Bond Yield: What is it and how is it calculated?

The yield of a bond is the return on invested capital that includes interest and capital gain. But how is it calculated and how can you assess whether you are getting a good deal or not? Before buying Btp or Bot, investors should always calculate the actual yield of the bonds, in order to immediately establish whether the investment is convenient.

This is why knowing the bond yield is an essential element when investing in the bond market. The formula for the calculation of the yield of a bond is anything but simple, because it depends on several variables and you need to know some financial and actuarial mathematical formulas.

Below is a complete guide to know which variables to consider and how to perform the calculations to be made.

What is a bond?

A bond is a debt security issued by public bodies, companies or international organizations that undertake to return the invested capital (nominal value) at maturity and to periodically pay interest, known as coupons. For the investor, it represents a source of bond income, while for the issuer it constitutes a debt security.

Understanding how bonds work helps to calculate how much they yield.

We can therefore summarize the factors that determine the yield of a bond:

• nominal capital: initial amount invested and repaid at maturity;
• coupons: periodic payments of bond interest (not provided for zero-coupon bonds);
• maturity: period within which the investment comes to an end.

How to calculate bond yields

The bond yield is made up of the sum of the interest on the bonds and the difference between the purchase price of the bond and the redemption or sale price.

To calculate the effective yield or yield to maturity, the future cash flow discounting formula is used, which evaluates each flow based on the time elapsed since the purchase.

Nominal yield

The simplest bond yield to calculate is the nominal yield, which represents the ratio between the annual coupon and the purchase price.

Nominal yield formula: R = C/P x 100

• R: yield (%)
• C: annual coupon
• P: purchase price

Example:
a Btp with a nominal value of 100 euros and an annual coupon of 4% purchased at 100 euros will have a yield equal to:
R = 4/100 x 100 = 4%

Effective yield

The effective yield takes into account additional variables such as the purchase price different from the nominal value, taxes and commissions.

Example:
let’s suppose a bond with a 10% coupon, issued at 97 and purchased at 94, with 1% commissions and a 4-year maturity. At maturity, the redemption value is 100 euros.

Let’s see all the steps for the total gross yield calculation:

Total Coupon = C × Nominal Value × Number of Years = 10 x 4 = 40 euros

Total Price = Purchase Price + Commissions = 94 + 0.94 = 94.94 euros

Gross Yield = [Total Coupon + (Redeem Value −Total Price)] / Total Price = 47.46%

• The annual gross yield will be 47.46%/4 = 11.86%

However, there are different types of bonds: convertible, fixed rate, floating rate, zero-coupon, structured and perpetual.

For variable rate bonds it is not easy to make calculations that are immediately usable; if, instead, we consider fixed rate bonds, we can calculate the yield using the mechanism just seen.

Relationship between bond price and yield

There is an inverse relationship between the price of a bond and its yield. When the price falls, the yield increases.

For example, if the price of the bond falls from 100 to, let’s imagine, 90 euros (the reasons for the fall in the value of the securities can be many and will not be analyzed here; for simplicity we will refer to a generic fall in the demand for bonds) there will be two effects:

• whoever holds the bond will now be able to sell it at a market value of 90, suffering what in jargon is called a capital loss if the bond is actually sold;
• the bond that is sold at 90 euros will still receive a fixed coupon of 4 euros every year: now, however, the interest is no longer 4%, but 4.4%, since 4.4%=(4\90)*100.

So, if the price (nominal value) of the bond falls, the rate of return perceived on that bond rises. This principle is crucial to understanding how market variations affect the yield of bonds.

Taxes and commissions in calculating the yield

The impact of taxes and commissions can reduce the actual yield. Italian bonds are subject to Government bond tax equal to 12.5% on coupons and capital gains.

The yield in this case is given by the sum of the net annual coupon (i.e. the value of the coupon received minus 12.5%, the tax on the coupon)) and the capital gain (or loss) (i.e. the difference between the redemption value and the purchase price of the bond), net of taxes.

The latter, divided by the number of years to maturity. We divide the whole by the purchase price, increased by the commissions, and multiply by 100.

To be clearer, let’s calculate the net yield of the bond considered in the previous example.

Gross Yield = [Total Coupon + (Redeem Value−Total Price)] / Total Price = 47.46%

The Total Net Yield will be 47.46% x (1- 0.125) = 41.53%

Annual Net Yield = 41.53% / 4 = 10.38%

How Much Do Bonds Yield?

Bond yields depend on factors such as market interest rates, duration and issuer risk. For example:

• 10-year BTPs: average yield of 3%.
• Short-term BOTs: lower but safer yield.

If a bond offers a gross annual coupon of 4.45% with semi-annual payments, but is purchased at a price of 106 and has a remaining term of 20 years, it is important to consider that, although the coupon seems attractive, at maturity the repayment of the principal will be equal to 100 and not the purchase price of 106.

Consequently, as maturity approaches, it is plausible to expect the price of the bond to tend to decrease towards the repayment value of 100. What is the end result? The effective net yield of this bond, maturing in 20 years, is equal to 3.41% per year and not 4.45%, precisely because the amount repaid by the issuer will be less than the purchase price.

To properly analyze a bond, it is essential to evaluate the reliability of the issuer and calculate the effective yield to maturity (YTM - Yield to Maturity). This indicator does not coincide with the nominal coupon of the bond (in this case 4.45%), but represents the rate of return that equalizes the purchase price of the bond with the present value of all expected future cash flows, including coupons and the repayment of capital.

Monitoring the bond yield is essential to evaluate investment opportunities in the bond market.

Original article published on Money.it Italy. Original title: Rendimento obbligazionario, cos’è e come si calcola?