Chapter 5, Problem 13PROB

Summary Introduction

The graph which shows the relationship between yields and maturities on a particular date is known as the yield curve, and this relationship is simply called the term structure of securities. The yield curve could be upward sloping where the long-term yields are higher than the short-term yields and is also known as normal yield curve. However, if the long-term yields are lower than the short-term yields then the slope with be downward sloping and is referred to as inverted or abnormal yield curve.

Interest rate consists of risk-free rate, real risk-free rate and inflation premium, and a risk premium such as liquidity risk (LP), default risk (DRP) and maturity risk (MRP). Since, real risk-free rate generally remains constant, it is the changes in the expectation of risk premium and inflation which affects the interest rate of the security. Hence, inflation expectation is the most significant reason for changes in yield and determination of yield curve.

Interest rate or yield on treasuries can be determined using the below equation, where default risk premium DRP and liquidity premium (LP) is zero, as treasuries are considered as liquid and default free investment. Maturity risk premium (MRP) is there as they have differing maturity securities issued.

$\begin{array}{c}{r}_{Treasury}=r_{RF}+MRP\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\left(r^{*}+IP\right)+MRP\end{array}$

Expectation theory states that the shape of the yield curve depends on the expectation of future inflation rate and hence an increasing inflation rate will result in an upward sloping curve whereas a decreasing rate would result in downward sloping curve.

Inflation is expected to be 1.5% in Year 1 and Year 2 and would settle for a rate greater than 1.5% thereafter. Yield in year 1 and 2 will remain the same and on 3-year bond will be 0.5% more than yield in Year 1 and 2. The bond is risk free and has a real risk-free rate of 2%.