Option risk Calculate and compare the risk (betas) of the following investments: (a) a share of Amazon stock; (b) a one-year call option on Amazon; (c) a one-year put option; (d) a portfolio consisting of a share of Amazon stock and a one-year put option; (e) a portfolio consisting of a share of Amazon stock, a one-year put option, and the sale of a one-year call. In each case, assume that the exercise price of the option is $900, which is also the current price of Amazon stock.
a)
To determine: Risk (beta) share of Company A’s stock
Explanation of Solution
The stock beta of Company A’s stock is 1.5
b)
To determine: One year call option on Company A.
Explanation of Solution
Given information:
Current stock selling price (P) is $900
Exercise price (EX) is $900
Standard deviation (σ) is 0.25784
Risk free rate (rf) is 0.01 annually,
t = 1
Stock beta is 1.5
Calculation of value of call option:
The value of
The value of
Therefore,
Hence, the value of call option is $96.39
Person X has investing $509.86 and he borrows $413.48,
Calculation of option beta:
Therefore, the option beta is $7.93
c)
To determine: One year put option.
Explanation of Solution
Calculation of one year put option:
From the put-call parity relationship,
Therefore, to replicate the put pay-offs, person X would buy a call with $400 as an exercise price and invest the present value of exercise price and sell the short stock.
The risk can be as follows,
Therefore risk is -6.7
d)
To determine: One share stock plus one put option.
Explanation of Solution
Calculation of one share plus one option:
It is related to previous question, except the stock positions cancel out, which leaves us with an exercise price of $900 investment in the present value of exercise price.
The risk can be as follows,
Therefore, risk is 0.77 which partially hedged the position.
e)
To determine: One share stock plus one put option minus one call option.
Explanation of Solution
Calculation of one share plus one option minus one call option:
It is related to previous question, except the all call positions cancel out, which leaves us with an investment in the present value of exercise price.
The risk can be as follows,
Therefore, risk is 0.00 which reduced our position to risk-free loan.
Want to see more full solutions like this?
Chapter 21 Solutions
PRIN.OF CORPORATE FINANCE
- Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?arrow_forwardUsing the following information, calculate the overall payoff on the option given the stock price at maturity. Exercise price: 50.00 Premium: 7.00 Call / put: Call Long / short: Short Stock price at maturity 40.00 Select one: A) (7.00) B) 7.00 C) 3.00 D) (3.00)arrow_forwardConsider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?arrow_forward
- Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04arrow_forwardGiven the following portfolio: Buy one call option on the stock XYZ with a strike price of $51.1 at a premium of $2. Sell two put options on the stock XYZ with a strike price of $56.5 at a premium of $1.5. Assume both option expire the same time. When the market price of the stock XYZ at expiration of all options is $54, the profit of the portfolio is $arrow_forwardAssume that the value of a call option using the Black-Scholes model is $8.94. The interest rate is 8 percent, and the time to maturity is 90 days. The price of the underlying stock is $47.38, and the exercise price is $45. Calculate the price of a put using the put-call parity relationship.arrow_forward
- Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option Xarrow_forwardSuppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.arrow_forwardYou are given the following information about the stock of Company ABC: Share price $80 risk free rate of interest is 6%, time to expiration is 6 months, annualised standard deviationis 0.5 and exercise price is $85. Calculate the appropriate call value of the stock according to the Black-Scholes option pricing formula. (Show your workings in full) Calculate an appropriate put premium. (Show your workings in full)arrow_forward
- A call option with a current value of $6.20. A put option with a current value of $6.70. Both options written on the same stock and both with 1 year until expiration. The current price of the stock is $52.00 and the prevailing risk-free rate is 7.00%. What must be the striking price of either option? Via Excel please!arrow_forwardWhich of the following positions in options benefit if the underlying stock price increases? Assume the options have several months remaining until the exercise date. a. Short position in call and long position in put b. Short position in both call and put c. Long position in a put d. Long position in call and short position in put e. Short position in a call f. Short position in a put g. Long position in a callarrow_forwardConsider an investment portfolio that consists of three different stocks, with the amount invested in each asset shownbelow. Assume the risk-free rate is 2.5% and the market risk premium is 6%. Use this information to answer thefollowing questions.Stock Weights BetasChesapeake Energy 25% 0.8Sodastream 50% 1.3Pentair 25% 1.0a) Compute the expected return for each stock using the CAPM and assuming that the stocks are all fairly priced.b) Compute the portfolio beta and the expected return on the portfolio.c) Now assume that the portfolio only includes 50% invested in Pentair and 50% invested in Sodastream (i.e., a twoassetportfolio). The yearly-return standard deviation of Pentair is 48% and the yearly-return standard deviation ofSodastream is 60%. The correlation coefficent between Pentair’s returns and Sodastream’s returns is 0.3 What is theexpected yearly-return standard deviation for this portfolio?arrow_forward
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENTIntermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning