Question

Suppose the current price of ACME Ltd. shares is $20 and in 3 months it will be either $18 or $22. Assume that the ACME stock does not pay any dividends, the continuously compounded risk-free interest rate is 12% per annum and markets are frictionless. Assume you have a portfolio of 10,000 ACME shares and you want to use portfolio insurance to protect the value of the portfolio from falling below $21 per share in 3 months.

a) What steps should be taken now to protect the portfolio? Show your calculations.

b) Show the cashflows on the insured portfolio now and in 3 months when the stock price is $18 or $22. Show your calculations.

Answer 1

a) To insure the shares in case it falls below $21 we need to buy put option with strike price of $21 expiring 3 months from now.

To value the put we will use binomial method,

if stock goes $18 in 3 months, payoff from put = Max(Strike - Spot,0) = Max(21-18,0) = $3

if stock goes $22 in 3 months, payoff from put = Max(Strike - Spot,0) = Max(21-22,0) = $0

Therefore the PV of put = (50%*3 + 50%*0) * e^(-rt)

= (50%*3 + 50%*0) * e^(-12%*3/12) = 1.455

Therefore we will buy 10000 put cost $1.455 each

b) Cash flow now = -1.455*10000 = $-14550

Cashflow in case of $18

Cashflow = payoff from put = Max(Strike - Spot,0)*10000 + Spot price*10000 = (Max(21- 18,0) + 18)*10000 = 210000

Cashflow in case of $23

Cashflow = payoff from put = Max(Strike - Spot,0)*10000 + Spot price*10000 = (Max(21- 23,0) + 23)*10000 = 230000

Therefore the value does not go below 210000 of $21/share