There are three main ways to approach forecasting fixed-income returns. The first is discounted cash flow. This method is really the only one that is precise enough to use in support of trades involving individual fixed-income securities.

The second approach is the risk premium approach, which is often applied to fixed income, in part because fixed-income premiums are among the building blocks used to estimate expected returns on riskier asset classes, such as equities.

The third approach is to include fixed-income asset classes in an equilibrium model. Doing so has the advantage of imposing consistency across asset classes and is especially useful as a first step in applying the Black–Litterman framework.

**DCF Models**

The DCF analysis of fixed income securities is useful when there are known future cash flows, or when cash flows can be estimated reasonably accurately. The DCF analysis supports the use of yield to maturity (YTM) as an estimate of expected return.

Yield to maturity (YTM)—the single discount rate that equates the present value of a bond’s cash flows to its market price—is by far the most commonly quoted metric of valuation and, implicitly, of expected return for bonds. For bond portfolios, the YTM is usually calculated as if it were simply an average of the individual bonds’ YTM, which is not exactly accurate but is a reasonable approximation.

Assuming cash flows are received in full and on time, there are two main reasons why realized return may not equal the initial yield to maturity.

- First, if the investment horizon is shorter than the amount of time until the bond’s maturity, any change in interest rate (i.e., the bond’s YTM) will generate a capital gain or loss at the horizon.
- Second, the cash flows may be reinvested at rates above or below the initial YTM.

An implication of the second bullet is that falling interest rates will decrease reinvestment returns, and vice versa.

The overall gain or loss to the investor will depend on the investment horizon. For an investment horizon that is shorter than the Macaulay duration, the capital gain impact will be more dominant than the reinvestment impact, meaning that falling interest rates will result in a higher realized return.

For an investment horizon longer than the Macaulay duration, the reinvestment risk dominates, meaning that falling interest rates will result in a lower realized return (YTM).

Note that the** Macaulay duration** can be calculated from modified duration (i.e., by multiplying modified duration by the bond’s YTM).

**Risk Premium Models**

The building block approach starts with a risk-free rate and then adds compensation for additional risks. The required return will include the one-period default-free rate, a term premium, a credit premium, and a liquidity premium.

**The short-term default-free rate**– In principle, the short-term default-free rate is the rate on the highest-quality, most liquid instrument with a maturity that matches the forecast horizon. In practice, it is usually taken to be a government zero-coupon bill at a maturity that is issued frequently—say, every three months. This rate is virtually always tied closely to the central bank’s policy rate and, therefore, mirrors the cyclical dynamics of monetary policy. Secular movements are closely tied to expected inflation levels. Futures contract rates provide useful proxies for this expected path of short-term interest rates.**Term premium**– While the rates implied from the spot yield curve gives us useful information about the term premium, the real term premium cannot be derived from the yield curve alone. Empirical evidence suggests that the term premiums are positive and are related to duration. There are four primary drivers of the term premium:- Inflation uncertainty: Higher inflation levels typically correspond to higher inflation uncertainty, causing nominal yields to rise and the term premium to increase.
- Recession hedge: When inflation is caused by strong aggregate demand, nominal bond returns are negatively correlated with growth, corresponding to low term premiums. When inflation is caused by strong aggregate supply, nominal bond returns are positively correlated with growth, corresponding to higher term premiums.
- Supply and demand: The relative supply of short- and long-term default-free bonds determines the slope of the yield curve, which influences the level of term premiums.
- Business cycles: The slope of the yield curve and level of term premiums are also related to the business cycle.Other indicators also influence the term premium forecasts:

- Cochrane and Piazzesi curve factor: a measure that captures both the slope and curvature of the yield curve.
- Kim and Wright premium: a three-factor model of the term structure.
- Slope of the yield curve.
- Supply indicator: proportion of debt with a maturity greater than 10 years.
- Cyclical proxies: corporate profit-to-GDP ratio, business confidence, unemployment rate.

**Credit premium**– The credit premium compensates for the expected level of losses and for the risk of default losses, both of which are components of the credit spread.**Liquidity premium**– Liquidity tends to be the highest at the earliest stages of a bond’s life, typically during the first few weeks only. Securities with the highest liquidity are the newest sovereign bond issues, current coupon mortgage-backed securities, and some high quality corporate bonds. As a general rule, liquidity is higher for bonds that are :- issued at close to par or market rates,
- new
- large in size
- issued by a frequent and well-known issuer
- simple in structure
- of high credit quality