Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
Question
Book Icon
Chapter 15, Problem 7PS
Summary Introduction

(A)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Pay off from a call option:

The payoff from a call contract for its holder is the current price of the underlying asset less the strike price. So, lower the strike price compared to the current price of the underlying asset, higher is the value of the call option. In other words, the worth of call options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is more than the strike price. And the worth of a call option dictates the purchase price of a call option. More worthy the call option, higher will be its purchase price.

When the strike price is more than the stock price, the exercise of call option will cause negative cash flow. So, in that case, call option is not exercised and causes zero payoff.

Profit from a call option:

The profit from a call contract for its holder is the payoff from a call option less its purchase price, paid earlier.

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Pay off from a put option:

The payoff from a put option contract for its holder is the strike price less the current price of the underlying asset. So, higher the strike price compared to the current price of the underlying asset, higher is the value of the put option. In other words, the worth of put options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is less than the strike price. And the worth of a put option dictates the purchase price of a put option. More worthy the put option, higher will be its purchase price.

When the strike price is less than the stock price, the exercise of put option will cause negative cash flow. So, in that case, put option is not exercised and causes zero payoff.

Profit from a put option:

The profit from a put contract for its holder is the payoff from a put option less its purchase price, paid earlier.

A long straddle:

It is a portfolio where both call and put options on a stock with the same strike price and with the same expiration date are bought. It is beneficial and investors practice it when they believe there will be a large deviation in the stock price but they are not certain about the direction of the movement of stock price.

To compute:

  1. The most one can lose on the given position.

Expert Solution
Check Mark

Answer to Problem 7PS

  • The most one can lose on the given position is $15.5.
  • Explanation of Solution

    In case of a long straddle, the payoff to a straddle is the sum of the payoff of call option and the payoff of put option. Similarly the profit for the portfolio is the sum of the profit/loss of call option and the profit/ loss of put option.

    The situation where the most one can lose on the given position is one with stock price equals to strike price. In this case, there will be no payoff from call option as well as put option. Then the maximum loss will be the sum of premium of call option and the premium of the put option.

    Given:

    Call premium (C) = $7

    Put premium (P) = $8.50

    Calculation:

      PortfolioPayoff=Payofffromcall+Payofffromput=$0+$0atS=X=0Profitfromportfolio=PayofffromputPutpremium+Payofffromcallcallpremium=0$8.5+0$7=$15.5

    Summary Introduction

    (B)

    Call option:

    A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

    Pay off from a call option:

    The payoff from a call contract for its holder is the current price of the underlying asset less the strike price. So, lower the strike price compared to the current price of the underlying asset, higher is the value of the call option. In other words, the worth of call options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is more than the strike price. And the worth of a call option dictates the purchase price of a call option. More worthy the call option, higher will be its purchase price.

    When the strike price is more than the stock price, the exercise of call option will cause negative cash flow. So, in that case, call option is not exercised and causes zero payoff.

    Profit from a call option:

    The profit from a call contract for its holder is the payoff from a call option less its purchase price, paid earlier.

    Put option:

    A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

    Pay off from a put option:

    The payoff from a put option contract for its holder is the strike price less the current price of the underlying asset. So, higher the strike price compared to the current price of the underlying asset, higher is the value of the put option. In other words, the worth of put options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is less than the strike price. And the worth of a put option dictates the purchase price of a put option. More worthy the put option, higher will be its purchase price.

    When the strike price is less than the stock price, the exercise of put option will cause negative cash flow. So, in that case, put option is not exercised and causes zero payoff.

    Profit from a put option:

    The profit from a put contract for its holder is the payoff from a put option less its purchase price, paid earlier.

    A long straddle:

    It is a portfolio where both call and put options on a stock with the same strike price and with the same expiration date are bought. It is beneficial and investors practice it when they believe there will be a large deviation in the stock price but they are not certain about the direction of the movement of stock price.

    To compute:

    The profit or loss from the given straddle if stock price is $88

    Expert Solution
    Check Mark

    Answer to Problem 7PS

    The loss from the given straddle if stock price is $88, is $7.50.

    Explanation of Solution

    In case of a long straddle, the payoff to a straddle is the sum of the payoff of call option and the payoff of put option. Similarly the profit for the portfolio is the sum of the profit/loss of call option and the profit/ loss of put option.

    Given:

    Stock price (S) = $88

    Strike price (X) = $80

    Call premium (C) = $7

    Put premium (P) = $8.50

    Calculation:

    PortfolioPayoff=Payofffromcall+Payofffromput=SX+XS=$88$80+0Payofffromputis0ifS>X=$8Profitfromportfolio=PayofffromputPutpremium+Payofffromcallcallpremium=0$8.5+$8$7=$7.5

    Summary Introduction

    (c)

    Call option:

    A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

    Pay off from a call option:

    The payoff from a call contract for its holder is the current price of the underlying asset less the strike price. So, lower the strike price compared to the current price of the underlying asset, higher is the value of the call option. In other words, the worth of call options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is more than the strike price. And the worth of a call option dictates the purchase price of a call option. More worthy the call option, higher will be its purchase price.

    When the strike price is more than the stock price, the exercise of call option will cause negative cash flow. So, in that case, call option is not exercised and causes zero payoff.

    Profit from a call option:

    The profit from a call contract for its holder is the payoff from a call option less its purchase price, paid earlier.

    Put option:

    A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

    Pay off from a put option:

    The payoff from a put option contract for its holder is the strike price less the current price of the underlying asset. So, higher the strike price compared to the current price of the underlying asset, higher is the value of the put option. In other words, the worth of put options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is less than the strike price. And the worth of a put option dictates the purchase price of a put option. More worthy the put option, higher will be its purchase price.

    When the strike price is less than the stock price, the exercise of put option will cause negative cash flow. So, in that case, put option is not exercised and causes zero payoff.

    Profit from a put option:

    The profit from a put contract for its holder is the payoff from a put option less its purchase price, paid earlier.

    A long straddle:

    It is a portfolio where both call and put options on a stock with the same strike price and with the same expiration date are bought. It is beneficial and investors practice it when they believe there will be a large deviation in the stock price but they are not certain about the direction of the movement of stock price.

    To compute:

    The stock price at which one will break even the straddle

    Expert Solution
    Check Mark

    Answer to Problem 7PS

    The stock price at which one will break even the straddle is $95.5 if stock price is more than the strike price while the stock price at which one will break even the straddle is $64.5 if stock price is less than the strike price.

    Explanation of Solution

    The stock price at which one will break even the straddle should be one that causes no profit and no loss from the given portfolio. There can be two break even points. One is for the stock price more than the strike price and another is for the stock price less than the strike price. For each one case, profit from portfolio should be made zero and then solve for the stock price as shown below to get the required stock prices at which one will break even the straddle.

    Given:

    Stock price = S

    Strike price (X) = $80

    Call premium (C) = $7

    Put premium (P) = $8.50

    Calculation:

    Case 1: S>X

    PortfolioPayoff=Payofffromcall+Payofffromput=SX+XS=S$80+0Payofffromputis0ifS>XProfitfromportfolio=PortfoliopayoffPutpremiumcallpremium0=S$80$8.5$7SolvingforS,S=$95.5

    Case 2: X>S

    PortfolioPayoff=Payofffromcall+Payofffromput=SX+XS=0+$80SPayofffromcallis0ifX>SProfitfromportfolio=PortfoliopayoffPutpremiumcallpremium0=$80S$8.5$7SolvingforS,S=$64.5

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