1. Suppose you have the choice of investing in (A) a zero-coupon bond, which cos
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Question
1. Suppose you have the choice of investing in (A) a zero-coupon bond, which costs $500 today, pays no coupon during its life, compounds semi-annually, and then pays $1,000 after 10 years, or (B) a bond which costs $750 today, pays $25 in interest semiannually, and matures at the end of 10 years. What are the Semi-Annual yields to maturity of the two bonds?
(A) _____________________________ (B) _____________________________
Which is best? C)_______________________
2. Note - all Calls and Puts are lots of 100 shares and Price at expiration is $50.
a
Long Put
$75
Strike Price
$12
premium paid
Profit
b
Short Put
$38
Strike Price
$8
premium received
Profit
c
Long Call
$38
Strike Price
$12
premium paid
Profit
d
Short Call
$38
Strike Price
$10
premium paid
Profit
2. Note - all Calls and Puts are lots of 100 shares and Price at expiration is $50.
a
Long Put
$75
Strike Price
$12
premium paid
Profit
b
Short Put
$38
Strike Price
$8
premium received
Profit
c
Long Call
$38
Strike Price
$12
premium paid
Profit
d
Short Call
$38
Strike Price
$10
premium paid
Profit
Explanation / Answer
Solution:
1.) Yield to Maturity(YTM) = {Annual Coupon + [(Par Value - Market Price) / Number of Payment Periods]} / [(Par Value + Market Price) / 2]
Bond a -
Semi-Annual Yield to Maturity
= {0 + [(1,000-500) / (10*2)]} / [(1,000+500) / 2]
= {500 / 20} / [1,500 / 2]
= 25 / 750
= 0.0333
Semi - Annual YTM of Bond a = 3.33%
Bond b -
We assume the par value to be $1,000.
Semi-Annual Yield to Maturity
= {25 + [(1,000 - 750) / (10*2)] / [(1000 + 750) / 2]
= {25 + [250/20]} / [1750 / 2]
= 37.50 / 875
= 0.0429
Semi - Annual YTM of Bond b = 4.29%
c) The best is Bond b with a semi - annual YTM of 4.29%.
2.)
a) Long Put-
In a long put the investor has the right to sell.
Profit on exercise of long put option = [(Strike price - Price at expiration) * Number of shares] - Premium paid.
Profit on exercise of long put option
= [($75 - $50) * 100] - $12
= 2,488
Profit = $2,488.
b) Short Put-
Under short put the investor has the obligation to purchase if the other party decides to exercise the option.
In this case the strike price is lower than the price at expiration and thus, the other party will not exercise its right to sell. Hence, the only profit available to investor is the premium.
Profit = $8.
c) Long Call -
A long call option gives the investor the right to buy.
Profit on exercise of long call option = [(Price at expiration - Strike price) * Number of shares] - Premium paid
Profit on exercise of long call option
= [(50 - 38) * 100] - 12
= 1,188
Profit = $1,188.
d) Short Call -
Under short call the investor has the obligation to sell if the other party decides to exercise the option.
In this case, the strike price is lower than the market price and hence, the other party will exercise the option to purchase shares at a price lower than market price.
Thus the investor in short put faces the following losses on exercise of option:
Loss = [(Price at expiration - Strike price) * Number of shares] - Premium received.
Loss = [(50 - 38) * 100] - 10 = 1,190
Loss = $1,190.
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