5. (5 points) You are a research analyst supporting the corporate bond desk at LifeCo and
have been asked to consider investing in synthetic convertible notes (SCN) as a new asset
class for the Equity Linked GIC portfolio.
You are given the following information for an SCN:
Face amount: $100 million
Maturity: 7 years
Coupon: 4% paid annually
Strike: 1.3 ´purchase price
Purchase price: par
Index: S&P 500
At-the-market swap rate on LIBOR: 7.5%
(a) List and briefly describe the 3 factors that impact price volatility and performance
sensitivity of structured notes.
(b) Calculate the up- front payment the swap dealer receives on the hedge.
(c) Calculate the annual internal rate of return (IRR) over the term of the SCN for the
following 2 scenarios of annual returns of the S&P 500 index:
Scenario Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
1 -5% -7% 12% 0% 16% 8% -1%
2 8% 15% 3% 9% -6% 20% -10%
(d) Analyze the suitability of this SCN for the asset portfolio backing LifeCo’s Equity
Linked GICs.
COURSE 8: Fall 2002 - 6 - GO ON TO NEXT PAGE
Investment
Morning Session
6. (7 points) A risk- free investment, R, and investments S and T have the following Ito
processes:
dR 0.05Rdt 0.10Rdz1
dS 0.10Sdt 0.20Sdz2
dT 0.03Tdt 0.20Tdz3
The correlation matrix for R, S and T is known.
The payoff of a European derivative, F, is determined from the values of R, S and T on
F’s exercise date.
(a) Formulate an expression for the process followed by F using constants where
possible.
(b) Describe the steps required to value F using a Monte Carlo simulation.
COURSE 8: Fall 2002 - 7 - GO ON TO NEXT PAGE
Investment
Morning Session
7. (11 points) A regulatory proposal would require companies to disclose the value of
options granted to their employees. Your CFO is concerned that under this proposed
regulation, changes in your firm’s stock price will create earnings volatility, and has
identified two options programs which would impact earnings under this proposal.
Price at purchase Purchasing rights
Stock Option
Plan (SOP)
market price that
prevailed when the
option was granted
employees are given the right to purchase
shares of the firm’s stock at the end of two
years
Employee Stock
Purchase Plan
(ESPP)
80% of the market
price at the beginning
of the year
stock is delivered to employees at the end of
the year if the stock price is above the
discounted level at that time, however, if the
price is below this level, the employee’s
money is returned and no stock is delivered
•The options granted under the SOP from year-end 1999 have expired.
•At year-end 2000, options on 10,000 shares were granted under the SOP when the
stock price was $24.
•At year-end 2001, options on 15,000 shares were granted under the SOP when the
stock price was $30.
•Under the ESPP, employees have subscribed to purchase $360,000 worth of stock in
2002.
It is January 1, 2002. The firm pays a continuous annual dividend of 3.0%, the stock’s
annual volatility is 40%, and the risk free rate is 5.0%. There are no exchange-traded
options available on this stock.
(a) List the options embedded in these two programs.
(b) Propose alternatives to hedge against changes in the stock price.
(c) Determine the probability that the options granted under the ESPP will finish inthe-
money.
(d) Calculate the delta of the portfolio of options under the SOP and ESPP programs
and interpret the sign of the delta.
(e) Determine the total value of the options granted under these two programs.
(f) Select a second order measure that can be used to hedge variations in value and
describe how it would be applied.
COURSE 8: Fall 2002 - 8 - STOP
Investment
Morning Session

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