Yield to maturity: calculation methods, formula, indicators, examples

2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16

Professional investors often talk about how one bond has a high yield to maturity and the other has a low yield. Based on this judgment, they decide whether to buy a particular security. For a beginner in the investment business, ignorance and inability to determine yield to maturity and calculate risks can result in capital losses.

Coupon or discount bond - what's the difference

There are two main types of bonds according to the method of obtaining income: coupon and discount. The difference between the first and the second is that coupon bonds are paid twice. The first time on the coupon, and the second time completely on paper. A discount bond is a security that is sold at a price below par, that is, the owner of such a paper will receive income in the form of the difference between the purchase price and the sale price.

The yield level of both coupon and discount bonds depends on the price at which they were purchased, what is their face value. It is assumed that payments on them will be made within the specified period.completely, no matter what the situation was on the market before, at what price they were sold.

Government and corporate bonds

Yield to maturity of a bond can be calculated and paid in rubles or in foreign currency (Eurobonds). The most secure (risk-free) are government securities issued by the Federal Treasury, since payments will be made on them in any case. The government can print money at any time and raise taxes to pay for it. Government bonds are issued with maturities of 1, 2, 5, 10 and 20 years.

Bonds can be issued not only by the Federal Treasury, but also by some large private companies or corporations. This makes it possible to attract funds at a lower interest rate than banks offer. The yield on such bonds is often higher (because of the higher risk) than on government securities. They are issued with maturities ranging from a few months to three years.

Where and how can I buy bonds

An investor can purchase debt securities at bank branches, on the stock exchange, from individuals or legal entities that sell them outside the stock market. They can be purchased during a personal visit to the institution at the box office or remotely using modern means of communication. Bonds can be in both documentary and non-documentary forms.

Most often, securities are bought at the bank at the current rate or atthe order of the investor or broker. A distinction must be made between speculation and investment. Speculation is carried out with the aim of reselling a security and making a profit from the exchange rate difference, while the speculator can take out a loan to purchase securities. Investments mean the purchase of bonds and other securities in an investment portfolio for long-term storage, up to the full repayment of the debt by the borrower.

How the yield of a simple bond is calculated

Calculating the yield to maturity of a discounted bond is quite simple. The formula for calculating is as follows:

Yield=(Cn-Cp)/Cp x 365/Cdn x 100, where:

Tsn - face value (sales).

CPU - purchase price.

Cdn - how many days until the maturity of the bond.

As follows from the formula, the yield to maturity rate is not a fixed value, but depends on the price at which the securities are quoted on the market, as well as on the maturity. The longer the loan term, the lower the annual rate of return. However, the value of an issued debt security is affected not only by the ratio of supply and demand, but also by the financial policy of the state, which can set a price corridor.

For example, if the Treasury has set a maximum rate of 8%, then this is the maximum allowable rate of return. An investor can buy it at a lower rate of return, but this already depends on the demand for the security. For example, a bond issued at the original price of 920 rubles with a face value of1000, you can buy at a price not lower than the original one. Buying it at a price above face value does not make sense.

It also makes no sense to buy bonds with maturities significantly longer than a year. From the above formula, it can be seen that in this case, the percentage of income will decrease significantly.

Formula for calculating a speculative security

If it is purchased not for the purpose of investment, but in order to resell it, then the profitability (loss) is calculated as follows:

Yield=(selling price - buying price) / buying price.

A negative number means a loss on the trade. This development rarely happens. Losses on transactions with bonds most often occur due to the inexperience of the speculator or investor, from his impatience, or when the bond owner urgently needs money.

Calculation example

200 government bonds were purchased at a price of 936 rubles apiece. The nominal value is 1000 rubles. The bonds are simple, no coupon. Maturity 1 year.

Calculation.

Yield to maturity on purchased bonds was:

Yield=(1000-936/936) x 365/365 x100=0.068, which is 6.8%.

Income from the purchase of 200 bonds amounted to 12,720 rubles.

However, this is not enough to calculate the level of profitability and profitability of investments. It is necessary to compare the yield to maturity per annum on bonds and the annual rate on bank deposits and the inflation rate. This is done in order to evaluatehow risky buying a bond is justified. At the time of calculation, the bank rate on deposits with Sberbank for a period of 1 year was 3.5%, and the inflation rate (according to Rosstat) was 4.5%. This means that the yield on the bond is higher than these two indicators and the investment is a profitable investment of capital.

Coupon bond yield how to find out

Yield to maturity on coupon bonds is calculated based on the fact whether it was with a torn coupon (that is, with a paid premium). or the previous owner did not use it. Note that coupon bonds are more expensive than discount bonds, for example, the price of a paper with a face value of 1000 rubles can be 980 rubles. That is, the profit from each bond will be only 20 rubles per year. However, there are some nuances here. So, for coupon bonds, payments are made several times a year, which you need to ask when buying. Payments in the "Current Trades" nomination can be made once a quarter or every six months. Also, payments are made when the coupon bond closes.

If it is sold without a coupon (the previous owner already used it), then the formula for calculating the yield to maturity of a bond is exactly the same as for a debt security with a discount. If there is a coupon, then the following formula is used:

Yield=(premium/purchase price) + (nominal value - purchase price/purchase price)^maturity in years)

No-coupon coupon bonds usually cost the same as discounted bonds, although it all depends on supply and demand in the market.

An example of calculating the yield of a coupon bond (with a coupon)

An investor has purchased 150 bonds with a coupon while compiling a portfolio. The market price of each is 810 rubles plus a premium of 150 rubles. The nominal value is 1000 rubles. Maturity is 2 years, premium is paid at the end of the first year.

Decision.

Income on the bond (if the premium is not used at the time of redemption) will be 1150 rubles. The rate of return of a coupon bond to redemption from a completed transaction, together with a premium, will be:

(150/810) + (1000 - 810 / 810))^2=18.5% + 5.5%=24%

If the security was purchased after the premium was paid or the previous owner tore off the coupon, then the yield rate of the coupon bond will be:

(1000 - 810/810))^2=5.5% per annum.

As a result, in two years the owner will receive a total of 340 (150+190) rubles of income from each bond or 51,000 rubles from invested funds for two years of holding the bond. Of these, 28,500 rubles is income without a premium.

Possible risks

Bonds are considered risk-free securities. However, the risk of capital loss (partially or completely) exists. This is the risk of bankruptcy of the issuer (country default), inflation and devaluation of the national currency. A striking example is the situation with the Russian ruble. Foreign investors are in no hurry to buy ruble-denominated Russian government bonds, as a strong depreciation of the ruble led to the OFZ yield to maturitynegative. On the stock exchange, bonds are sold with a yield of 7-8%, and the ruble has fallen against the dollar and the euro by 20-25% over the year.

There is also market risk. For example, an investor bought a bond with a discount with a maturity of 1 year for 930 (nominal price 1,000 rubles), and two hours after the transaction, it fell in price and began to cost 870 rubles. This does not mean that the yield to maturity will be lower (the investor will receive a face value of 1,000 rubles at the end of the term), but the security could have been bought cheaper and made a bigger profit.

How to calculate risk

Mathematical multifactorial models are used to calculate the risk. To build these models, investors use techniques and methods applicable in mathematical statistics and probability theory. When performing complex calculations, special computer programs are used. The essence of factor analysis is that the factors are summarized, and based on their total influence, a forecast is built. This makes it possible not only to determine the yield to maturity of the bond, but also to predict the development of negative events, the probability of default or rising inflation.

Factors affecting yield changes

When calculating the risk of investing in government bonds in the factor model, the following indicators are used:

• The level of growth (decrease) of the country's GDP for the reporting period.
• Inflation rate.
• Government debt.
• Presence or absence of conflicts in the territorystate.
• The level of public confidence in the government (probability of revolution or nationalization of the economy).
• Availability of assets: enterprises, mines, farmland, etc.
• The level of industrial development in the country.
• Stability of the exchange rate in which payments are nominated.
• Unemployment rate.

These are not all factors that can be used in investment risk analysis. The investor assigns a numerical value of probability to all the listed factors. For example, it was expected that the level of GDP would increase by 2%, but it grew by 4%. This means that production and tax revenues in the country are growing, that is, the issuing state will have the funds to pay off the bond holders. When calculating the risk of future yield to maturity, the formula is as follows:

Risk=A1+A2+A3+…+An, where A1, A2, …An are factors that negatively or positively affect the attractiveness of an object for investment. As sources, they use statistical data (of the same Russian Rosstat) and information from rating agencies.

Example of risk level calculation

Government bonds of country N are on sale.

1. GDP growth this year was 2%, although 3% was predicted.
2. Trade turnover for the current turnover increased by 7%.
3. Farmers have suffered losses due to the locust invasion this year. One tenth of the crop was lost.
4. Inflationfor basic consumer goods was only 2% instead of the expected 6%.
5. The index of prices for shares of large companies and corporations rose by 50 points or 2.2%.

Decision.

It is necessary to determine the weight and level of influence of each factor on the financial stability of country N. In this case, two approaches are used: they use the percentage increase (decrease) that occurred or assign a certain share of value to each factor (at the discretion of the investor). Below is an example of calculating the first method, that is, percentages are added and negative values are subtracted.

-1 + 7 + (-10) + 4 + 2, 2=0.8%

This means that there are more positive factors than negative ones. But this is only in a specific example. In fact, investors have to deal with even more factors. They have to process a large amount of information and use various ratios to determine the ratio of yield to maturity and the risk of buying a bond. But this is the only way to ensure the safe storage of capital.

Relationship between return and risk

As you know, there is no big income without risk. This applies both to entrepreneurial activity and to investing in securities. Countries that issue OFZs with high yields to maturity tend to have economic problems. Such securities are cheap due to low demand for them from investors.

High bond yields don't always meanthe profitability of the deal. The most profitable and safe American, British and Japanese government bonds have low yields and high reliability.