You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = $50?
A) ½ share of stock and $25 in bills
B) 1 share of stock and $50 in bills
C) ½ share of stock and $26.19 in bills
D) 1 share of stock and $25 in bills

Question

Quizplus · Accepted Answer

The hedge ratio is −0.5. A portfolio comprising one share and two puts would provide a guaranteed payoff of 55, with present value of 55/1.05 = 52.38. Therefore,
S + 2P = 52.38
50 + 2P = 52.38
P = 1.19
The protective put strategy = 1 share + 1 put = 50 + 1.19 = 51.19
The goal is a portfolio with the same exposure to the stock as the protective put portfolio. Since the hedge ratio is −0.5, you hold 1 − 0.5 = 0.5 shares of stock. The cost is $25 for the ½ share of stock. You place your remaining funds, $26.19, in bills earning 5%.
 11eaaae8_8b45_2314_a4b8_4de6ddeef953_TB6474_00 The stock plus bills strategy duplicates the cost and payoff of the protective put strategy.

You Would Like to Hold a Protective Put Position on the Stock