Determine the security in each case that would most likely have the higher price

Question

Determine the security in each case that would most likely have the higher price. In each case, clearly and fully explain your answers.

a. Two U.S. Treasury bonds with the same remaining maturity. One has a 3% coupon and the other a 4% coupon, and their required return is 3%.

b. Two call options on the same stock. The options have the same maturity, but one has an exercise price of $35 and the other has an exercise price of $40.

c. Two put options on two different stocks. The stocks currently sell for $50 and $51. The puts have the same maturity and exercise prices.

d. In answering part c, do you need to make any assumptions about the two underlying stocks?

Explanation / Answer

a. The one with the higher coupon rate i.e. 4% will be of higher price since everything else being equal, the bond with the higher coupon payment will have higher coupon cash flow.

b. The security with exercise price of 35$ will be worth higher since it has a lower exercise price. The one with 40$ as exercise price can be considered to be out of the money option with less premium upfront

c. The put on the stock price with price 50$ will have higher worth since it is can be closer than the exercise price. It is expected to receive premium when the share price fall below 50 while for the latter once the price needs to fall below 51.

d. Yes, the underlying assumption is that the volatility of both the stocks is same and does not impact the price of put. If the volatility component of 51$ stock is higher than it may be worth more that the 50$ put premium.

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