Inv ch 15,16,17

how much would a buyer have to pay for one call option contract if the call is 14.15?

$1415 14.15 * 100shares

An investor buys a call at a price of $5.00 with an exercise price of $50. At what stock price will the investor break even on the purchase of the call?

55

Time Value

Option Cost-Intrinsic Value

All else being equal, is a call option on a stock with a lot of firm-specific risk worth more than one on a stock with little firm-specific risk? The betas of the stocks are equal.

Yes... Holding beta constant, the stock with high firm-specific risk has higher total volatility. Therefore, the option on the stock with a lot of firm-specific risk is worth more.

The one-year futures price on a particular stock-index portfolio is 1,306, the stock index currently is 1,300, the one-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,300 investment in the index portfolio is $7. Required: By how much is the contract mispriced?

Explanation: From parity: F0 = [1,300 × (1 + 0.03)] - 7 = 1,332 Actual F0 is 1,306, so the futures price is $26 below its "proper" or parity value.

The current level of the S&P 500 is 760. The dividend yield on the S&P 500 is 5%. The risk-free interest rate is 4%. Required: What should a futures contract with a one-year maturity be selling for? (Round your answer to 1 decimal place.)

Explanation: Futures price = 760 × (1 + 0.04 − 0.05) = 752.4

You purchase a Treasury-bond futures contract with an initial margin requirement of 17% and a futures price of $115,000. The contract is traded on a $15,500 underlying par value bond. Required: If the futures price falls to $110,000, what will be the percentage loss on your position?

Explanation: Margin = 115,000 × 0.17 = 19,550.00. Total $ loss = 115,000 - 110,000 = 5,000. Total % loss = 5,000 / 19,550.00 = 25.58% loss

Suppose the value of the S&P 500 stock index is currently $1,395. If the one-year T-bill rate is 6% and the expected dividend yield on the S&P 500 is 2%, what should the one-year maturity futures price be? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

F0 = S0(1 + rf - d) = 1,395 × (1 + 0.06 - .02) = 1,450.80

If you know value of call and put, value of stock is

Put=call-S+K/e^rf(timeleft) (SOLVE FOR S)

If you know value of call, value of put is...

Put=callprice-price of stock+strikeprice/e^rf(time left)

On January 1, you sold one March maturity S&P 500 Index futures contract at a futures price of 790. The contract multiplier is $250. Required: If the futures price is 840 on February 1, what is your profit(loss)?

Selling a contract is a short position. If the price rises, you lose money. Loss = (840 - 790) × 250 = $12,500

Imagine that you are holding 5,400 shares of stock, currently selling at $44 per share. You are ready to sell the shares, but would prefer to put off the sale until next year due to tax reasons. If you continue to hold the shares until January, however, you face the risk that the stock will drop in value before year-end. You decide to use a collar to limit downside risk without laying out a good deal of additional funds. January call options with a strike price of $49 are selling at $2, and January puts with a strike price of $39 are selling at $3. (a) What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $34? (b) What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $44? (c) What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $54?

The collar involves purchasing a put for $3 @ strike = $39 and selling a call for $2 @ strike = $49. The value of the portfolio is as follows. Stock price = $34 Long Put = 2 Short Call = 2 Total = 38 x 5,400 = $205,200 Stock price = $44 Long Put = -3 Short Call = 2 Total = 43 x 5,400 = $232,200 Stock price = $54 Long Put = -3 Short Call = -3 Total = 48 x 5,400 = $259,200

The call option is ___ sensitive to changes in interest rates.

The call option is more sensitive to changes in interest rates. The option elasticity exceeds 1.0. In other words, the option is effectively a levered investment and is more sensitive to interest rate changes.

Would you expect a $1 increase in a call option's exercise price to lead to a decrease in the option's value of more or less than $1?

The call price will decrease by less than $1. The change in the call price would be $1 only if: (i) there were a 100% probability that the call would be exercised; and (ii) the interest rate were zero.

Calls have hedge ratios less than

1.0. For equal numbers of shares controlled, the dollar exposure of the calls is less than that of the stocks, and the profit potential is less.

Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes in interest rates than the rate of return of the underlying bond?

More Sensitive

Intrinsic Value

Price of stock-strike price S-K

You are very bullish (optimistic) on stock EFG, much more so than the rest of the market. Select the portfolio strategy that will give you the biggest dollar profit if your bullish forecast turns out to be correct. $100,000 invested in calls where K=50 vs $100,000 invested in stock and 10 call contracts (100 shares each) where K= 50 vs 1,000 shares of stock

$100,000 invested in calls where K=50 AND for 2nd one... 1,000 shares of stock

You establish a straddle on Intel using September call and put options with a strike price of $47. The call premium is $6.80 and the put premium is $9.80. What is the most per share you can lose on this position? What is your profit or loss per share if Intel is selling for $60 in September? At what stock prices will you break even on the straddle?

(a) Maximum loss = 6.80 + 9.80 = 16.60 per share (b) Profit / loss = 60 - 47 - 16.60 = -3.60 (c) There are two break even prices: 63.60 and 30.40

The multiplier for a futures contract on the stock market index is $260. The maturity of the contract is one year, the current level of the index is 870, and the risk-free interest rate is 0.6% per month. The dividend yield on the index is 0.3% per month. Suppose that after one month, the stock index is at 908. Required: (a) Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly. (b) Find the one-month holding-period return if the initial margin on the contract is $10,000

(a) The initial futures price is: F0 = 870 × (1 + 0.006 - 0.003)12 = 901.84 In one month, the futures price will be: F0 = 908 × (1 + 0.006 - 0.003)11 = 938.42 The increase in the futures price is 36.58, so the cash flow will be: 36.58 × 260 = $9,510.80 (b) The holding period return is: $9,510.80/$10,000 = .9511 = 95.11%

You buy a share of stock, write a one-year call option with X = $19, and buy a one-year put option with X = $19. Your net outlay to establish the entire portfolio is $18. The stock pays no dividends. Required: What must be the risk-free interest rate?

5.56

Calls have higher elasticity than for ...

Calls have higher elasticity than shares. For equal dollar investments, the capital gain potential for calls is higher than for stocks.