### Study notes from a previous year's CFA exam:

d. describe the investment objectives, structure, payoff, and risks(s) of a protective put position;

e. calculate and interpret the value at expiration, profit, maximum profit, maxi- mum loss, and breakeven underlying price at expiration for covered calls and protective puts;

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**Subject 4. Protective Puts**

A

**protective put**(portfolio insurance) is an investment management technique designed to protect a stock portfolio from severe drops in value. It involves holding a stock portfolio and buying a put option on the portfolio. At expiration:

- Maximum profit = S
_{T}- S_{0}- p_{0}= unlimited - Maximum loss = S
_{0}- X + p_{0} - Breakeven profit = S
_{0}+ p_{0} - Expiration value = Max(S
_{T}, X) - Profit at expiration = Max(S
_{T}, X) - S_{0}- p_{0}

Portfolio insurance limits the amount of loss on a portfolio by balancing that loss with the gain from a LONG put option. It also reduces the potential gain on a portfolio as a result of the premium paid for the put option. The "insurance" part of portfolio insurance, then, is the limitation of potential loss. The insurance is not free, however. The cost of the insurance is the put option premium.

This strategy is like a long position in a call. A trader can buy a call and invest the extra proceeds in a bond in order to replicate a position in an insured portfolio.

**Equivalence to Long Asset/Short Forward Position**

As discussed in reading 41,

**delta**measures how the option price changes as the underlying asset price changes.

- Call deltas: 0 to 1
- Put deltas: 0 to -1
- The delta of the underlying: 1
- The delta of an at-the-money option: 0.5 for call and -0.5 for put

That reading shows that three different positions have the same delta: an at-the-money covered call, an at-the-money protective put, and a long stock/short forward position.

#### Practice Question 1

In the protective put and insurance analogies, the insurance premium is similar to the ______ in a put option.A. time value

B. price of stock

C. exercise priceCorrect Answer: A

#### Practice Question 2

An at-the-money protective put position (comprised of owning the stock and the put) ______.I. protects against loss at any stock price below the strike price of the put

II. has limited profit potential when the stock price rises

III. returns any increase in the stock's value, dollar for dollar, less the cost of the put

IV. provides a pattern of returns similar to a stop-loss order at the current stock priceCorrect Answer: I and III

#### Practice Question 3

An exporter in the U.S. is expecting a payment of BP 5 million in three months. He is planning to hedge the position using options. He should ______.A. buy call options

B. buy put options

C. write put optionsCorrect Answer: B

#### Practice Question 4

A portfolio insurance strategy consists of a ______.A. LONG stock portfolio and SHORT stock index put

B. LONG stock portfolio and LONG stock index put

C. SHORT stock portfolio and LONG stock index putCorrect Answer: B

#### Practice Question 5

In the protective put and insurance analogies, the face value of an insurance policy is similar to the ______ in a put option.A. time value

B. price of stock

C. exercise priceCorrect Answer: C

#### Practice Question 6

An investor would likely buy a protective put under which of the following conditions?A. The investor is concerned about downward price movement in the stock.

B. The investor wishes to leverage an anticipated rise in the stock price.

C. The investor does not anticipate a significant change in stock price in the near term.Correct Answer: A

An investor would likely buy a protective put (portfolio insurance) if he/she were concerned about a downward price movement in the stock.

#### Practice Question 7

An investor owns a stock portfolio that closely follows the Standard & Poor's 500 Index (S&P 500). He purchases one S&P 500 stock index put option. The investor's position now has portfolio insurance with the following characteristics:Portfolio position: LONG S&P 500

Portfolio purchase price: $1427.21

Option position: LONG 1 put option

Underlying asset: S&P 500 Index

Exercise price: $1225

Premium: $3

Expiration date: November 30

The expiration-day price of the S&P 500 is S

_{T}= $1500. The expiration-day profit/loss for the portfolio insurance is ______.

A. + 72.79 + 0 - 3 = $69.79

B. + 72.79 + 0 + 3 = $75.79

C. - 72.79 + 275 - 3 = $199.21Correct Answer: A

Profit at expiration = Max(S

_{T}, X) - S

_{0}- p

_{0}= 1500 - 1427.21 - 3.00 = $69.79

#### Practice Question 8

An investor owns a stock portfolio that closely follows the Standard & Poor's 500 Index (S&P 500). He purchases one S&P 500 stock index put option. The investor's position now has portfolio insurance with the following characteristics:Portfolio position: LONG S&P 500

Portfolio purchase price: $1427.21

Option position: LONG 1 put option

Underlying asset: S&P 500 Index

Exercise price: $1225

Premium: $3

Expiration date: November 30

The expiration-day price of the S&P 500 is S

_{T}= $1500. The breakeven point for the portfolio insurance is ______.

A. 1427.21 + 3 = $1430.21

B. 1500 - 3 = $1497

C. 1225 + 3 = $1228Correct Answer: A

Breakeven point = S

_{0}+ p

_{0}= 1427.21 + 3 = $1430.21

#### Practice Question 9

Suppose the return distribution of a stock is a bell-shaped curve. Buying a put option does which of the following?A. Truncates the left side of the curve and moves the whole bell curve to the right.

B. Truncates the left side of the curve and moves the whole bell curve to the left.

C. Truncates the right side of the curve and moves the whole bell curve to the right.

D. Truncates the right side of the curve and moves the whole bell curve to the left.Correct Answer: B

#### Practice Question 10

In an insurance policy, the deductible is the amount of loss the insured is willing to bear. In a put option, the deductible is the ______.A. option premium

B. exercise price minus the option premium

C. stock price minus the exercise priceCorrect Answer: C

In general, the higher the deductible, the lower the cost of insurance (option premium).

#### Practice Question 11

Suppose an investor buys one share of stock and a put option on the stock. What will be the value of her investment on the final exercise date if the stock price is below the exercise price?A. The value of two shares of stock

B. The value of one share of stock minus the exercise price

C. The exercise price.Correct Answer: C

#### Practice Question 12

An at-the-money call option will have a delta that is about ______.A. -0.5

B. 0.5

C. 1Correct Answer: B

#### Practice Question 13

Which one has a delta of 1.0?A. A long in-the-money call

B. A long out-of-money put

C. A long position in the underlying assetCorrect Answer: C

#### Practice Question 14

The likelihood of loss with an insurance policy is similar to the ______ in a stock put option.A. time value

B. volatility of stock

C. time until option expirationCorrect Answer: B

#### Practice Question 15

In an insurance policy, the deductible is the amount of loss the insured is willing to bear. A stock is selling at $21.85. A one-month $20 strike put is selling for $1.38. The deductible of the put is ______.A. $1.38

B. $1.85

C. $0.47Correct Answer: B

The deductible is the stock price minus the exercise price.

#### Practice Question 16

An investor buys 100 baskets of the Standard and Poor's 500 stock index for $1,400 each. She insures the portfolio by buying put options. What is the effect of the put options?A. The upside risk of the insured portfolio is truncated and the downside risk is reduced relative to the uninsured portfolio.

B. The downside risk of the insured portfolio is truncated and the upside return of the insured portfolio is lower relative to the uninsured portfolio.

C. The insured portfolio does better than the uninsured portfolio whenever the market declines.Correct Answer: B

This truncates the left-hand side of the return distribution.

#### Practice Question 17

The profits and losses from an equity portfolio insured using puts would have the same profit and loss characteristics as they would from ______.A. being long a call option

B. writing covered puts

C. writing covered callsCorrect Answer: A

Being long a call has limited downside risk, as does portfolio insurance.

#### Practice Question 18

Your research department has just made a sound presentation arguing that the equity markets are due for a severe correction in the short term. Which of the following strategies would be most suitable to safeguard the portfolio that you manage?A. Long futures contracts on an equity index

B. Buy put options on an equity index

C. Buy call options on an equity indexCorrect Answer: B

If you expect stock prices to decline, then you'll want to enter into an agreement that will allow you to sell shares at a pre-determined price. This way, you are effectively locking in the future value of the shares. There are only two strategies that will enable you to carry out this transaction. First, buying a put will give you the "right" to deliver these shares at a pre-determined price. Second, selling stock index futures will "obligate" you to deliver these shares at a pre-determined price.

#### Practice Question 19

Which of the following statements is (are) true with respect to insuring a portfolio by way of a protective strategy?I. The strategy requires the sale of put options while owning the underlying asset.

II. If the price of the underlying asset increases dramatically, then an insured portfolio will perform much better than an uninsured portfolio.

III. The cost of portfolio insurance will rise as the volatility of the underlying asset increases.

IV. The upside potential for an insured portfolio is unlimited.

A. I and IV

B. III only

C. III and IVCorrect Answer: C

I is incorrect because this strategy requires the purchase of put options while owning the underlying asset.

II is incorrect because if the price of the underlying asset increases dramatically, an insured portfolio will underperform an uninsured portfolio. The cause of this underperformance is that fact that an insured portfolio always lags behind an uninsured portfolio by the amount of the premium.

#### Practice Question 20

A market participant sells a customized over-the-counter put option on the stock when the stock is trading at $38. The put has an exercise price of $36 and the put seller receives $2.25 in premium. The price of the stock is $35 at expiration. The profit or loss for the put seller at expiration is ______.A. -$2.15

B. $1.25

C. $2.25Correct Answer: B

Profit = max (0, -value of put at expiration + premium) = max (0, -(X-S) +premium) = -1+2.25 = $1.25

#### Practice Question 21

An investor owns a stock portfolio that closely follows the Standard & Poor's 500 Index (S&P 500). He purchases one S&P 500 stock index put option. The investor's position is now portfolio insurance with the following characteristics:Portfolio position: LONG S&P 500

Portfolio purchase price: $1427.21

Option position: LONG 1 put option

Underlying asset: S&P 500 Index

Exercise price: $1225

Premium: $3

Expiration date: November 30

The expiration-day price of the S&P 500 is S

_{T}= $1500. The expiration-day value for the portfolio insurance is ______.

A. $1,500

B. $1,427.21

C. $1,225Correct Answer: A

The expiration value of a protective put is Max(S_{T}, X) = Max (1,500, 1,427.21) = 1,500.

#### Practice Question 22

An at-the-money put option will have a delta that is about ______.A. -0.5

B. 0.5

C. 1Correct Answer: A

Note that put deltas range from 0 to -1.