Are the following statements true or false? Provide a short justification for your answer. (You are...

Are the following statements true or false? Provide a short justification for your answer. (You are evaluated on your justification.) Remember that a statement is false if any part of the statement is false.

e) A 10-year coupon bond always has lower duration than a 10-year zero-coupon bond, regardless of the size of the coupons.

f) The stocks of Merck and Google are traded at the same price of $37 a share. The historical returns of Merck are more volatile than those of Google and exhibit higher systematic risk. In addition, given the coming health reform proposal, it is generally believed that Merck may have a negative alpha in the future. It is known that neither Merck nor Google will pay dividends in a month. Consider now forward contracts on these two stocks with one month to maturity. The forward price of 100 shares of Merck should be lower than the forward price of 100 shares of Google.

g) Consider two European call options for stock A, with the same expiration date. The strike price on the first option, K1, is lower than the strike price on the second, K2. The price of the K1-strike option should be at least as high as the price of the K2-strike option.

Solutions

Expert Solution

e) True

Duration is a measure of interest rate risk. Higher the interest rate risk, the higher is the duration. In a zero-coupon bond, there are no intermediate cash-flows. However, in a coupon bond, the intermediate cash-flows can be invested at the market yield thus reducing the market interest rate risk. Hence, a 10-year coupon bond always has lower duration than a 10-year zero-coupon bond, regardless of the size of the coupons.

f) False

The forward price mainly depends on the risk-free rate, the time to maturity and the stock price. All 3 are same in case of both the stocks. Hence, we cannot say that the forward price of 100 shares of Merck should be lower than the forward price of 100 shares of Google.

g) True

A call option pays off when the stock price at maturity is higher than the strike price If the stock price at maturity is above K2, then it should be above K1 and the payoff should be higher in case the strike price is K1. Hence, in order to prevent an arbitrage situation, the price of the K1-strike option should be at least as high as the price of the K2-strike option.

jeff jeffy answered 1 year ago

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