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The call sells at an implied volatility (11.00%) that is less than recent
historical volatility (12.00%); the put sells at an implied volatility (14.00%)
that is greater than historical volatility.
The call seems relatively cheap; the
put seems expensive.
40.
True.
The call option has an elasticity greater than 1.0.
Therefore, the call’s
percentage rate of return is greater than that of the underlying stock.
Hence the GM
call responds more than proportionately when the GM stock price changes in
response to broad market movements.
Therefore, the beta of the GM call is greater
than the beta of GM stock.
41.
True.
The elasticity of a call option is higher the more out of the money is the
option.
(Even though the delta of the call is lower, the value of the call is also
lower.
The
proportional
response of the call price to the stock price increases.
You
can confirm this with numerical examples.)
Therefore, the rate of return of the call
with the higher exercise price responds more sensitively to changes in the market
index, and therefore it has the higher beta.
42.
As the stock price increases, conversion becomes increasingly more assured.
The
hedge ratio approaches 1.0.
The price of the convertible bond will move onefor
one with changes in the price of the underlying stock.
43.
Salomon believes that the market assessment of volatility is too high.
Therefore,
Salomon should sell options because the analysis suggests the options are
overpriced with respect to true volatility.
The delta of the call is 0.6, while that of
the put is 0.6 – 1 = –0.4.
Therefore, Salomon should sell puts and calls in the ratio
of 0.6 to 0.4.
For example, if Salomon sells 2 calls and 3 puts, the position will be
delta neutral:
Delta = (2
×
0.6) + [3
×
(–0.4)] = 0
44.
Using the true volatility (32%) and time to maturity T = 0.25 years, the hedge ratio
for Exxon is N(d
1
) = 0.5567.
Because you believe the calls are underpriced
(selling at an implied volatility that is too low), you will buy calls and short 0.5567
shares for each call you buy.
45.
The calls are cheap (implied
σ
= 0.30) and the puts are expensive (implied
σ
= 0.34).
Therefore, buy calls and sell puts.
Using the “true” volatility of
σ
= 0.32, the call delta is 0.5567 and the put delta is: 0.5567 – 1.0 = –0.4433
Therefore, for each call purchased, buy: 0.5567/0.4433 = 1.256 puts
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46.
a.
To calculate the hedge ratio, suppose that the market index increases by 1%.
Then the stock portfolio would be expected to increase by:
1%
×
1.5 = 1.5% or 0.015
×
$1,250,000 = $18,750
Given the option delta of 0.8, the option portfolio would increase by:
$18,750
×
0.8 = $15,000
Salomon’s liability from writing these options would increase by the same
amount.
The market index portfolio would increase in value by 1%.
Therefore, Salomon Brothers should purchase $1,500,000 of the market
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 Spring '13
 Ohk
 hedge ratio, Riskless Portfolio

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