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Unformatted text preview: Department of Economics Fall 2010 University of California, Berkeley Economics 100B Problem Set #5 Suggested Solutions Page 1 of 10 Problem Set #5 Suggested Solutions 1. (2 points total) a. ( point) Why does an increase in bond prices make the interest rate fall? A bond is just an I.O.U. from the borrower to the lender. What distinguishes a bond from any other I.O.U. is that a bond can be sold. The original lender who received the bond initially can hold onto that bond until it matures (until the borrower has to repay the amount borrowed), or can sell the bond to someone else before it matures and then the new bond-holder will hold onto the bond until it matures. When that bond is sold, the price it sells for is the price of the bond. From the borrowers perspective, the interest rate paid on bonds is the cost of borrowing. To a lender, the interest rate is the rate of return for lending. To understand the relationship between bond prices and interest rates, focus on the lenders perspective. The rate of return on a bond is the dollar return on the bond divided by the price paid for the bond. Lets think about a discount bond , which is a bond that sells for a discount relative to its face value (how much the bond-holder will receive when the bond matures). The dollar return is the face value of the bond minus the price paid for the bond. The higher the price paid for the bond, the smaller the dollar return. The smaller dollar return is being compared to a higher base (higher price of the bond). So both because the dollar return decreases and the base increases, an increase in the price of the bond lowers the rate of return on the bond. And the rate of return on the bond is just the bonds interest rate. You can also explain the relationship between bond prices and interest rates using a coupon bond or a perpetuity bond . With a perpetuity bond, the bond itself never matures. With a coupon bond, the maturity date is far off in the future. In both cases, the bond pays an annual dividend, the annual dollar earnings. The annual rate of return on the bond is then the annual dollar earnings divided by the price paid. The annual dollar earnings are fixed in dollar value. The higher the price, the smaller is that fixed annual earnings relative to the price of the bond. That is, the smaller is the rate of return on the bond. And the rate of return on the bond is just the bonds interest rate....
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- Spring '08