# Net profits of options and securities using CAPM

Calculating net profits of options and securities using CAPM.

1. Calculate the net profits of each option under the following assumption. Also indicate if the option is ITM, ATM, or QTM.

Strike price of options = $100

Premium of options =$10

a.) Long position of Call option if the stock price is $125 and if the stock price is $85.

b.) Short position of Put option if the stock price is $125 and if the stock price is $85.

2. You expect the IBM to hit $120 per share with expected dividends of $2.50 in one year. Its current price is $105 and your research estimates the beta at 1.15. Market risk premium is .07 and the U.S. T-bill is expected to yield .05. Is the IBM a good investment? Conduct security analysis using CAPM. Can you also explain your answers.

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1. Calculate the net profits of each option under the following assumption. Also indicate if the option is ITM, ATM, or OTM.

If the current market price is more than the strike price, the call option is in-the-money (ITM). If the current market price is less than the strike price, the call option is out-of-the-money (OTM). If the current market price is the same as (or close to) the strike price, the call option is at-the-money (ATM)

A put option is in-the-money (ITM) when the strike price is higher than the market price of the underlying asset. A put option is at-the-money (ATM) when the price of the underlying security is equal (or close) to its strike price. A put option is out-of-the-money (OTM) when the price of the underlying security is greater than the strike price.

Strike price of options = $100

Premium of options =$10

a.) Long ...

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The solution explains the calculation of net profits of options and securities using CAPM

19 Questions on Derivatives: beta of a hedge fund, put option, CAPM, Capital Asset Pricing Model, investors, risk averse, portfolios, mean, variance, highest return portfolio, efficient frontier, abnormal returns, equity mutual funds, riskless return, options position, time to maturity, interest rates, convexity of a puttable bond, futures contracts, gold, initial margin, margin calls, volatility, Palm, 3COM, financial markets, beta calculation, value of a put option, exercise price, maturity, arbitrage opportunity, riskless return, call, 6-month forward rate, Canadian dollars, US dollars, implied volatility, historical volatility, SPX, floating to fixed swap, LIBOR, swap counterparty

For each of the following 8 statements determine if it is true, false or uncertain. You must justify your answer with a one-sentence explanation.

1. The beta of a hedge fund is usually close to one.

2. Suppose you hold a share of stock and a put option on that share. If the stock price is below the exercise price when the option expires the value of your position is the value of the stock.

3. There is a much greater outstanding volume of futures contracts as opposed to forward contracts because futures contracts are much more flexible in terms of settlement dates, amounts, etc.

4. The CAPM (Capital Asset Pricing Model) would be an accurate way to estimate the cost of equity for a company like Federal Express.

5. Assume that all investors are risk averse and select portfolios based on mean and variance. Then the highest return portfolio is always on the efficient frontier.

6. It is easier to earn "abnormal returns," i.e., returns greater than what investments of similar risk earn, by investing in financial rather than real assets.

7. If the price of a stock has gone up for ten consecutive trading days then on the eleventh day we would expect its price to decline.

Assume that we have the following monthly return data on 2 U.S. equity mutual funds. Assume the riskless return is 0.4% per month and the SPX return was 1.4% and its standard deviation was 3.0% per month over this period. You must show your computation to get any credit for your answer.

Fund A Fund B

Realized return 0.012 0.015

Standard deviation of return 0.06 0.08

Beta 1.5 2

8. Give an example of an options position that increases in value as the time to maturity decreases.

9. If interest rates rise, the convexity of a puttable bond will increase ______ an otherwise equivalent non-puttable bond.

a. more than

b. the same as

c. less than

d. actually the convexity will decrease

10. Assume you are short 2 futures contracts for 100 ounces of gold with initial margin of $2,000 each; maintenance margin is $1,500 per contract. Assume the price is initially $500 per ounce. If the price at the end of day 1 is $495 and $493 on day 2, how much money do you have in your margin account (assuming no withdrawals and assuming you make all margin calls) at the start of day 3?

11. Which of the asset A or B has the higher volatility? Both calls have one year to expiration and the riskless rate is 3%.

Option Exercise price Stock price Option price

Call on asset A 95 100 13.7

Call on asset B 60 50 6.10

12. Briefly explain why you think the Palm/3COM story is relevant to the study of financial markets.

13. The following diagram shows the beta calculation for a given firm using weekly data. What can you say about its performance over the time period represented by these data? Why?

The diagram below plots the value of a put option with an exercise price of $100 and one year to maturity.

14. Draw the value of a put option on the same security as in the previous question with an exercise price of $100 and 6 months to maturity.

For each of the following 3 questions determine whether or not an arbitrage opportunity exists. If one exists, describe how you could exploit this arbitrage. All options are written on the same underlying stock, which has a current price of $100 with annual standard deviation of return = .3. The riskless return is 4%.

15. Call with exercise price of 100 costs $20; Call with exercise price of 110 costs $13; Call with exercise price of 120 costs $5. All three options have a one-year maturity.

16. Call with a one-year maturity and an exercise price of 100 costs $20; put with a 2-year maturity and an exercise price of 100 costs $16.

17. The current one-year riskless rate in the U.S. is .05 and the current one-year riskless rate in Canada is .04. The spot rate shows that a Canadian dollar is 0.846 US$. The 6-month forward rate for converting Canadian to US dollars is 0.88.

18. Data have shown that the implied volatility of SPX puts is higher than the historical volatility of the SPX. How could you take advantage of this phenomenon?

19. Suppose you enter into a floating to fixed swap (i.e., you want to have certainty in your interest payments). The current swap rate for a 3-year maturity is LIBOR for 4.9% fixed. Assume that you are borrowing $10 million at LIBOR. Assume the swap payments are made annually. If at the end of year 1 LIBOR is 4.0%, how much do you pay to (or receive from) the swap counterparty?

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