spot rates, future rates and yield curve

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The yield curve, or the term structure of interest rates, “is the pattern of yields on riskless bonds, based on their maturity” and “describes the relationship between the yields of risk-free zero-coupon bonds and their time-to-maturity.” The yield curve could either be downward sloping, flat, upward sloping, or even with bumps at various points of the curve. A downward sloping yield curve indicates that short-term rates are higher than long-term rates. A flat yield curve indicates that the yield to maturity of riskless bonds across all maturities is equal. Upward sloping yield curves, the focus on this section, indicates that long-term rates are higher than short-term rates. One could argue that this may be the typical yield curve as longer-term investors have to be paid a premium for taking on both interest rate and market risks. But yield curves take on various shapes and don't just follow a specific shape. From mid-2006 to 2007, the yield curve in the US market was mostly flat or downward sloping.

There are different kinds of term structures of interest rates. Using the yields to maturities across various maturities of zero coupon bonds (as in section A of this assignment) results in a spot term structure.

Considering only pure discount, or zero-coupon, bonds, the yield curve can indicate the returns that the bonds provide across various maturities. An upward sloping yield curve has lower short-term, or near-term rates, and higher longer-term rates. This means that the returns of bonds with longer maturities are higher than those with shorter maturities.

There are four theories that are utilised to explain the rationale for the shapes taken by the yield curve. These are: (1) segmented market theory, (2) expectations theory, (3) liquidity premium theory, and (4) Preferred habitat theory. The rest of this section goes through each of the theories in detail.

Segmented Market Theory

The segmented market theory argues that investors have specific preferences in the maturities decided on with the reason for this approach being that investors are very risk averse. Thus, there is very little movement in the maturities that investors play in. The resulting yield curve is then driven by where the investors mostly end up based on their requirements. For an upward sloping yield curve, the segmented market theory will then argue that at the particular instance, there is a greater number of investors in the short-term maturity period and hence driving down the rates, with the longer-term rates being driven up as there are less investors in the space.

One could look at banks as having specific preferences. Banks are seen to prefer upward sloping yield curves given the business model of borrowing at short-term rates and lending over the longer-term periods. Other financial companies also generally benefit and favour an upward sloping yield curve as it allows the firms to pursue carry trades (i.e. borrow short and lend long). The banking and financial companies' model thus relies on low short-term rates for lower borrowing costs and higher longer-term rates to achieve a margin over their cost of funds.

Expectations Theory

The expectations theory is based on the assumption that investors' expectations drive the slope of the yield curve and the if the yield curve were upward sloping, then this means that investors are expecting future spot rates to become higher than the current spot rates, hence the upward sloping shape of the yield curve.

The key limitation of the expectations theory is the assumption that investors are risk-neutral. This means that investors have no risk preferences. However, this is very rarely the case as almost all, if not all, investors have a risk level that affects the investment decisions and, ultimately, results in preferences for products with characteristics that match risk levels. Nevertheless, this theory is oft mentioned in articles and reports when yield curves are discussed. For example, an upward sloping yield curve is attributed to expectations of higher interest rates in the future as well as expectations that the economy will continue to perform well.

Liquidity Premium Theory

Another theory touching on the shape of the yield curve is the liquidity premium or liquidity preference theory. For this particular theory, the assumption is that there is a shortage of lenders in specific maturities in the yield curve, and where the shortages are, the borrowers will need to drive up the rates to encourage the investors to participate in the investment. This would typically be the case for longer-term maturities where investors would see the investment as riskier and thus require a premium. Based on this, the explanation for an upward sloping yield curve is that there is a relative lack of longer-term investors, and borrowers need to drive up the rates in order to tap the investors at those specific maturities. An upward sloping yield curve thus indicates, from this theory, that longer-term investors are in short supply and the borrowers are increasing the rates for longer-term maturities to enhance the yield and encourage investors for the longer-term investment. There certainly is an argument for this theory as an increase in the slope of the yield curve (upward sloping) positively relates to changes in the rate of the longer-term and less liquid securities.

The limitation in this theory is that the expectations of the investors in terms of the rates are not factored in. The key impact, as presented by the theory, is driven by the lenders and the rates being offered to investors. There is a similarity in this theory with the expectations theory in that both project increased future spot rates with an upward sloping yield curve.

Preferred Habitat Theory

The preferred habitat theory combines the arguments of the segmented market theory as well as the liquidity premium theory. In this instance, both the preference for specific maturities and the premium currently existing in some maturities are the key drivers of the decision on the specific maturity to invest in. This supply to specific maturities coupled with the demand by borrowers will then result in a specific shape for the yield curve. An upward sloping yield curve as explained by this theory means that


It would seem that each of the theories presented have their specific limitations in explaining the term structure of interest rates completely. I would argue that each has its own merits and that it is likely that a number of factors come into play in the decision of investors as well as the requirement of borrowers. Thus, a combination of the different theories probably best explain the resulting yield curve and the dynamics that it goes through depending on the factors in play at the particular moment.

An upward sloping yield curve has rates that are higher over the longer- term horizon. This could be driven both by expectations by investors of higher spot rates in the future while, at the same time, also buoyed by demand at that point and specific preferences. It is important to note that investors have different criteria in deciding and that each investor could even fall in the different theories with some, for example, basing their decision on their expectations, and some in their maturity preferences.

Investors are not the only players affecting the slope of the yield curve. The government and policy makers also have an influence in the resulting shape of the yield curve. An upward sloping yield curve could indicate that policy makers may look to increase interest rates in the future. This would be a positive sign for the market as it could indicate that the economy is going strong, and is thus viewed by market participants as a bullish sign and a good reflection of an expanding economy. Central banks have a number of avenues in which to have potential impact on the resulting interest rates and yield curve.

Also a factor is the situation that organisations are in. For example, while banks could have specific expectations which drive their decisions relating to the yield curve, the recent credit crisis has shown the importance of liquidity and how this has affected the decisions made by banks, thus impacting on and adding another factor on the yield curve.


The shape of the yield curve is affected by many factors and not one specific theory is able to explain the rationale behind the shape completely. The factors that come into play which would affect the shape of the yield curve includes the following: (1) preferences of investors, (2) expectations of investors, (3) supply and demand of bonds, in this case, at the particular time, (4) external influences such as government policymakers, and (5) liquidity premium attached to specific maturities. Note that there are some overlaps in each of the factors defined as impacting the shape of the yield curve. Also, these are the key factors but not necessarily the only factors as some investors and industry players may have their own criteria in deciding and thus also impact or influence indirectly the shape of the yield curve.

For the upward sloping yield curve, this could mean, based on the factors above, a combination of factors where investors have a preference for shorter-term maturities as this is driving down the short-term rates, some investors are expecting future spot rates to be higher, shorter-term rates driven by higher demand by investors and lower supply from borrowers, government is favouring stimulating the economy, and short supply of investors in the longer maturities.