Imagine you are a provider of portfolio insurance You are es

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

Solution

a-1) Current Value of Portfolio S0 $50.00 Million Floor promised to clients, 0% return X $50.00 Million Volatility ?^2 = .25^2 0.0625 Risk-free rate = r 0.04 T = Horizon of program 4 years d1 = (ln(S/K)+(r + ?2/2)^t)/ ? ?t d1 = (ln(48.50/50)+(.042 + .0625/2)x4)/ .25 ?4 0.586 Normal Distribution N( d1) using NormDIST 0.721062243 put delta is: N(d1) – 1 -27.89% Portfolio in bills 27.89% a-2) Portfolio in equity = 1 - 27.89% 72.11% b-1 Current Value of Portfolio S0 = $50M x 97% $48.50 Floor promised to clients, 0% return X $50.00 Volatility ?^2 = .25^2 0.0625 Risk-free rate = r 0.04 T = Horizon of program 4 d1 = (ln(S/K)+(r + ?2/2)^t)/ ? ?t d1 = (ln(50/50)+(.042 + .0625/2)x4)/ .25 ?4 0.525081585 Normal Distribution N( d1) using NormDIST 0.700236762 put delta is: N(d1) – 1 -29.98% Portfolio in bills 29.98% Amount held in bills = $48.50 x 29.98% $14.54 Millions