## The yield curve part III – measuring the yield

##### Published: Jun 2005

So far we have looked at what a yield curve is, its different shapes and how it is used. This month we begin our review of yield measurements – of which there are several. The principal ones are yield to maturity and current yield. Here we examine the former.

### Yield to maturity

The yield to maturity (YTM) measure has many aliases – yield, redemption yield, gross redemption yield (GRY) and internal rate of return (IRR). All refer to the total return you receive by holding an investment, typically a bond, until it matures. In other words, YTM equals the interest you receive from the time you purchase an investment until maturity, plus any gain or loss. It is the most commonly used measure to value bonds – thus in our example of YTM below, we refer to a bond.

Calculating YTM involves the following complex equation. It requires the identification, through trial and error, of ‘r’, which is the interest rate used to calculate the current value of future interest payments and the redemption payout. Thankfully, some calculators (e.g. HP12C) and programs (e.g. Microsoft Excel) have a built-in function to carry out the calculation.

$$c\: 1\:+\:r\:-\:1\:+\:c\: 1\:+\:r\:-\:2\:+\:…\:+\:c\: 1\:+\:r\:-\:n\:+\:B\: 1\:+\:r\:-\:n\:=\:P$$

Where:

• $$c\: = \:annual \:coupon\: payment\: (as\: a \:currency\: value,\: not\: a\: percentage).$$
• $$n\:= \:number\: of \:years\: to\: maturity.$$
• $$B\:= \:par \:value \:on \:maturity.$$
• $$P\:= \:bond’s\: purchase\: price\: today.$$

So, for a four-year bond, paying annual 3% coupons, with a price of £95 and par value of £100, the YTM would be 4.39%.

$$3\: 1\:+\:r\:-\:1\:+\:3\: 1\:+\:r\:-\:2\:+\:3\: 1\:+\:r\:-\:3\:+\:3\: 1\:+\:r\:-\:4\:+\:100\: 1\:+\:r\:-\:4=\:95$$

Investors prefer to analyse bonds by YTM because it takes account of:

• The initial investment amount, i.e. the bond’s purchase price, which gives any appreciation or depreciation in the bond’s price.
• The interest payments, i.e. the coupon payments.
• The amount of interest earned on interest.

Since YTM calculates a bond’s total expected rate of return, investors can compare bonds with different coupon rates, different maturities and different credit qualities.

The disadvantages of this measurement are:

• It assumes the investor retains the bond until maturity.
• It assumes the investor can reinvest the interest/coupon payments at the same rate – in practice, this may not happen.