Question

The common stock of Company XLT and its derivative securities currently trade in the market at the following prices and contract terms:

- Stock XLT ; Price ($) 26.00, Exercise Price ($) -
- Call option on Stock XLT ; Price ($) 5.80, Exercise Price ($) 25.00
- Put option on Stock XLT ; Price ($) 4.30, Exercise Price ($) 25.00

Both of these options will expire 91 days from now, and the annualized yield for the 91-day Treasury bill is 5.0%. (Assume face value is $100.)

How to construct a synthetic Treasury bill position?

Answer 1

To construct a synthetic Treasury bill position, you can use a combination of the stock and its derivative securities. This involves buying a put option on the stock, short selling the stock, and investing the proceeds in risk-free Treasury bills.

Step-by-step explanation:

To construct a synthetic Treasury bill position, you can use a combination of the stock and its derivative securities. In this case, the derivative security is a put option on Stock XLT with a price of $4.30 and an exercise price of $25.00.

Since a put option gives you the right to sell the underlying stock at the exercise price, you can use it to create a synthetic Treasury bill position.

Here's how you can construct the synthetic Treasury bill position:

1. Buy the put option on Stock XLT for $4.30 per share.
2. Short sell the same number of shares of Stock XLT at the current market price.
3. Invest the proceeds from the short sale in risk-free Treasury bills.

This combination of buying the put option and short selling the stock replicates the payoff of owning a Treasury bill. When the stock price is below the exercise price at the expiration of the put option, you exercise the put option and sell the stock at the exercise price. If the stock price is above the exercise price, you let the put option expire and keep the proceeds from the short sale, which can be invested in Treasury bills.