Investments final part 2
20. 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 Intrinsic value = 34 - 30 = 4
Option Price Characteristics: Stock price (S)
- call price + - put price -
Difference between a call and put option
-Difference is the "time value" of the option. - With time the price curve moves closer to the intrinsic value (value if exercised today). • In general, do not want to exercise call early (put: maybe).
Ina binomial option model with free subintervals. The probability that the stock price moves up every possible time is
12.5%
A put option on a stock with a current price of $33 has an exercise price of $35. the price of corresponding call option is $2.25. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration. What should be the value of the put?
2.25-33+35/(1+.04)^(3/12) + 0= 3.91 (call price-current price)+(exercise price/(1+rfr)^ (m/12)
A call option on Jupiter Motors stock with an exercise price of $75 and one-year expiration is selling at $3. A put option on Jupiter stock with an exercise price of $75 and one-year expiration is selling at $2.50. If the risk free rate is 8% and Jupiter pays no dividends, what should the stock price be?
2.50=3.00-So+75/(1+.08)+0 So=69.94
At expiration, the time value of an at the money put option is always A. equal to zero. B. equal to the stock price minus the exercise price. C. negative. D. positive. E. None of these is correct.
A
At expiration, the time value of an in the money call option is always A. equal to zero. B. positive. C. negative. D. equal to the stock price minus the exercise price. E. None of these is correct
A
At expiration, the time value of an in the money put option is always A. equal to zero. B. negative. C. positive. D. equal to the stock price minus the exercise price. E. None of these is correct.
A
Before expiration, the time value of an at the money call option is always A. positive. B. equal to zero. C. negative. D. equal to the stock price minus the exercise price. E. None of these is correct.
A
Delta is defined as A. the change in the value of an option for a dollar change in the price of the underlying asset. B. the change in the value of the underlying asset for a dollar change in the call price. C. the percentage change in the value of an option for a one percent change in the value of the underlying asset. D. the change in the volatility of the underlying stock price. E. None of these is correct.
A
If the stock price increases, the price of a put option on that stock __________ and that of a call option __________. A. decreases, increases B. decreases, decreases C. increases, decreases D. increases, increases E. does not change, does not change
A
Other things equal, the price of a stock put option is negatively correlated with the following factors A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. the time to expiration, the stock volatility, and the exercise price
A
Other things equal, the price of a stock put option is positively correlated with the following factors except A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. None of these is correct
A
The dollar change in the value of a stock call option is always A. lower than the dollar change in the value of the stock. B. higher than the dollar change in the value of the stock. C. negatively correlated with the change in the value of the stock. D. higher than the dollar change in the value of the stock and negatively correlated with the change in the value of the stock. E. lower than the dollar change in the value of the stock and negatively correlated with the change in the value of the stock.
A
The elasticity of a stock call option is always A. greater than one. B. smaller than one. C. negative. D. infinite. E. None of these is correct.
A
The percentage change in the stock call option price divided by the percentage change in the stock price is called A. the elasticity of the option. B. the delta of the option. C. the theta of the option. D. the gamma of the option. E. None of these is correct.
A
Constant growth
A form of the dividend discount model that assumes dividends will grow at a constant rate.
At expiration, the time value of an at the money call option is always A. positive. B. equal to zero. C. negative. D. equal to the stock price minus the exercise price. E. None of these is correct
B
Before expiration, the time value of an in the money call option is always A. equal to zero. B. positive. C. negative. D. equal to the stock price minus the exercise price
B
The price of a stock put option is __________ correlated with the stock price and __________ correlated with the striking price. A. positively, positively B. negatively, positively C. negatively, negatively D. positively, negatively E. not, not
B
A hedge ratio for a call is always A. equal to one. B. greater than one. C. between zero and one. D. between minus one and zero. E. of no restricted value.
C
A hedge ratio for a call option is ________ and a hedge ratio for a put option is ______. A. negative, positive B. negative, negative C. positive, negative D. positive, positive E. zero, zero
C
A hedge ratio of 0.70 implies that a hedged portfolio should consist of A. long 0.70 calls for each short stock. B. short 0.70 calls for each long stock. C. long 0.70 shares for each short call. D. long 0.70 shares for each long call. E. None of these is correct
C
A hedge ratio of 0.85 implies that a hedged portfolio should consist of A. long 0.85 calls for each short stock. B. short 0.85 calls for each long stock. C. long 0.85 shares for each short call. D. long 0.85 shares for each long call. E. None of these is correct.
C
Before expiration, the time value of an in the money put option is always A. equal to zero. B. negative. C. positive. D. equal to the stock price minus the exercise price. E. None of these is correct.
C
If the stock price decreases, the price of a put option on that stock __________ and that of a call option __________. A. decreases, increases B. decreases, decreases C. increases, decreases D. increases, increases E. does not change, does not change
C
Prior to expiration A. the intrinsic value of a call option is greater than its actual value. B. the intrinsic value of a call option is always positive. C. the actual value of a call option is greater than the intrinsic value. D. the intrinsic value of a call option is always greater than its time value. E. None of these is correct
C
Prior to expiration A. the intrinsic value of a put option is greater than its actual value. B. the intrinsic value of a put option is always positive. C. the actual value of a put option is greater than the intrinsic value. D. the intrinsic value of a put option is always greater than its time value. E. None of these is correct
C
The elasticity of a stock put option is always A. positive. B. smaller than one. C. negative. D. infinite. E. None of these is correct.
C
The elasticity of an option is A. the volatility level for the stock that the option price implies. B. the continued updating of the hedge ratio as time passes. C. the percentage change in the stock call option price divided by the percentage change in the stock price. D. the sensitivity of the delta to the stock price. E. volatility level for the stock that the option price implies and the percentage change in the stock call option price divided by the percentage change in the stock price.
C
A hedge ratio for a put is always A. equal to one. B. greater than one. C. between zero and one. D. between minus one and zero. E. of no restricted value
D
All the inputs in the Black-Scholes Option Pricing Model are directly observable except A. the price of the underlying security. B. the risk free rate of interest. C. the time to expiration. D. the variance of returns of the underlying asset return. E. None of these is correct.
D
Before expiration, the time value of an at the money put option is always A. equal to zero. B. equal to the stock price minus the exercise price. C. negative. D. positive.
D
Other things equal, the price of a stock call option is negatively correlated with the following factors A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. the stock price, the time to expiration, and the stock volatility.
D
Other things equal, the price of a stock call option is positively correlated with the following factors except A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. None of these is correct.
D
The gamma of an option is A. the volatility level for the stock that the option price implies. B. the continued updating of the hedge ratio as time passes. C. the percentage change in the stock call option price divided by the percentage change in the stock price. D. the sensitivity of the delta to the stock price. E. the volatility level for the stock that the option price implies and the percentage change in the stock call option price divided by the percentage change in the stock price.
D
The price of a stock call option is __________ correlated with the stock price and __________ correlated with the striking price. A. positively, positively B. negatively, positively C. negatively, negatively D. positively, negatively E. not, not
D
A call option has an intrinsic value of zero if the option is A. at the money. B. out of the money. C. in the money. D. at the money and in the money. E. at the money and out of the money.
E
A put option has an intrinsic value of zero if the option is A. at the money. B. out of the money. C. in the money. D. at the money and in the money. E. at the money and out of the money
E
Other things equal, the price of a stock call option is positively correlated with the following factors A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. the stock price, the time to expiration, and the stock volatility
E
Other things equal, the price of a stock put option is positively correlated with the following factors A. the stock price. B. the time to expiration. C. the stock volatility. D. the exercise price. E. the time to expiration, the stock volatility, and the exercise price
E
Which of the inputs in the Black-Scholes Option Pricing Model are directly observable A. the price of the underlying security. B. the risk free rate of interest. C. the time to expiration. D. the variance of returns of the underlying asset return. E. the price of the underlying security, the risk free rate of interest, and the time to expiration
E
All else being equal, is a put option on a high beta stock worth more than one on a low-beta stock? The firms have identical firm-specific risk.
Higher beta a implies higher total stock volatility. The value of the put option increases as the beta increases.
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.
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.
All else being equal, is a put option on a high-beta stock worth more than one on a low-beta stock? The firms have identical firm-specific risk
Holding firm-specific risk constant, higher beta implies higher total stock volatility. Therefore, the value of the put option increases as beta increases.
If a stock is priced correctly, it will offer investors a ___ return
If a stock is priced correctly, it will offer investors a fair return. It's expected return = required return
The ______ is the stock price minus the exercise price, or the profit that could be attained by immediate exercise of an in-the-money call option.
Intrinsic value
A call option with a strike price of $50 on a stock selling at a $55 costs $6.50. What are the call options intrinsic and time values?
Intrinsic=(Selling Price- Strick Price) 55-50=5 Time Value=( C-Intrinsic Value) (6.50-5=1.50)
liquidation value
Net amount that could be realized by selling the assets of a firm after paying the debt.
present value growth opportunities PVGO
Net present value of a firm's future investments.
Time value of the option: waiting is valuable.
Option might be more in the money at time T.
dividend payout ratio
Percentage of earnings paid out as dividends (1-b)
Price with Growth opportunities
Price = No-growth value per share + PVGO Po=E1/k +PVGO
Put-Call Parity
Put=C-So+PV(X)+PV(Div)
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?
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.
Should the rate of return on the of a call option on a long term Treasury Bond be more of less sensitive to changes in interest rates than the rate of return of the underlying bond?
The call option is more sensitive to changes in interest rates. The option elasticity exceeds 1.0. The option is effectively a levered investment and is more sensitive to interest rate changes.
All else being equal, will a call option with a high exercise price have a higher or lower hedge that one with a low exercise price?
The call option with a high exercise price has a lower hedge ratio. Both d1 and N(d1) are lower when X is higher. Holding else equal, as the call option is less in the money, the hedge ratio is also lower.
If the stock price falls and the call price rises, then what has happened to the call option's implied volatility?
The call option's implied volatility has increased. If this were not the case, then the call price would have fallen.
Would you expect a $1 increase in a call options 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 rates were zero.
Would you expect a $1 increase in a call option's exercise price to lead to a decrease in the options value of more or less than $1?
The call will decrease by less that $1. The change in call price would only be $1 if there was a (i) 100% probability that the call would be exercise and (ii) the interest rates were zero.
replacement cost
The cost to replace a firm's assets. "Reproduction" cost. Another measure of firm value is the replacement cost of assets less liabilities.
market capitalization rate (k)
The market-consensus estimate of the appropriate discount rate for a firm's cash flows.
earnings management
The practice of using flexibility in accounting rules to improve the apparent profitability of the firm.
intrinsic value of a share
The present value of a firm's expected future net cash flows discounted by the required rate of return
plowback ratio (b)
The proportion of the firm's earnings that is reinvested in the business (and not paid out as dividends). b= 1- dividend payout ratio.
If the time to expiration falls and put price rises, then what has happened to the put options implied volatility?
The put option's implied volatility has increased. If this were not the case then the put price would have fallen.
If the time to expiration falls and the put price rises, then what has happened to the put option's implied volatility?
The put option's implied volatility has increased. If this were not the case, then the put price would have fallen.
tobin's q
The ratio of market value of the firm to replacement cost.
Implication of GGM: stock vs dividend growth
The stock price is expected to grow at the same rate as dividends.
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.
The stock with high firm-specific has higher total volatility. The option the stock with a lot of firm-specific risk is worth more.
The constant growth version of the DDM asserts that if dividends are expected to grow at a constant rate forever, the intrinsic value of the stock is determined by the formula
V0= D1/ (k-g)
Investor preferences when ROE > k
When ROE exceeds k, the firm offers attractive investment opportunities, so the value of the firm is enhanced as those opportunities are more fully exploited by increasing the plowback rate.
Investor preferences when ROE = k
When ROE just equals k, the firm offers "break-even" investment opportunities with a fair rate of return. In this case, investors are indifferent between reinvestment of earnings in the firm or elsewhere at the market capitalization rate, because the rate of return in either case is 12%. Therefore, the stock price is unaffected by the plowback rate.
Investor preferences when ROE < k
When the expected ROE is less than the required return, k, investors prefer that the firm pay out earnings as dividends rather than reinvest earnings in the firm at an inadequate rate of return. That is, for ROE lower than k, the value of the firm falls as plowback increases.
does the value of a put option increase with the volatility of the stock?
Yes, put values also increase as the volatility of the underlying stock increases
If a stock price increases, the price of a put option on the stock will __ and the price of a call option on the stock will __
decrease, increase
Investor A bought a call option that expires in 6 months. Investor B wrote a put option with a 9-month maturity. All else equal, as the time to expiration approaches, the value of investor A's position will __ and the value of investor B's position will ___
decrease; increase
If price does not equal intrinsic value, the rate of return will
differ from the equilibrium return based on the stock's risk.
The expected growth rate of earnings is related both to
expected profitability and dividend policy g= ROE on new investment *b
This version of the DDM is simplistic in its assumption of a constant value of ???
g
All else equal, call option values are ___ if the ___ is lower
higher; exercise price
Investor A bought a call option, and investor B bought a put option. All else equal, if the underlying stock price volatility increases, the value of investor A's position will ______ and the value of investor B's position will _______.
increase ; increase
Investor A bought a call option, and investor B bought a put option. All else equal, if the interest rate increases, the value of investor A's position will ______ and the value of investor B's position will _______.
increase, decrease
The actual return will depend on the rate at which the stock price is predicted to revert to its
intrinsic value.
When Growth Prospects decided to reduce current dividends and reinvest some of its earnings in new investments,
its stock price increased.
When the constant growth assumption is reasonably satisfied and the stock is selling for its intrinsic value, the formula can be inverted to infer the market capitalization rate for the stock???
k= (D1/P0) + g
earnings retention ratio
plowback ratio
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
Hedge ratios for long call positions are ____and hedge ratios for long put positions are ___
positive; negative
A put 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
positive;positive
Option Price Characteristics Increasing stock volatility
put price + - call price +
price earnings ratio (P/E)
the current market price divided by earnings per share (Po/EPS). A useful measure of the market's assessment of the firm's growth opportunities.
Dividend discount models give estimate???
the intrinsic value of a firm
The intrinsic value of a call option is equal to
the stock price minus the exercise price
The _____ is the difference between the actual price and the intrinsic value
time value
book value
An accounting measure describing the net worth of common equity according to a firm's balance sheet.
Which of the following will increase the value of a put option
an increase in the volatility of the underlying stock
Option Price Characteristics: strike price (K)
call price - - put price +