FI 414 Ch 8 (1-20), 9 (21-40), 10 (41-50) Hw

A call option has an exercise price of $30 and a stock price of $34. If the call option is trading for $5.25, what is the intrinsic value of the option?

$4.00 Intrinsic value = S0 − X = $34.00 − $30.00 = $4.00

The common stock of the Avalon Corporation has been trading in a narrow range around $40 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $40 is $3, and a call with the same expiration date and exercise price sells for $4. Suppose you write a strap and the stock price winds up to be $42 at contract expiration. What was your net profit on the strap?

$700 Selling a strap entails selling two calls and selling one put. Initial income = 2C0 + P0 = [2 × $4.00 + $3.00] × 100 = $1,100. If the final stock price is $42, the position profit is found as: Profit = [−2 × Max ($0, $42 − 40) + Max ($0, $40 − $42)] × 100 + $1,100 = $700

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now. Using the Black-Scholes option pricing model, the call option should be worth __________ today.

$9.62

Which of the following statements is (are) correct?

If a market is strong-form efficient, it is also semistrong- and weak-form efficient.

If you anticipate a dramatic a decline in stock prices, which naked strategy will make you the most profit?

Long put

A covered call strategy benefits from what environment?

Price stability

Insiders are able to profitably trade and earn abnormal returns prior to the announcement of positive news. This is a violation of which form of efficiency?

Strong-form efficiency

Proponents of the EMH typically advocate __________.

a passive investment strategy

If the Black-Scholes formula is solved to find the standard deviation consistent with the current market call premium, that standard deviation would be called the __________.

implied volatility

Choosing stocks by searching for predictable patterns in stock prices is called _________.

technical analysis

The current stock price of Howard & Howard is $64, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of H&H's stock is 20%. You want to purchase a put option on this stock with an exercise price of $55 and an expiration date 73 days from now. Using Black-Scholes, the put option should be worth __________ today.

$0.07

A call option has an exercise price of $35 and a stock price of $36.50. If the call option is trading at $2.25, what is the time value embedded in the option?

$0.75 Time Value = Call Premium − Intrinsic Value = C − max(0, S0 − X) = $2.25 − ($36.50 - $35.00) = $0.75

Bill Jones inherited 5,000 shares of stock priced at $45 per share. He does not want to sell the stock this year due to tax reasons, but he is concerned that the stock will drop in value before year-end. Bill wants to use a collar to ensure that he minimizes his risk and doesn't incur too much cost in deferring the gain. January call options with a strike of $50 are quoted at a cost of $2, and January puts with a $40 exercise price are quoted at a cost of $3. If Bill establishes the collar and the stock price winds up at $35 in January, Bill's net position value including the option profit or loss and the stock is __________.

$195,000 Position value = 5,000 shares × $45 share = $225,000.To establish a collar, you would need 5,000/100 = 50 options. You would buy the 50 puts at a cost of $3 × 100 × 50 = $15,000 and write the 50 calls, earning a premium of: $2 × 100 × 50 = $10,000 The initial cost is $15,000 − $10,000 = $5,000. If the stock price in January is $35, then profit can be found as: Profit = [Max ($0, $40 − $35) − Max ($0, $35 − $50)] × 100 × 50 − $5,000 = $20,000 New stock value = 5,000 shares × $35 = $175,000 Net position value = $175,000 + $20,000 = $195,000

An investor is bearish on a particular stock and decided to buy a put with a strike price of $25. Ignoring commissions, if the option was purchased for a price of $0.85, what is the break-even point for the investor?

$24.15 Breakeven = $25.00 − $0.85 = $24.15 →At $24.25, profit = $0.00

You are cautiously bullish on the common stock of the Wildwood Corporation over the next several months. The current price of the stock is $50 per share. You want to establish a bullish money spread to help limit the cost of your option position. You find the following option quotes: Wildwood CorporationUnderlying Stock price: $ 50.00 Expiration Strike Call Put June$ 45.00$ 8.50$ 2.00 June$ 50.00$ 4.50$ 3.00 June$ 55.00$ 2.00$ 7.50 Suppose you establish a bullish money spread with the puts. In June the stock's price turns out to be $52. Ignoring commissions, the net profit on your position is __________.

$250 To establish a bull money spread with puts, you would buy the 45 put at a cost of $2 and write the 55 put, earning the $7.50 premium. The initial revenue is ($7.50 − $2)(100) = $550. ST = $52 at contract maturity in June Profit = P45,June − P55,June + Initial revenue Profit = [Max (0, $45 − $52) − Max (0, $55 − $52)] × 100 + $550 = $250.

Given a stock price of $18, an exercise price of $20, and an interest rate of 7%, what are the intrinsic values which will occur for a one-period binomial Call option model if the stock price goes up to $23 or down to $16?

$3 and $0 Intrinsic Value = max($0, S0 − X) Intrinsic ValueU = max($0, $23 − $20) = $3.00 Intrinsic ValueD = max($0, $16 − $20) = $0.00

A put on Sanders stock with a strike price of $35 is priced at $2 per share, while a call with a strike price of $35 is priced at $3.50. The maximum per-share loss to the writer of an uncovered put is __________, and the maximum per-share gain to the writer of an uncovered call is __________.

$33; $3.50 Maximum per-share loss to put writer = ($0 − $35) + $2 = −$33 if stock price is $0 at expiration. Maximum per share gain to call writer = 3.50 if stock price is below $35 at expiration.

An investor purchases a long call at a price of $2.50. The strike price at expiration is $35. If the current stock price is $35.10, what is the break-even point for the investor?

$37.50 Break even = $35.00 + $2.50 = $37.50 →At $37.50, profit = $0.00

The stock price of Bravo Corporation is currently $100. The stock price a year from now will be either $160 or $60 with equal probabilities. The interest rate at which investors invest in riskless assets is 6%. Using the binomial option pricing model, the value of a put option with an exercise price of $135 and an expiration date 1 year from now should be worth __________ today.

$38.21 Selling the stock and buying a 1-year discounted note with a $160 face value will give the same payoff as investing in (1/0.75) puts.

The stock price of Harper Corporation is $33 today. The risk-free rate of return is 6%, and Harper Corporation pays no dividends. A put option on Harper Corporation stock with an exercise price of $30 and an expiration date 73 days from now is worth $0.95 today. A call option on Harper Corporation stock with an exercise price of $30 and the same expiration date should be worth __________ today.

$4.31 C = S0 − Xe−rt + P

A stock is trading at $50. You believe there is a 60% chance the price of the stock will increase by 10% over the next 3 months. You believe there is a 30% chance the stock will drop by 5%, and you think there is only a 10% chance of a major drop in price of 20%. At-the-money 3-month puts are available at a cost of $650 per contract. What is the expected dollar profit for a writer of a naked put at the end of 3 months?

$475

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Company. What would have been the cost of a protective put portfolio?

$51.19 At t=0, stock price equals $50. At t=1, the price will either increase to $50 × (1+0.10) = $55, or decrease to $50 × (1−0.10) = $45, the payoffs for these scenarios are 0 and 5 respectively. A portfolio comprising one share and two puts would provide a guaranteed payoff of 55, with present value of $55/1.05 = 52.38. Therefore: S0 + 2P = $50 + 2P = $52.38 Solve for P: P = $1.19 The protective put strategy = 1 share + 1 put = $50.00 + $1.19 = $51.19

You buy one Huge-Packing August 50 call contract and one Huge-Packing August 50 put contract. The call premium is $1.25, and the put premium is $4.50. Your highest potential loss from this position is __________.

$575 Highest loss comes when S T = $50 (stays at $50) Loss = ($1.25 + $4.50) × 100 = $575

A call option on Juniper Corporation stock with an exercise price of $75 and an expiration date 1 year from now is worth $3 today. A put option on Juniper Corporation stock with an exercise price of $75 and an expiration date 1 year from now is worth $2.50 today. The risk-free rate of return is 8%, and Juniper Corporation pays no dividends. The stock should be worth __________ today.

$69.73 S0 = C + Xe−rt − P = $3.00 + $75.00 × e−0.08 × 1.0 − $2.50 = $69.73

Even if the markets are efficient, professional portfolio management is still important because it provides investors with: 1. Low-cost diversification 2. A portfolio with a specified risk level 3. Better risk-adjusted returns than an index

1 and 2 only

Among the important characteristics of market efficiency is (are) that: 1. There are no arbitrage opportunities. 2. Security prices react quickly to new information. 3. Active trading strategies will not consistently outperform passive strategies.

1, 2, and 3

Each listed stock option contract gives the holder the right to buy or sell __________ shares of stock.

100

In a binomial option model with three subintervals, the probability that the stock price moves up every possible time is __________.

12.50% With three subintervals there are23 = 8. possible paths to the four possible terminal stock prices. Three up moves would be one path out of the possible eight, so the probability of three up moves is 1/8 = 12.50%.

A longer time to maturity will unambiguously increase the value of a call option because: 1. The longer maturity time reduces the effect of a dividend on call price. 2. With a longer time to maturity the present value of the exercise price falls. 3. With a longer time to maturity the range of possible stock prices at expiration increases.

2 and 3 only

If you know that a call option will be profitably exercised, then the Black-Scholes model price will simplify to __________.

S0 − PV(X)

The weak-form of the EMH states that __________ must be reflected in the current stock price.

all past information, including security price and volume data

Assume that a company announces unexpectedly high earnings in a particular quarter. In an efficient market one might expect __________.

an abnormal price change immediately after the announcement

A __________ is an option valuation model based on the assumption that stock prices can move to only two values over any short time period.

binomial model

A European call option gives the buyer the right to __________.

buy the underlying asset at the exercise price only at the expiration date

If the gross profit is positive and the net profit is negative, you will __________.

exercise the option

According to the semistrong-form of the efficient market hypothesis, ____________.

future changes in stock prices cannot be predicted from any information that is publicly available

A call option on Brocklehurst Corporation has an exercise price of $30. The current stock price of Brocklehurst Corporation is $32. The call option is __________.

in the money

In the Black-Scholes model, as the stock's price increases, the values of N(d1) and N(d2) will __________ for a call and __________ for a put option.

increase; decrease

At contract maturity the value of a call option is __________, where X equals the option's strike price and ST is the stock price at contract expiration.

max (0, ST − X)

At contract maturity the value of a put option is __________, where X equals the option's strike price and ST is the stock price at contract expiration.

max (0, X − ST)

You write a put option on a stock. The profit at contract maturity of the option position is __________, where X equals the option's strike price, ST is the stock price at contract expiration, and P0 is the original premium of the put option.

min (P0, ST − X + P0)

A higher-dividend payout policy will have a __________ impact on the value of a put and a __________ impact on the value of a call.

positive; negative

If you have an extremely "bullish" outlook on the stock market, you could attempt to maximize your rate of return by __________.

purchasing out-of-the-money call options

The common stock of the Avalon Corporation has been trading in a narrow range around $40 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $40 is $3, and a call with the same expiration date and exercise price sells for $4. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement?

sell a straddle

If you combine a long stock position with selling an at-the-money call option, the resulting net payoff profile will resemble the payoff profile of a __________.

short put

What combination of variables is likely to lead to the lowest time value?

short time to expiration and low volatility

The potential loss for a writer of a naked call option on a stock is __________.

unlimited

Evidence supporting semistrong-form market efficiency suggests that investors should __________.

use a passive trading strategy such as purchasing an index fund or an ETF

A call option with several months until expiration has a strike price of $55 when the stock price is $50. The option has __________ intrinsic value and __________ time value.

zero; positive

You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Company. Suppose the desired put options with X = 50 were traded. What would be the hedge ratio for the option?

−0.5 At t=0, stock price equals $50. At t=1, the price will either increase to $50 × (1+0.10) = $55, or decrease to $50 × (1−0.10) = $45, the payoffs for these scenarios are 0 and 5 respectively.