Bond Yield Curve and term structure


The Yield curve shows the relationship between interest rate over its maturity term.  Maturity term is the duration of the loan.  Thus there are many yield curves across different contract lengths.  Every bond has its own unique yield curve, and this relationship of yield over its maturity tenor/term is referred to as the “term structure of interest rates.”

Yields are further classified as follows:

Nominal Yield: This the coupon rate of a particular bond i.e. a bond with a 10% coupon rate has a nominal yield of 10%

Current Yield: This yield measures current income from the bonds as a percentage of its prevailing price.  It is the income that is generated periodically from an investment portfolio.

Yield to Maturity: Reflects the total compounded return an investor earns by holding a bond to its maturity.

Yield to Call: Yield to Call is calculated the same way as Yield to Maturity, but assumes that a bond will be called, or repurchased by the issuer at a call price/face value before the maturity date.  Thus Yield to Call is the compounded return at the point the bonds are “called.”

A yield curve depicts yield spreads that arise over different tenors due to difference in maturity and thus points to the overall term structure of interest rates.  This relationship is affected by economic fundamentals and consumer expectations.  Normally the term structure is upward sloping, which means that the bond yields usually rise with maturity. At a rudimentary level there are a few variables that can cause the demand and supply of bonds to change and thus impact its long term yields and thus term structure.

Demand Functions:

  • Wealth Affect: Economic growth creates wealth, thus the immediate demand for bond increases and consequently depresses current yield in favor of long term yieldsDemand Change Affecting Bond yields
  • Expected Returns (ROI): If investors forecast that interest rates would lower in the future, then they would buy more interest bearing instruments in the immediate future viz-a-viz long term.  This would make the term structure slope upwards
  • Inflation: Since purchasing power is eroded with inflation, thus investors would invest short term if they felt that long term inflation would rise. This would depress the current yield, as price, driven by a rightward shift in demand function, pushing the price up and yields down.
  • Bond Risk: Short term investments may be deemed less risky than long term investment, causing higher demand for short term maturing bonds viz-a-viz long term bonds. This would increase the demand for short term bonds and reduce their yields and cause the term structure to slope upwards.  On a similar note the Pure Expectations Theory postulates that yield curve reflect investor’s perception of future short term interest rates and that bond prices are established strictly on the basis of future interest rate expectations and not maturity horizon.  The maturity risk premium is zero long-term interest rates are simply a product of current and expected future short-term interest rates.

Computationally if an investor wants to buy a 2-year bond 1 year from now then he would look at the 1-year interest rate and use that value to calculate the value interest rate for year 2 at the end of year 1.

Equation:         (1 + Y1) x (1 +Y2) = (1 + Y12)

Y1 = 1st year yield

Y2 = 2nd year yield

Y12 = yield of a bond maturating in 2 years

The calculation would yield an upward sloping yield curve.

  • Liquidity: Investors demand for highly liquid bonds is higher than less liquid bonds, thus shifting the demand function for these bonds. The Liquidity Preference Theory, specifies that investors require a higher liquidity on long term bonds and because of this premium long-term yields tend to be higher
  • Information cost: A decrease in cost for acquiring information on bonds, shifts their demand rightward and increases their price and yield oppositely.
  • The Preferred Habitat Theory states that investors have a distinct investment horizon, and require a premium in interest rates outside their preferred maturity horizon.

Supply Functions:

  • Profit Expectations: An increase in corporate profits would increase supply of bonds as firms would purchase Supply Change Affecting Bond yieldsdebt for capital expenditure, which would lower bond prices and increase their yield.
  • Taxation: Imposition of tax would reduce incentive for capital expenditure and thus the supply of bond would shift inwards increasing price and reducing yields.
  • Inflation: Inflation reduces the purchasing power parity, and thus weakens currency. Thus if inflation were to persist then businesses and governments would borrow in the short term and pay in the long term when the currency is weaker i.e., “cheap dollar.”  This would shift supply of bonds rightwards and reduce bond prices and increase current yields.

Term Structure and Economic Performance:

Generally, the slope of the yield curve has been a good leading indicator of economic performance.  An upward
sloping yield curve has preceded a growing economy and a negatively sloping yield curve has been a predecessor to economic slowdown.  A flat yield curve has corresponded to a transitory state.Term Structure

The assumption of an economic upturn in conjunction with an upward sloping yield curve is the notion that interest rates will begin to rise significantly in the future.  Consequently, the Yield to Maturity increases because of an associated risk of higher inflation on the longer horizon that is brought about by rapid economic expansion.  Thus investors require a higher return over their investment horizon.  Similarly, an inverted yield curve is a harbinger of recession, and the term structure inverts.  It is based on the assumption that interest rates in the future would decline to spur the economy out of a slowdown.  It would not be uncommon for yield curves to invert 12-18 months prior to an economic slowdown.

Utility of the Yield Curve:

Yield curves is a stable leading economic indicator and thus signals well in advance on how the economy may perform in the foreseeable future.

Yield curve is also used as a benchmark to price other fixed income securities based on their risk class.  This is done by adding a risk premium to treasury bonds.  For example, a 3-year high quality bond may be priced 50 basis points over a 2-year treasury bond and similarly a riskier bond may be priced 100 basis points over a 2-year treasury bond.

Also yield curves may be used to price bonds, the values of which are based present value of future cash flows and principal.  If different interest rate forecasts are applied to a given bond, and estimation of its undervaluation or overvaluation may be arrived at and accordingly the investment decision applied.


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