Alex has a portfolio consisting of the below: A borrowing of €100 at the risk-free rate, a long position in a six-month put option on stock AA with an exercise price of €200 (1.e., EX = €200), and . a short position in a six-month put option on stock AA with an exercise price of €100 (i.e., EX = €100). Provide two other combinations of loans, options, and the underlying stock that would give Alex the same payoffs.

EBK CONTEMPORARY FINANCIAL MANAGEMENT
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Chapter8: Analysis Of Risk And Return
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3.
Alex has a portfolio consisting of the below:
A borrowing of €100 at the risk-free rate,
a long position in a six-month put option on stock AA with an exercise price
of €200 (1.e., EX = €200), and
a short position in a six-month put option on stock AA with an exercise price
of €100 (i.e., EX = €100).
a.
Provide two other combinations of loans, options, and the underlying stock that
would give Alex the same payoffs.
b. Today is 16 December 2021. A pension fund has a $50 million obligation due
exactly 7 years from now and pays 3% interest (compounded annually) on this
obligation. Assume that the term structure is flat.
How many AAPL and MSFT bonds should the pension fund buy to form a portfolio
that will ensure that the pension fund will meet its obligation in 7 years' time?
AAPL bond has a modified duration of 19.85 and MSFT bond has a modified
duration of 3.65.
Use the information provided in the table below. Note that the quoted price is the
clean price.
MSFT
AAPL
Price ($)
Yield (%)
Par value ($)
Modified duration (%)
Last coupon date
Coupon frequency
Day count principle
Maturity
967.606
3
1,000
19.85
08 Aug 2021
annually
30/360
08 Aug 2050
1065.597
3
1,000
3.65
03 May 2021
annually
30/360
03 May 2025
Transcribed Image Text:3. Alex has a portfolio consisting of the below: A borrowing of €100 at the risk-free rate, a long position in a six-month put option on stock AA with an exercise price of €200 (1.e., EX = €200), and a short position in a six-month put option on stock AA with an exercise price of €100 (i.e., EX = €100). a. Provide two other combinations of loans, options, and the underlying stock that would give Alex the same payoffs. b. Today is 16 December 2021. A pension fund has a $50 million obligation due exactly 7 years from now and pays 3% interest (compounded annually) on this obligation. Assume that the term structure is flat. How many AAPL and MSFT bonds should the pension fund buy to form a portfolio that will ensure that the pension fund will meet its obligation in 7 years' time? AAPL bond has a modified duration of 19.85 and MSFT bond has a modified duration of 3.65. Use the information provided in the table below. Note that the quoted price is the clean price. MSFT AAPL Price ($) Yield (%) Par value ($) Modified duration (%) Last coupon date Coupon frequency Day count principle Maturity 967.606 3 1,000 19.85 08 Aug 2021 annually 30/360 08 Aug 2050 1065.597 3 1,000 3.65 03 May 2021 annually 30/360 03 May 2025
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