Expected inflation

Current inflation can be a component of the nrfr as term to maturity lengthens, but this is only so in the short term maturity area and in a low and stable inflation environment. As term to maturity lengthens current inflation is replaced increasingly by expected inflation (e7r) (as in the Fisher equation), which could he higher or lower. The equation is (see Figure 10):

Liquidity-sacrifice premium

The component that takes us to the many risk-free-rates (rates on government securities) that exist is what is generally called the liquidity-sacrifice premium (Isp).

In the case of short-term securities, liquidity (i.e. command over money) is sacrificed only for a brief period, and therefore there is little rate premium involved (it is zero at 1-day maturity, of course). However, as the term to maturity of government securities increases, the lender moves further away from a state of liquidity, and requires compensation for this. This may be explained as follows:

Lenders favour short-term investments because they have better command over their resources. Although liquid government bond markets exist in many countries and lenders can dispose of long-term bonds at will, this is never 100% certain, or the markets can be non-efficient at times in terms of price discovery. Therefore, lenders require a higher level of inducement as term increases to part with liquidity.

Borrowers prefer to borrow long rather than short because:

• Corporate entities usually borrow to purchase capital goods that have a long-term life.

• The availability of funds in short-term rollovers is uncertain.

• The short-term borrowing rate at each rollover is uncertain.

This is particularly pertinent to certain fledgling markets because rollover of short-term debt at market rates, or rollovers per se, cannot be taken for granted. Borrowers are prepared to pay a rate premium for the availability of funds for longer periods (assuming that the productivity of the project to be funded allows this).

For these reasons (i.e. the asymmetry of demand and supply), the rate premium is positive33 and increases with term to maturity. It however, increases at a decreasing rate as the term to maturity increases because the lender differentiates less at the long end. For example, lenders will differentiate less between 25-year and 30-year bonds compared with 1-year and 5-year bonds in terms of the rate premium demanded.

We now arrive at the many points that make up the zero coupon government bond yield curve34 (government ZCYC). The components of each point are shown in Figure 11 (keep in mind that the rrfr is a 1-day rate):

composition of nominal rates

Figure 11: composition of nominal rates

The above explanation is not entirely hypothetical: we know from practice that the normal shape of the yield curve is upward-sloping and that it levels-off at the longer end.

Credit risk premium

The rates of interest on government securities are the lowest in the markets because they are risk-free. The rates of interest on the debt instruments of other non-government issuers are benchmarked against the equivalent term rates on government securities. For example, the 10-year bonds of prime-rated ABC Company may trade at 100 basis points (bp) over the 10-year government bond rate. This is the credit risk premium demanded by the lenders.

The credit risk premium and the yield curve for corporate securities may be depicted as in Figure 12. It is assumed that the yield curve is also a ZCYC and that the rates apply to the bonds of AAA-rated borrowers (i.e. homogenous corporate bonds in terms of risk).

The credit risk premium becomes larger with term to maturity. This is simply because the probability of the various risk-events attached to non-government securities taking place increases with term to maturity.

With the addition of the credit risk premium (ca) to the equation, we are now "explaining" the nominal rates of AAA-rated companies (nrc); each point on the corporate ZCYC is composed as follows:

composition of nominal rates

Figure 12: composition of nominal rates


A number of countries have fledgling financial markets and they are generally illiquid, i.e. it is difficult to sell securities in the secondary market at what should be the fair market price. Others may not have secondary markets at all. In such markets lenders may still have a need for long-term securities (for example an assurer wishing to match annuity liabilities). The government or a corporate entity may also have a need to issue long-term bonds to finance a long-term project (for example government for the construction of a power plant).

It will be evident that in illiquid secondary markets or where such markets do not exist the lenders will demand what can be called an illiquidity premium (ip) (illiquidity here referring to lack of secondary market turnover). Clearly in such markets a yield curve will not exist (because it is unlikely that government will borrow at enough maturity points).

On the ridiculous assumption that an active market does exist and that government wishes to borrow by the issue of non-marketable securities, the non-marketable risk-free yield curve will be benchmarked on the risk-free rates on marketable securities and the equation becomes:

Figure 13 depicts this unlikely equation.

composition of nominal rates

Figure 13: composition of nominal rates

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