Question

Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $140 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 6.4% 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)buysell $  million of (Click to select)billsequity and use the proceeds to (Click to select)buysell (Click to select)equitybills.

Answer 1

Solution:

Explanation:

S0= 140 (current value of portfolio)

X= 140 (floor promised to clients, 0% return)

?= .25 (volatility)

r= .064 (risk-free rate)

T= 4 years (horizon of program)

a. d1 = [ln (S0/X) + (r + ?^2/2)T]/?sqrt(T)

d1 = [ln (140/140) + (0.064 + 0.25^2/2)(4)]/0.25*sqrt(4)

d1 = 0.762

The put delta is: N(d1) – 1 = 0.7770 – 1 = –.2230

Place 22.30% of the portfolio in bills, 77.70% in equity ($77.70 million)

b. At the new portfolio value, the put delta becomes –.2416 or 24.16%, so that the amount held in bills shouldbe: ($97 million ×.2416) = $23.44 million. The manager must sell $1.14 million of equity and use the proceeds to buy bills.