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An investor puts together the following portfolio: The investor deposits $1000 into a 1-year CD that pays i = 2.1%. The investor writes a put

An investor puts together the following portfolio:

The investor deposits $1000 into a 1-year CD that pays i = 2.1%.

The investor writes a put option on TomCo stock, agreeing to sell 100 shares at the price of $100 for each share in 1 year if the buyer exercises the option.

The investor collects $30 for the put option. Use the 1-year CD interest rate of i = 2.1% to determine future value.

Analysts model the spot price S of TomCo stock in 1 year with PDF

fS(s) =1/100 (s 90) 90 s < 100

1/100 (110 s) 100 s 110

What is the probability the investor makes a profit from this portfolio after 1 year?

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