, and the writer of the option is ahead $5. As the srock's price exceeds $50, the buyer of the option starts ro gain (breakeven will come at $55, when the value of the stock equals the strike price and the option premium). However, as the price of the srock moves upward, the seller of the option starts to lose (negative figures will start at $55, when the value of the stock equals the strike price and the option premium).

The profit/loss diagram for the buyet (long) and wri ter (short) of the call option we have been discussing at expiration is presented in Figure 1. This profitlloss diagram illustrates the following:

• The maximum loss for the buyer of a call is the loss of the $5 premium (at any

SS $50).

•The breakeven point for the buyer and seller is the strike price plus the premium (at

S= $55).

•The profit potential to the buyer of the option is unlimited, and, conversely, the potential loss to the writer of the call option is unlimited.

Study Session 17 Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

The call holder will exercise the option whenever the srock's price exceeds the strike

price at the expiration date.

•The greatest profit the writer can make is the $5 premium (at any S 'S $50) .

•The sum of the profits between the buyer and seller of the call option is always zero; thus, options rrading is a zero-sum game. There are no net ptofits at losses in the marker. The long profits equal the short losses.

Proj;'ssors Notl': Please notice that option profit diagrams shoul the gain or loss to the long and/or shorr option positions. They differ from the payoi/diagrams thllt we used in our options relJiew in thclt profit diagrams reflect the cost ofthe option (i. e., the option premium).

Figure 1: Profit/Loss Diagram for a Call Option

Long call

option has a gain of $5, As the srock's p~ama~~7buyerof the put option stans ro gain (breakeven will come at $<jJ:;CwdlaB6.654fi9>f the srock equals the srrike price less the option premium). Howevml~:~1;irtp.ooi<!flj:~~VQfRIc~6ct'ilwnward,the seller of the option starts ro lose (negative profits will stan at $45, when the value of the stock equals the strike price less the option premium).

Figure 2 shows the profit/loss diagram for the buyer (long) and seller (shan) of the put option that we have been discussing. This profitlloss diagram illustrates that:

• The maximum loss for the buyer of a pUt is the loss of the $5 premium (at any S 2: $50).

Study Session 17

Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

Figure 2: Proht/Loss Diagram for a Put Option

1)1l .Ii t

$45

-$45

$45 X = $50

Example: Option profit calculations

Suppose that both a call option and a put option have been written on a stock with an

exercise price of $40. The current stock price is $42, and the call and put premiums are $3 and $O.75,r~speetively.. .

Calculate the profit to the long andshortpositions for both the put and the cal! with an expiration day stock price of $35 and with a price at expiration of $43.

Answer:

Profit will be Co!uputed as ending option valuation - initial option cost.

Stock tit $35:

Long call: $0 - $3 '" -$3. The option finished out-of-the-money, so the premium is lost.

•Shorr call: $3 - $0 = $3. Since the option finished our-of-the-money, the call writer's gain equals the premium.

Study Session 17

Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

•Long put: $5 - $0.75 = $4.25. You paid $0.75 for an option that is now worth $5.

•Short put: $0.75 - $5 = -$4.25. You received $0.75 for writing the option but you face a $5 loss because the option is in-the-money.

Stock at $43:

•Long call: -$3 + $3 = $0. You paid $3 for the option, and it is now worrh $3. Hence, your net profit is zero.

•Short call: $3 - $3 = $0. You received $3 for writing the option and now face

valuation for a net profit of zero.

•Long put: -$0.75 - $0 = -$0.75. You paid $0.75 for the put option and the option is now worthless. Your net profit is -$0.75.

•Shorr put: $0.75 - $0 = $0.75. You received $0.75 for writing the option and keep the premium because the option finished out-of-the-money.

A buyer of puts or a seller of calls will profit when the price of the underlying asset decreases. A buyer or calls or a seller of putS will profit when the price or rhe underlying asset increases. In general, a pur buyer believes the underlying aSSet is overvalued and will decline in price, while a call buyer anticipates an increase in the underlying asset's price.

Determine the value at expiration, profit, maximum proht, maximum loss, breakcven underlying price at expiration, and general shape of the graph or a covered call suategy and a protective put strategy, and explain rhe rd, m;1IlJgcl1lcnt :lpplication strategy.

Proji'SSor's Note: Whmever we combine options with assets or other options, the

~options/assets minus the proceeds from the option/asset sales (short positions). The profits and losses on a position are simply the vrzlue ofall the assets/options in the positions at expiration minus the net cost.net cost ofthe combined position is simply the sum ofthe prices paid fir the long

In writing covered calls, the term covered means that owning the srock covers the obligation to deliver srock assumed in writing the call. Why would you write a covered call? You feel the srock's price will not go up any time soon, and you want to increase your income by collecting the call option premium. To add some insurance that the stock won't get called away, the call writer can write out-of-the-money calls. You should know that this strategy for enhancing one's income is not without risk. The call writer is trading the stock's upside potential fir the call premium.

Figure 3 illustrates the profit/loss of a covered call position at option expiration date. When the call was written, the srock's price was $50. The caIl's strike price was $55, and the call premium was $4. The call is out-of-the-money. From Figure 3, we can observe that at expiration:

•If the stock closes below $50, the option will expire worthless, and the option writer's loss is offset by the premium income of $4.

Srudy Session 17

Cross-Reference to CFA lnst·itute Assigned Reading #72 - Risk Management Applications of Option Strategies

•Breakevenjor the pOi'ition is at $46 = $50,- $4. Breakeven price = So - call premium.

•If the srock closes between $50 and $55, the option will expire worrhkss. Since this option was an out-of-the-money call, the option writer will get any srock appreciation above the original srock price and below the strike price. So the gain (premium plus srock appreciation) will be between $4 and $9.

•If srock closes above $55, the strike price, the writer will get nothing more. The maximum gain is $9 on the covered out-of-the-money call.

•The rnaxinlllnJ loss occurs if the stock price goes to zero; the net cost of the position ($46 = $50 stock loss offset by $4 premium income) is the maximum loss.

Figure 3: Covered Call Profit and Loss for S = SO, C = 4, X = 55

slOck

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The desirability of writing a covered call to enhance income depends upon the chance that the srock price will exceed the exercise price at which the trader writes the call. In this example, the writer of the call thinks the srock's upside potential is less than the buyer expects. The buyer of the call is paying $4 to get any gain above $55, while the seller has traded the upside potential above $55 for a payment of $4.

A protective put is an investment management technique designed to protect a stock from a decline in value. It is constructed by buying a srock and put option on that stock.

Look at the profitlloss diagrams in Figure 4. The diagram on the left is the profit from holding the stock. If the srock's value is up, your profit is positive and if the stock's value is down, your profit is negative. Profit equals the end price, ST' less the initial price St'

That is, profit = ST - St' The diagram on the right side of" Figure 4 is the profit graph from holding a long pur. If the market is up, you lose your premium payment, and if the market is down, you have a profit.

The value of the put at termination will be max[O, X - ST]' Your profit will be max[O, X - 5T ] less the price of the put.

Study Session 17 Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

Figure 4: Protective ~ut Components

Figure 5 shows the profits from the combination of a long put and a long stock (i.e., a protective put), Here it is assumed that the swck is purchased at $100 and that a put with a srrike price of $1 00 is purchased for $4. Note that the put described in Figure 5 is at the money.

Figu re 5: Protective Pu t

What we should observe in Figure 5 is that:

A protective put cuts your downside losses (maximum loss = $4) but leaves the upside potential alone (unlimited upside gains).

•Your maximum loss occurs at any price below $100.

•Losses between $0 and $4 occur for stock prices between $100 and $104.

•You will not make a profit until the stock price exceeds $104 (breakeven).

•Breakeven price = So + premium.

Note that a protective put (stock plus a put) has the same shape profit diagram as a long calf.

It could be replicated with a bond that pays (X - premium) at expiration and a call at X.

Professor's Note: Recall that this relation was the basis fOr our derivation ofputcalf parity. The p[Jyoffi at expiration are identicalfor a protective put (S + P) and

(~ a fiduciary calf (I + ~)T-[ + C , a calf with an exercise price equal to X and a

pure discount bond that pays X at expiration.

Srudy Session 17

Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

KEy CONCEPTS

LOS 72.a

Cdl option value at expiration is Max (0, S - X) and profit (loss) is

Max (0, S - X) - option case.

A call hU)'LL (fJut seller) anticipates an increase (decrease) in the value of the underlying assce.

A put buyer (put seller) anticipates a decrease (increase) in the value of the underlying

asset.

LOS n.b

•The purpose of selling a covered call is to enhance income by trading the srock's upside potential for the call premium.

•The upside potenrial on a covered call is limited to (X - So) + call premium received. The maximum loss is the net cost (So - premium).

• A protective pur is a strategy ro protect against a decline in the value of the stock.

•A protective pur consists of buying a share of srock and buying a pur. Profits and losses are measured relative to the net cost (So + premium).

•Maximum gains on a protective put are unlimited, but reduced by the put premium paid. Maximum losses are limited to (So - X) + put premium paid.

Study SessiolJ 17

Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

I.A call option sells for $4 on a $25 stock with a strike price of $30, Which of the following statements is lemt (/ccurtlte?

A. At expiration, the buyer of the Clil will not make a profit unless the srock's

A.$50.

B.$55.

C.$<10.

3.Which of the following is the riskiest single-option transaction?

A.Writing a call.

B.Buying a put.

C.Writing a put.

4.An investor will likely exercise a put option when the price of the srock is:

A.above the strike price.

B.below the strike price plus the premium.

C.below the strike price.

6.At expiration, the value of a call option must equal:

A.the larger of the strike price less the stock price or zero.

B.the stock price minus the strike price, or arbitrage will occur.

A.gain will be $12.

B.loss will be $40.

C.loss will be unlimited.

8.Which of the following combinations of options and underlying investments have similarly shaped profitlloss diagrams? A:

A.covered call, and a short stock combined with a long call.

B.short put option combined with a long call option, and a protective put.

C.long call option combined with a shorr put option, and a long Slack posmon.

Study Scssion 17

Cross-Reference to CFA Institute Assigned Reading #72 - Risk Management Applications of Option Strategies

ANSWERS - CONCEPT CHECKERS

1.A The buyer will nor have a ncr profir unless rhe srock price exceeds $34 (strike price plus rhe premium). The other sraremenrs are rrue. Ar $30 the option will be exercisl:d, bur rhe wrirer will only lose money in a net sense whcn rhe sLOck's priec exceeds

X -I C = $30 + $4. The covered call's maximum gain is $4 premium plus $5 appreciarion.

2.A This assumes rhe price of rhe srock falls to zero and you get to sell for $55. Your profit would be $55 - 5 = $50.

3.A When buying either a call or a pUt, the loss is limired to rhe amount of the premium. When writing a put, the loss is limired to the strike price if rhe srock falls ro zero (however, the writcr keeps the premium). When writing an uncovered call, the srock could go up infinitely, and rhe wrirer would be forced ro buy rhe srock in rhe open marker and ddivcr ar the srrike price--pOlelHial losses arc unlimited.

4.C The owner of a put profits when rhe srock falls. The pur would be exercised when rhe price of the stock is below rhe srrike price. The amount of the premium is used to determine net profits to each party.

5.C The grearest loss the put writer can have is the strike price minus the premium received equals $65. The other statemelHS arc tme. The greatest profir rhe put writer can make is

rhe amOUlH of rhe premium. The greatesr profir for a put buyer occurs if rhe srock falls to zero and the buyer makes the strike price minus the premium. Since oprions are a zero-sum game, the maximum profit to the writer of the pllt must equal the maximum loss to the buyer of the put.

6.C At expiration, the value of a call must be equal to its intrinsic value, which is

Max[O, S - Xj. If the value of the stock is less rhan the strike price, rhe intrinsic value is

7. A As soon as the stock rises to the exercise price, the covered call writer will cease to realize

a profit because the short call moves into-rhe-money. Each dollar gain on the srock is then offset wirh a dollar loss on the short call. Since the option is $10 out-of-the- money. the covered call writer can gain this amount plus the $2 call premium. Thus, the maximum gain is $2 = $12. However, because the investor owns the stock,

he or she could lose $40 stock goes to zero, but gain $2 from the call premium. Maximum loss is $38.

8.C A combined long call and a short put. with exercise prices equal to the current stock price, will have profitsllosses at expiration nearly identical to those of a long stock position.

Professor's Note: The easiest way to see this is to draw the payoffdiar,ram for the combined option positions.

The following is a review of the Alternative Investments principles designed to address the learning outcome statements set forth by CFA Institute@. This topic is also covered in:

ALTERNATIVE INVESTMENTS

Study Session 18

EXAM Focus

LOS 73.a: Differentiate between an open-end and a closed-end fund, and explain how net asset value of a fund is calculated and the nature of fees charged by investment companies.

Managed investment companies (mutual funds) are formed to collectively manage assets for a group of investors. Investment companies can be classified into one of two categories, depending upon the liquidity they provide or do not provide to their II1vestors.

An open-end investment company, or open-end fund, stands ready to redeem shares at the closing value on any rrading day. Shares of a closed-end company, or closed-end

fund, are rraded (after issuance) in the secondary markets through organized exchanges (e.g., NYSE). Thus, the liquidity of an open-end fund is provided by the investment company that manages it, whereas the liquidity of a closed-end fund is determined in the open market.

The managers of an open-end fund may charge a fee, or "load," to the investors upon purchase (a front-end load) or at redemption (a back-end load). A fund that charges no fee at purchase or redemption is called a "no-load" fund. All funds, regardless of whether they are load or no-load funds, will charge ongoing fees on an annual basis, which may include management fees, administrative fees, and distribution (marketing) fecs, which are referred to as 12b-l fees in the U.S.

The shares of a closed-end fund will be issued at a small premium to the value of the underlying assets, the premium serving as compensation for issuance costs. The

investment company will also charge an ongoing management fee. Since a closed-end fund is traded in the secondary market subsequent to issuance, the redemption cost for the investor is simply the commission charged on the sale of shares and a portion of the bid/ask spread of the shares. The terms "load" and "no-load" are not applicable to closed-end funds.