Question

In: Finance

A friend of yours believes that Apple stock is now overvalued. As a result, she expects...

A friend of yours believes that Apple stock is now overvalued. As a result, she expects that their stock price, now at $115 per share, will not go up any further. She is prepared to back up her conviction by offering you the following bet. If in exactly one year from now Apple stock price is higher than $115/share, she will give you two hundred times the amount of the difference (e.g., suppose the price in one year is $120 per share, you will get $1,000). On the other hand, if the price in one year ends up below $115/share, you will have to give her two hundred times the amount of the difference (e.g., suppose the price in one year is $112 per share, you will have to give her $600). Suppose that the expected return on Apple stock is 10% p.a. Suppose also that the current risk-free rate is 2% p.a. and Apple does not plan to pay dividends in the next year. What is the value of this bet to you? [Hint: Write out the payoff of the bet. What does the payoff look like?]. Please answer this assuming continuous compounding is used.

Solutions

Expert Solution

Value of option as per risk netural mehtod

The probaility of increasing price is as follows:

The value of bet is as follows:

The vaue of bet is $20.2

jeff jeffy answered 2 years ago
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