Question

Imagine you are a provider of portfolio insurance. You are establishing a four-yearprogram. The portfolio you manage is currently worth $100 million, and you promise toprovide a minimum return of 0%. The equity portfolio has a standard deviation of 25%per year, and T-bills pay 5% per year. Assume for simplicity that the portfolio pays nodividends (or that all dividends are reinvested).

a. What fraction of the portfolio should be placed in bills? What fraction in equity?

b. What should the manager do if the stock portfolio falls by 3% on the first day of trading?

Short answer

a. 25.78% portfolio in bills and 74.22% in equity

b. Sell $1.18 million equity should be sold to buy bills.

Step-by-step solution

Given information

S₀= 100 (current value)

X = 100 (0% return promise)

σ= .25 (volatility)

r = 0.05 (risk free rate)

T = 4 years (horizon of program)

Calculation of portfolio fraction

Put delta = N(d₁) – 1

= 0.7422 – 1

= -.2578

This implies 25.78% portfolio in bills and 74.22% in equity

Estimation of manager’s action in case of stock fall

At the new value, the put delta = -.2779

This implies that the amounts held in bills = $97 million x .2779 = $26.96 million

This implies that $1.18 million equity should be sold to buy bills.