Question

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.)

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 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.

Answer 1

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