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 $220 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% 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.)

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

The manager must (Click to select) buy or sell $_____ million of (Click to select)bills or equity and use the proceeds to (Click to select) sell or buy (Click to select)bills or equity.

Put delta		%
Amount held in bills	$	million

Solution

a-1) Current Value of Portfolio S0 $220.00 Million Floor promised to clients, 0% return X $220.00 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(220/220)+(.04 + .0625/2)x4)/ .25 ?4 0.57 Normal Distribution N( d1) using NormDIST 0.715661151 put delta is: N(d1) – 1 -28.43% Portfolio in bills             28.43% a-2) Portfolio in equity = 1 - 28.43% 71.57% b-1 Current Value of Portfolio S0 = $220M x 97% $213.40 Floor promised to clients, 0% return X $220.00 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(213.40/220)+(.04 + .0625/2)x4)/ .25 ?4 0.509081585 Normal Distribution N( d1) using NormDIST 0.69465248 put delta is: N(d1) – 1 -30.53% Portfolio in bills             30.53% Amount held in bills = $213.40 x 30.53% $65.16 Millions b-2 The manager must sell $2.61 million of equity and use the proceeds to buy bills . Total value of Portfolio $220.00 Million Less: Equity Investment = $220 x 71.57% -$157.45 Million Less: T-bill investment = -$65.16 Million Sell the equity and use the proceeds to buy bills. -$2.61 Million