In previous issues, we explained the purpose of yield curves and looked at different yield measurements – the main ones being yield to maturity (YTM) and current yield. This month we explore different bases for yield curves.

There are a number of different bases on which to construct the graph of a yield curve. The four main ones are yield, forward rate, par yield and zero coupon yield. These use different bond profiles to construct the expected term structure from which the yield curve is drawn.

#### 1. Yield curve (YTM curve)

The yield to maturity curve (often referred to simply as the yield curve) is the most common type of yield curve. This uses the yield to maturity (YTM) measurement examined in June’s Calculator Corner and is subject to the same limitations. The yield curve demonstrates the 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.

#### 2. Forward rate curve

The forward rate curve (also referred to as the forward rate) is based on the aforementioned standard yield curve. It 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. Indeed, the forward rate curve illustrates the forward interest rates for each period shown on the yield curve. This curve is used to illustrate the prices of interest rate derivative instruments.

#### 3. Par yield curve

Ideally, the yield curve is built using the yield to maturity of a coupon-bearing instrument (eg bond) whose market price is par. By choosing bonds trading at par, the investor can eliminate the distortion caused by the different coupon rates payable on differently priced bonds. The yield on a par bond is the same as the market rate. Lower coupon bonds will sell at a discount to compensate the investor for taking a below market coupon yield. Similarly, an investor will have to pay more for a bond with a coupon that is set at above current market rates. In either case, this distorts the yield curve on similar risk instruments.

Since bonds pay different coupon rates, it is rare for many to be trading at par. Therefore it can be difficult to find bonds from which to construct a par yield curve.

#### 4. Zero coupon yield curve

This is perhaps the most straightforward of yield curves to build. A zero coupon instrument is one which does not pay any interest (coupon) over the course of the term. Instead, the holder of the instrument (eg bond) is rewarded with a repayment of 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.

Since there is only one payment, calculating the yield from its price (which is of course 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 couponbearing bonds.