Yield measurements

Published: Jun 2008

There are two methods commonly used to measure the rate of return on an investment: yield to maturity and current yield.

Yield to maturity

Yield to maturity (YTM) has many aliases – yield, redemption yield, gross redemption yield (GRY) and internal rate of return (IRR). All refer to the total interest you receive from purchase to maturity of an investment, typically a bond, plus any gain or loss.

Calculating YTM involves the following 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.

$$\mathrm{c1\:+\:r^{–1}\:+\:c1\:+\:r^{-2}\:+\:…\:+\:c1\:+\:r^{–n}\:+\:B1\:+\:r^{–n}}=\mathrm{P}$$

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%.

$$\mathrm{31\: +\:r^{-1}\:+31\:+\:r^{-2}\:+\:31\:+\:r^{–3}\:+\:31\:+\:r^{–4}\:+\:1001\:+\:r^{–4}}=\mathrm{95}$$

Due to the complexity of this equation it is usually worked out using specialist calculators or computer programmes. The popularity of YTM lies in its ability to take into account the initial investment amount, the interest payments and 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, maturities and credit qualities. The disadvantages lie in its assumption of bond retention until maturity and re-investment of the interest/coupon payments at the same rate as the bond’s yield – in practice, this may not happen.

Current yield

Also known as the running yield, flat yield or income yield, current yield is calculated by dividing the income received per annum (ie annual coupon or interest payments) by the purchase price of the investment, excluding any accrued interest. Unlike the YTM measurement, it overlooks any capital gain, or loss, on redemption/sale.

Expressed as an equation, the current yield is:

$$\mathrm{CY}=\frac{R}{P}*{100}$$

Where:

• CY = current yield expressed in %.
• R = coupon rate.
• P = purchase price of the investment.

In relation to a four-year bond, purchased at £95, paying annual 3% coupons, the current yield would be 3.16%.

$$\frac{3}{95}*{100}={\mathrm{3.16\%}}$$

Current yield is a much more straightforward calculation than YTM. However, drawbacks include the inability to take into account any potential capital appreciation or loss. This calculation also overlooks any interest on interest received. If a bond is purchased at a discount, the YTM will be greater than the current yield. If it is purchased at a premium, on the other hand, the current yield will be greater.

Other yields

Alternative yield measurements do exist but are less commonly used. For example, the Japanese bond market uses the simple yield to maturity measurement. This takes account of the capital gained or lost on the investment, but not the compound interest (that is the interest that can be earned on any interest received).

In the next issue, our series on yield curves will continue with a discussion of the various types of yield curve.