CALCU-The following scenario relates to questions

Solution by Steps

step 2

Substitute the given values into the CAPM formula:

E(R_A) = 4\% + 1.5 (6\%)

step 3

Calculate the market risk premium portion:

1.5 \times 6\% = 9\%

step 4

Add the risk-free rate to the market risk premium portion:

4\% + 9\% = 13\%

step 5

The required return of Stock A is therefore

13\%

11 Answer

C

Key Concept

CAPM

Explanation

The Capital Asset Pricing Model (CAPM) is used to determine the expected return on an asset based on its risk relative to the market.

Gateway Inc, a technology company, is considering taking a minority equity stake in a high-growth startup, VentureTech (VT). VT is privately held so does not have market pricing, but Gateway has estimated the potential value in one year could range from

8 million to

18 million. To protect the downside risk in the VT investment, Gateway is evaluating using put option contracts on a public comparable company, BigData Inc (BDI), that currently trades at

50 per share. Specifically, Gateway is considering: Buying 1-year BDI put options with a strike price of

45 for a premium of

3 Selling 1-year BDI put option with a lower strike price of

40 for a premium of $1 The 1-year risk-free rate is 4% 1) Construct a payoff diagram with the profits and losses for the put option spread at expiration. 2) Determine the breakeven underlying stock price for this option strategy. 3) Evaluate whether you would recommend this hedging approach to Gateway. Explain the key benefits and limitations. 4) Assume the BDI stock price have equal possibility to increase 10% or decrease 20% in every 6-month. Calculate the fair price of buying a 1-year European put option on BDI stock.

Solution by Steps

step 1

To construct the payoff diagram for the put option spread, we need to understand the payoffs for both the long put with a strike price of

45 and the short put with a strike price of

40

step 2

The long put gives the right to sell BDI stock at

45. If the stock price at expiration is below

45, the put option is exercised, and the profit is the difference between the strike price and the stock price, minus the premium paid ($3)

step 3

The short put obligates us to buy BDI stock at

40. If the stock price at expiration is below

40, the put option is assigned, and the loss is the difference between the strike price and the stock price, plus the premium received ($1)

step 4

The maximum profit occurs if the stock price is at or below

40, which is the strike price of the short put. The profit would be the difference in strike prices (

45 -

40 =

5) minus the net premium paid (

3 -

1 =

2), which is

3 per share

step 5

The maximum loss occurs if the stock price is at or above

45, which is the strike price of the long put. The loss would be the net premium paid, which is

2 per share

step 6

To find the breakeven point, we set the net profit to zero and solve for the stock price. The breakeven point is the lower strike price plus the net premium paid, which is

40 +

2 = $42

step 7

To evaluate the hedging approach, we consider the cost of the strategy, the protection it offers, and the potential for profit

step 8

To calculate the fair price of a 1-year European put option on BDI stock, we can use the binomial option pricing model, considering the given probabilities of stock price movements

[1] Answer

The payoff diagram would show a maximum profit of

3 per share if the stock price is at or below

40, and a maximum loss of

2 per share if the stock price is at or above

45.

[2] Answer

The breakeven underlying stock price for this option strategy is $42.

[3] Answer

The hedging approach using a put option spread can be recommended if Gateway Inc. is looking to protect against downside risk while limiting the cost of the hedge. The key benefit is the limited loss to the net premium paid, and the limitation is the capped profit potential.

[4] Answer

The fair price of the 1-year European put option on BDI stock would be calculated using the binomial option pricing model, which is not provided in the steps above.

Key Concept

Put Option Spread

Explanation

A put option spread involves buying and selling put options with different strike prices. It is used to hedge against downside risk while limiting the cost of the hedge. The payoff is limited on both the upside and downside.

Key Concept

Breakeven Point of an Option Spread

Explanation

The breakeven point of an option spread is the underlying stock price at which the strategy neither makes nor loses money, considering the net premium paid or received.

Key Concept

Binomial Option Pricing Model

Explanation

The binomial option pricing model is a method used to price options by considering the possible future movements of the stock price and the risk-free rate. It is useful for pricing European options.

What is the mathematical formula used to calculate the breakeven underlying stock price for the put option strategy?

Solution by Steps

step 1

Identify the strike price (K) and the premium paid (P) for the put option

step 2

The breakeven point for a put option is calculated by subtracting the premium from the strike price

step 3

Use the formula: Breakeven Stock Price = Strike Price - Premium Paid

step 4

Apply the formula with the given values of K and P to find the breakeven stock price

1 Answer

The breakeven underlying stock price for the put option strategy is given by the formula:

\text{Breakeven Stock Price} = K - P

.

Key Concept

Breakeven Point for Put Option

Explanation

The breakeven point for a put option is the stock price at which the option buyer recovers the premium paid for the option. It is calculated by subtracting the premium from the strike price.

Which of the following statements about the capital asset pricing model (CAPM) is true? A. It can be used to find the required return on any risky asset. B. It says that the expected return on a stock should equal the risk-free rate. C. It assumes that capital markets are perfectly competitive. D. It assumes investors can borrow at the risk-free rate.

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