Question

Imagine you are a provider of portfolio insurance. You are establishing a 4-year program. The portfolio you manage is currently worth $104 million, and you hope to provide a minimum return of 0%. The equity portfolio has a standard deviation of 22% 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. How much should be placed in bills? (Do not round intermediate calculations. Round your answer to 2 decimal places. Enter your answer in millions. Omit the "$" sign in your response.)

a-2. How much in equity? (Do not round intermediate calculations. Round your answer to 2 decimal places. Enter your answer in millions. Omit the "$" sign in your response.)

b-1. What is the delta of the new portfolio if the stock portfolio falls by 7% on the first day of trading? (Do not round intermediate calculations. Round your answer to 4 decimal places. Negative amount should be indicated by a minus sign.)

b-2. Complete the following (Do not round intermediate calculations. Round your answer to 2 decimal places. Enter your answer in millions. Omit the "$" sign in your response.):

Assuming the portfolio does fall by 7%, the manager should ________(buy/sell) $_______ million in stock.

Answer 1

a-1). Fund size = 104 million

Fee amount = put option premium

Black-Scholes model for calculating put option premium:

Total funds to be managed = 104 + 10.16 = 114.16 million

Put delta = N(d1) -1 = 0.7203 -1 = -0.2797

Sell off 27.97% of the stock portfolio, so remaining stock portfolio = 104*(1-27.97%) = 74.91 million

Amount of T-bills - total funds - stock portfolio = 114.16-74.91 = 39.25 million

a-2). Amount to be placed in equity = 74.91 million

b-1). If portfolio value drops by 7% then new portfolio value = 104*(1-7%) = 96.72 million

Again, Black Scholes model has to be used for calculating put delta:

N(d1) = 0.6623, so put delta becomes N(d1) -1 = 0.6623 -1 = -0.3377 (new delta)

b-2). Delta reduction required = -0.3377 -(-0.2797) = 0.0580 or 5.80%

So, sell 5.80% of new equity position = 5.80%*96.72 = 5.61 million

The manager should sell $5.61 million in stock.