Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $50 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 4.2% per year. Assume for simplicity that the portfolio pays no dividends (or that all dividends are reinvested).

a-1.What percentage of the portfolio should be placed in bills?(Input the value as a positive value. Round your answer to 2 decimal places.)

Portfolio in bills%

a-2.What percentage of the portfolio should be placed in equity?(Input the value as a positive value.Round your answer to 2 decimal places.)

Portfolio in equity%

b-1.Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading, before the hedge is in place?(Input the value as a positive value. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Put delta%Amount held in bills$million

b-2.What action should the manager take?(Enter your answer in millions rounded to 2 decimal places.)

The manager mustbuy or sell about ?$m

Using the black-shoes formula

and whereC₀

=

Current call option value.

S₀

=

Current stock price.

N(d)

=

The probability that a random draw from a standard normal distribution will be less thand. In Excel, this function is called NORMSDIST( ) or NORM.S.DIST( ).

X

=

Exercise price.

e

=

The base of the natural log function, approximately 2.71828. In Excel,e^xcan be evaluated using the function EXP(x).

=

Annual dividend yield of underlying stock. (We assume for simplicity that the stock pays a continuous income flow, rather than discrete periodic payments, such as quarterly dividends.)

r

=

Risk-free interest rate, expressed as a decimal (the annualized continuously compounded rate⁷on a safe asset with the same maturity as the expiration date of the option, which is to be distinguished fromr_f, the discrete period interest rate).

T

=

Time remaining until expiration of option (in years).

ln

=

Natural logarithm function. In Excel, ln(x) can be calculated using the built-in function LN(x).

=

Standard deviation of the annualized continuously compounded rate of return of the stock, expressed as a decimal, not a percent.