risk structure of interest rates

For given term to maturity, different bonds will earn different interest rates if, as we have already indicated, they are subject to different default risk,different of liquidity, or different tax treatment.
Different default risk consider two bonds, A and B, for which everything is the same; they have the same degree of liquidity, have the same term to maturity, and have the same tax treatment, and so on. Given this situation, the bonds will have the same market value, p; and because they have the same coupon payment, they will yield the same interest rate. Now suppose that corporation B, which issued bond B, experience some financial or economic woes and the bond rating services Lower Corporation B is ratings. Because the default risk is now relatively higher for bond B than for bond A, the demand for bond B will fall-causing its price to fall and its interest rate yield to rise. At the same time there will be an increase in the demand for bond A, causing its price to rise and its interest rate to fall. In short, there will now be an interest rate spread (difference) between bond A and bond B that reflects a risk premium.
Note that the interest rate on bond B will exceed the interest rate on bond A because each bond generates the same coupon payments but the price of bond A I higher than the price of bond B. another way to view this is to note that because the default risk is higher on bond B, investors require a higher interest yield on B. The prices of such bonds will adjust until the interest rate spread reflects their differential default risks. We conclude that different bonds yield different interest rate, in part because they are subject to different default risks.
different of liquidity Again consider two bonds, for which the circumstances are identical in all respects, bond c and bond D. suppose now that bond D becomes more liquid, perhaps because it is more widely traded. Following our previous analysis, we conclude that the demand for bond D rises while the demand for bond D rises while the demand for bond C falls , that the price of bond D rises while the prices of bond C rises. (Remember, if both bonds pay the same coupon value and their prices differ, they now yield different interest rates.)
We conclude that if different bonds are subject to different degrees of liquidity, they will earn different interest rates. Specifically, those bonds that are more liquid, other things constant, will earn lower interest rates than those bonds that are less liquid. Stated differently, investors will require a lower interest rate on bonds that are more liquid, other things constant.
This analysis explains why U.S. government securities, which are more liquid than corporation bonds (the market for an individual corporation is bonds (the market for an individual corporation is bonds is much thinner than the market for government securities), pay relatively low interest rates. Of course, U.S. government securities also sell at a low interest because of their extremely low default risk.
Different tax treatment Tax treatment securities are available for purchase. The value of the tax-exempt status of the income from bonds issued by municipal government is directly proportional to one is marginal tax bracket. As of 1991 there were only three brackets for federal personal income tax purposes: 15 percent, 28, and 31 percent, although because of a variety of phaseouts of deductions and exemptions the actual marginal tax rate can be as high as 35 percent for certain individuals. The value of nontaxable income is less for someone in the 15 percent bracket than in the 31 percent bracket.
In the marketplace, individuals in higher marginal tax brackets did up the price of the tax-free municipal bonds so that their yields fall below yields on equivalent taxable bonds. On the margin, actual yields of tax-exempts will reflect the marginal tax bracket of the marginal buyer of such bonds. That is why, on any given day, tax-exempt yields are less than taxable yields. Thus everyone who buys tax-exempts implicitly pays a tax, which is the difference between the interest yield on a municipal bond and the interest yield on an equivalent corporate bond. The purchase of tax-exempts only allows investors to escape explicit taxation.