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Tutorial 1 Solutions

Tutorial 1 Solutions - SEEM5480:Tutorial1Solutions...

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1 SEEM 5480: Tutorial 1 Solutions Question 1: Short‐term interest rates are usually more volatile than long‐term interest rates. Despite this, the rates of return of long‐term bonds are more volatile than returns on short‐term securities. How can these 2 empirical observations be reconciled? Answer: Think duration. The longer‐term bonds have longer durations and are thus more sensitive to yield/interest rate changes. Question 2: (From Problem Set 1, Question 1) Consider the following bond: Bond (a) is a 3‐year bond paying annual coupons at 4.5% and selling at par. Bond (b) has the same terms as bond 1 except that the coupons are paid semi‐annually. For the following parts, assume that markets have moved and the yield is now at 3.75%. a) Intuitively, at this new yield of 3.75%, will the prices of bond (a) and bond (b) increase, decrease or stay the same? Explain. Answer: Both bonds were at par, which means that the original yield equals the coupon rate at 4.5%. Hence a new yield at 3.75% signifies a decrease in yield. At this new yield, both bond prices will increase, as yield goes opposite to the price. b) Intuitively, which bond (a or b) has the higher price at this new yield? Answer: (a) will be higher. There are 2 ways to think about this: 1) Think Convexity : (a) has higher convexity, which means that there is more curvature to the relationship between price and yield (see graph in lecture). Hence at a lower yield, price will be higher.
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