Determination of Bond Prices for Some Parameter Values.

Abstract

A bond is a security that is issued in connection with a borrowing arrangement. The borrower issues (i.e. sells) a bond to the lender for some amount of cash. The arrangement obligates the issuer to make specified payments to the bondholder on specified dates. When the bond matures, the issuer repays the debt by paying the bondholder the bond’s par value (equivalently, its face value). An investor considering the purchase of a bond is usually not quoted a promised rate of return. Instead, the investor must use the bond price, maturity date, and coupon payments to infer the return offered by the bond over its life, which is called the yield to maturity. The relationship between yield to maturity and bond price were proved by Malkiel in his theorems. He showed how yield to maturity and bond prices movements depend on coupon rate, the time to maturity, and the existing yield to maturity. In this paper we prove the Malkiel theorems using simple algebra. The proofs will give a better understanding about the relationship of the movements in yield to maturity and bond prices. Keywords: bond prices, yield to maturity, Malkiel theorems.