Suppose a portfolio has assets that are worth $80 million, and the Nasdaq 100 index is
currently 6400. Assume that the beta of the portfolio with respect to the index is 0.8, and
there is no alpha. The expense ratio of the portfolio is 0.50% per year. The dividend yield of

the index is 1% per year. The risk-free interest rate is 2% per year. (The expense ratio, dividend
yield, and interest rate are simple rate in annual compounding.)
(a) How many contracts of put options should be purchased to protect the value of the port-
folio from falling below a floor value in one year? (Note that the contract size of Nasdaq
index options is 100.)
(b) The minimum increment of the strike price of Nasdaq 100 index options is 5 dollars. To
be simple, although unrealistic, let us ignore the cost of the put options. If you want to
set the floor value of the protected portfolio to be $77 million, what should be the strike
price in the put options? Demonstrate your results of the protection for various Nasdaq
index levels by creating the following spreadsheet.
Insurance Results
A B C D E F G
1 Nasdaq Nasdaq Residual Asset Asset Payoff of Protected
2 index return return return value options value
3 ST Rm(%) ε(%) Ra (%) Va ($m) Vp ($m) Vh($m)
4 7500 0.00
5 7000 0.00
6 6500 0.00
7 6000 0.00
8 5500 0.00
9 5000 0.00
10 4500 0.00
(c) Now, let us incorporate the cost of the put options. Suppose $295 is the premium of one
unit of Nasdaq index put option with the maturity and strike price you have chosen in the
previous question. Redo your spreadsheet by taking the cost of purchasing put options
into account. After this, what is the floor value of the protected portfolio?

Answer rating: 100% (QA)

a The number of contracts of put options to be purchased is found using the following equation Numbe... View the full answer