## FIXED INCOME

These are securities issued by a government or private company. If issued by a State are called Treasury bonds or Bills. They represent liability capital, and their basic characteristic is fixed return at maturity, which leads to lower risk. Theoretically, fixed income assets are associated to risk-free assets. Return for these assets can be summarised by the term structure, graphically represented by the yield curve. The yield curve shows the risk-free return associated with fixed income assets at different maturities. Fixed income assets can be switched to a stock according to pre-defined rules.
Typically, the fixed income equation can be represented as: , (1)

where the first right-hand side is the present fixed interest discounted by the interest rate , the second right-hand side is the discounted reimbursement value . The sum of these two values in equilibrium must be equal to in the left-hand side value (issue price).
If market interest rates do not change over time, the left-hand side always equals the right-hand side for the interest rate in each t up to maturity. This is also a necessary condition to issue the asset in the primary market in .
In the interest rate in the market can change. This leads to a market interest rate that is different from the asset interest rate . If differs from , and with fixed and , then changes. The market demands that the return for the asset aligns with the market return (this condition holds for a market without arbitrage possibilities). This can happen only if changes. The new will be higher than if the interest rate in the market is lower, and lower than if the market interest rate is higher. This mechanism defines the fixed income return in the secondary market. It is worth noting that at issuance, equals by definition. It is not possible to issue a fixed asset with a different interest rate from that of the market rate. The way to represent the fixed income interest rate at different maturities is the term structure. The graphic representation is the yield curve.
Graphic representation of the term structure through the yield curve of State/ American Government bond/bill market (May 20, 2005). The term structure represents information set for the market. The main theories that explain the structure are: i) expectation theory, ii) segmented market, and iii) liquidity premium. Each theory attempts to define and explain the slope and the modifications over time.
Bibliography
Mayo, H. B., 2007, Investments.
An Introduction, Thomson South-Western, Seventh Edition;
Fabozzi, F. J., 2006, Bond Markets, Analysis, and Strategies, Pearson Prentice Hall, Sixth Edition.
Editor: Rocco CICIRETTI