15. (8 points) BMC Olympiad Inc. is looking for a potential acquirer within the next 12
months. You have been asked to assess the company’s near-term credit risk exposure
before proceeding with an appraisal analysis of BMC Olympiad’s operating businesses.
You are given the following information:
•Company’s credit rating: BBB
•Risk-free rate: 5% per annum compounded continuously
•Market value of company’s assets today: $21 billion
•Market value of company’s equity today: $5 billion
•Company’s debt due to be repaid including interest one year from now:
$17 billion
•Volatility of equity returns: 80%
•Volatility of asset returns: 20%
•A company with similar credit risk has five-year corporate zero-coupon
bonds trading at 350 basis points above risk-free rate
•Assumed recovery rate in the event of a default: 40% (as percent of bond’s
no-default value)
(a) Estimate the risk-neutral probability that the company will default on its debt
using Merton’s model.
(b) Determine the expected loss on the debt and the expected recovery in the event of
a default.
(c) Compare the default probability produced by Merton’s model versus the
annualized risk- neutral default probability inherent in the company’s current
corporate bond pricing. Explain possible reasons for discrepancy between these
two estimates of default probabilities.
COURSE 8: Fall 2004 -16- GO ON TO NEXT PAGE
Investment
Afternoon Session
16. (8 points) BH Life is a small insurance company that has sold a product with a minimum
return guarantee. The investment guarantee is equivalent to a European put option on
the S&P 500 index with a notional amount equal to 5,000 times the index.
You are given the following information:
•Risk free rate is 2.5%
•Current index value is 1200
•Strike price is 1100
•Time to maturity is 1 year
•Black Scholes value of the put option with implied volatility of 22% is
$242,900
•No dividends
•Trading costs equal 0.10%
•Proceeds are invested at the risk-free rate
•Risk- free rate and volatility do not change during the year
The firm wishes to delta hedge the risk on the put with quarterly rebalancing by using
shares of a fund tha t track the S&P 500.
(a) (2 points) Calculate the expected profit at the time the product is sold assuming that
expected volatility is 22% and the put option was priced using a volatility of 25% per
year.
(b) (1 point) Calculate the initial hedge position the firm should hold for delta neutrality if
the volatility assumed in their hedge is 22%.
(c) (3 points) Calculate the firm’s net gain or loss on the transaction, assuming that over the
course of the year the S&P 500 takes the following path given below, and that the
volatility assumed in their hedge is 22%. N(d1) factors are provided for European
options with the same maturity date and strike price and a volatility of 22%.
Time Index Level 1 N d
Point of sale 1200
End of Quarter 1 1250 0.8051
End of Quarter 2 1150 0.6700
End of Quarter 3 1050 0.3783
End of Quarter 4 1000
(d) (2 points) Describe other risk management strategies the firm can use.
COURSE 8: Fall 2004 -17- GO ON TO NEXT PAGE
Investment
Afternoon Session
17. (4 points) You are considering investing in government issued fixed income securities in the
three countries listed below.
You are given the following information:
Country A B C
Continent Europe Asia Asia
Population 3M 400M 50M
Oil Exports 1B 150B 5B
Agriculture Exports 1B 150B 15B
Agriculture Domestic 3B 450B 40B
Manufacturing Exports 8B 150B 300B
Manufacturing Domestic 13B 600B 240B
Total GDP 26B 1500B 600B
Government type Stable Democracy Stable Democracy Emerging Democracy
Inflation Range 2%-20% 0%-30% 8%-16%
Infant deaths per 1000 1 3 5
Life expectancy 75 70 65
(a) Describe the risks of the potential investments and propose how to mitigate them.
(b) Rank the countries by their political stability and justify your ranking.
COURSE 8: Fall 2004 -18- GO ON TO NEXT PAGE
Investment
Afternoon Session

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