## Types of yield curve

##### Published: Aug 2008

In the previous issue of Treasury Today in China, we discussed the purpose of the yield curve and the two main calculations used to measure it – yield to maturity (YTM) and current yield. However, there are a number of different bases on which a yield curve may be constructed. Each uses a different bond profile to construct the expected term structure from which the yield curve is drawn.

Below we detail the four main types of curve:

### Yield to maturity (YTM) curve

As we discussed in the previous issue, YTM is a measurement of the total income a bond is expected to generate until maturity. The most common type of yield curve, the yield to maturity curve (or simply the yield curve), demonstrates a link between the returns (yields) and maturity dates for a group of instruments with the same risk. A typical example is a yield curve constructed from yields on treasury bills of different maturities issued by a government.

The disadvantage of YTM is its underlying assumption that all cash flows are reinvested at the same rate as the yield of the bond.

### Forward rate curve

The forward rate curve is a graph of the forward rates implied by the yield curve. This recognises that interest rates will vary at different times during the period and illustrates the forward interest rates for each period shown on the yield curve. This curve is used to determine the prices of interest rate derivative instruments.

### Par yield curve

Ideally, the yield curve is built using the YTM of a coupon-bearing instrument, such as a bond, whose market price is par (ie the same as its face value). In selecting bonds trading at par, an investor can eliminate the distortion caused by the different coupon rates payable on differently priced bonds. The yield on a par bond will be the same as the market rate.

Lower coupon bonds will be sold at a discount to compensate the investor for taking a below market coupon yield. Similarly, the investor will be required to pay more for a bond with a coupon that exceeds market rates. In either case, this distorts the yield curve on similar risk instruments.

As bonds pay different coupon rates, it is rare for many to be trading at par. As such, it may prove difficult to find bonds from which to construct a par yield curve.

### Zero-coupon yield curve

A zero-coupon instrument – such as a bond – is one that does not pay any interest (coupon) over the course of the term, but instead pays the investor the principal at maturity. Despite not earning any interest, investors gain from paying a discounted principal amount. Thus, all the yield is in the form of a capital gain.

The zero-coupon yield curve discounts that future single cash flow to gives its value today. Since there is only one payment, calculating the yield from its price (which is its net present value) is relatively simple. The advantage is that, in calculating the yield, the investor does not have to assume a reinvestment rate for any of the interim coupon payments associated with coupon-bearing bonds.