8.
a.
By writing covered call options, Jones receives premium income of $30,000.
If, in January, the price of the stock is less than or equal to $45, then Jones
will have his stock plus the premium income. But the
most
he can have at that
time is ($450,000 + $30,000) because the stock will be called away from him
if the stock price exceeds $45.
(We are ignoring here any interest earned over
this short period of time on the premium income received from writing the
option.)
The payoff structure is:
Stock price
Portfolio value
less than $45
10,000 times stock price + $30,000
greater than $45
$450,000 + $30,000 = $480,000
This strategy offers some extra premium income but leaves Jones subject to
substantial downside risk.
At an extreme, if the stock price fell to zero, Jones
would be left with only $30,000.
This strategy also puts a cap on the final
value at $480,000, but this is more than sufficient to purchase the house.
b.
By buying put options with a $35 strike price, Jones will be paying $30,000 in
premiums in order to insure a minimum level for the final value of his
position.
That minimum value is: ($35
×
10,000) – $30,000 = $320,000
This strategy allows for upside gain, but exposes Jones to the possibility of a
moderate loss equal to the cost of the puts.
The payoff structure is:
Stock price
Portfolio value
less than $35
$350,000 – $30,000 = $320,000
greater than $35
10,000 times stock price – $30,000
c.
The net cost of the collar is zero.
The value of the portfolio will be as
follows:
Stock price
Portfolio value
less than $35
$350,000
between $35 and $45
10,000 times stock price
greater than $45
$450,000
If the stock price is less than or equal to $35, then the collar preserves the
$350,000 principal.
If the price exceeds $45, then Jones gains up to a cap
of $450,000.
In between $35 and $45, his proceeds equal 10,000 times the
stock price.
The best strategy in this case would be (c) since it satisfies the two
requirements of preserving the $350,000 in principal while offering a chance
of getting $450,000.
Strategy (a) should be ruled out since it leaves Jones
exposed to the risk of substantial loss of principal.
Our ranking would be: (1) strategy c; (2) strategy b; (3) strategy a.
20-5