Professional investors in their work often say that one bond has a high yield to maturity, and the other is low. Based on this judgment, they decide whether to buy a particular security. Novice in the investment business, ignorance and inability to determine the yield to maturity and calculate risks can result in capital losses.
A bond with a coupon or at a discount - what is the difference
There are two main types of bonds by the method of generating 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 such a security that is sold at a price below the nominal, that is, the owner of such a security will receive income in the form of the difference between the purchase price and the sale price.
The yield on both coupon and discount bonds depends on the price at which they were purchased, and their nominal value. It is assumed that payments will be made in full on the specified date, regardless of what the market situation was before, at what price they were sold.
Government bonds and company bonds
The 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 and raise taxes at any time to pay it. Government bonds are issued with a maturity 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 raise funds at a lower percentage than banks offer. The yield on such bonds is most often higher (due to a higher risk) than on government securities. They are issued with a maturity of several months to three years.
Where and how to purchase 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 at a personal visit to the institution at the box office or remotely using modern means of communication. Bonds may have both documentary and non-documentary forms.
Most often, securities are bought at a bank at the current rate or by order of an investor or broker. In this case, one should distinguish between speculation and investment. Speculation is carried out with the aim of reselling the security and making profit due to exchange rate differences, while the speculator can take a loan to buy securities. Investments mean the purchase of bonds and other securities in the investment portfolio for long-term storage, up to the full repayment of the debt by the borrower.
How simple bond yield is calculated
Calculating the yield to maturity of a discount bond is quite simple. The formula for the calculation is as follows:
Profitability = (Tsn-Tsp) / Tsp x 365 / Kdn x 100, where:
Tsn - the price of face value (sale).
CP - purchase price.
Cdn - how many days until the bond is paid off.
As follows from the formula, the yield to maturity rate is not a fixed value, but depends on what price the securities are quoted on the market, as well as the maturity. The longer the loan term, the lower the annual rate of return. However, the cost of the 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 establish a price corridor.
For example, if the Treasury set a maximum rate of 8%, then this is the maximum allowable rate of return. An investor can purchase it with a lower level of profitability, but this already depends on the demand for a security. For example, a bond issued at an initial price of 920 rubles with a par value of 1000 can be bought at a price not lower than the original. Buying it at a price above face value does not make sense.
It also makes no sense to buy bonds, the maturity of which is much more than a year. It can be seen from the above formula that in this case, the percentage of income will significantly decrease.
The formula for calculating a speculative security
If it is acquired not for the purpose of investing, but in order to resell it, then profitability (loss-making) is calculated as follows:
Profitability = (sale price - purchase price) / purchase price.
A negative number means a loss on the transaction. This development of events is rare. Loss on transactions with bonds most often occurs due to the inexperience of the speculator or investor, his impatience or when the bondholder urgently needed money.
Calculation Example
200 government bonds were purchased at a price of 936 rubles apiece. The nominal value is 1000 rubles. Bonds are simple, without a coupon. The repayment term is 1 year.
Payment.
The yield to maturity of the purchased bonds amounted to:
Profitability = (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 an investment. It is necessary to compare the yield to maturity per annum on bonds and the rate per annum on bank deposits and the rate of inflation. This is done in order to assess how justified the risk of buying a bond. 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 bond yields are higher than these two indicators and investing is a profitable capital allocation.
Coupon bond yields how to find out
The yield to maturity on coupon bonds is calculated based on the fact whether it was with a torn off coupon (that is, with a premium paid). or the previous owner did not use it. Note that coupon bonds cost more than discount ones, 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. So, on coupon bonds, payments are made several times a year, what you need to ask when buying. Payments in the category "Current bidding" may be made once a quarter or once every six months. Payments are also made upon closing the coupon bond.
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 discounted debt paper. If a coupon is available, then the following formula is used:
Yield = (premium / purchase price) + (nominal cost - purchase price / purchase price) ^ period to maturity in years)
Coupon bonds without a coupon usually cost the same as discount bonds, although it all depends on supply and demand in the market.
Example of calculating the yield of a coupon bond (with coupon)
The investor, composing the portfolio, acquired 150 bonds with a coupon. The market price of each is 810 rubles plus a premium of 150 rubles. The nominal value of 1000 rubles. The repayment term is 2 years, the premium is paid at the end of the first year.
Decision.
The yield on the bond (in case of non-use of the premium at the time of repayment) will be 1,150 rubles. The yield rate of the coupon bond to maturity from a completed transaction along with the premium will be:
(150/810) + (1000 - 810/810)) ^ 2 = 18.5% + 5.5% = 24%
If the security was purchased after the payment of the premium or the previous owner tore off the coupon, the rate of return on the coupon bond will be:
(1000 - 810/810)) ^ 2 = 5.5% per annum.
As a result, for two years, the owner will receive in the amount of 340 (150 + 190) rubles of income from each bond or 51,000 rubles from invested funds for two years of keeping the bond at home. Of these, 28,500 rubles is income without a bonus.
Possible risks
Bonds are considered risk-free securities. However, the risk of loss of capital (partially or fully) exists. This is the risk of bankruptcy of the issuer (default of the country), inflation and devaluation of the national currency. A vivid example is the situation with the Russian ruble. Foreign investors are in no hurry to buy Russian ruble bonds of the state loan, since a strong depreciation of the ruble has led to the fact that OFZ yield to maturity is negative. Bonds are sold on the stock exchange with a yield of 7-8%, and the ruble fell 20-25% against the dollar and the euro.
There is also market risk. For example, an investor bought a bond with a discount maturity of 1 year for 930 (nominal price 1000 rubles), and it fell in price two hours after the transaction and began to cost 870 rubles. This does not mean that the yield to maturity will become less (the investor will receive a nominal value of 1,000 rubles at the end of the term), just a security could have been bought cheaper and made a lot of profit.
How to calculate risk
To calculate the risk, mathematical multi-factor models are used. To build these models, investors use techniques and methods applicable in mathematical statistics and probability theory. In the implementation of complex calculations, special computer programs are used. The essence of factor analysis is that factors are summarized, and a forecast is made based on their total influence. 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 likelihood of default or inflation growth.
Factors Affecting the Change in Profitability
When calculating the risk of investing in government bonds in a factor model, the following indicators are used:
- The level of growth (decrease) in the country's GDP for the reporting period.
- Inflation rate.
- The amount of government debt.
- The presence or absence of conflicts in the territory of the state.
- The level of public confidence in the government (the likelihood of a revolution or nationalization of the economy).
- Availability of assets: enterprises, mines, farmland, etc.
- The level of industrial development in the country.
- The stability of the exchange rate in which payments are denominated.
- Unemployment rate.
These are not all factors that can be used in analyzing investment risk. To all these factors, the investor gives a numerical value of probability. For example, it was expected that the level of GDP would increase by 2%, while it would grow by 4%. This means that production and tax revenues in the country are growing, that is, the state-issuer will have the funds to pay off bondholders. When calculating the risk of future yield to maturity, the formula has the following form:
Risk = A1 + A2 + A3 + ... + An,
where A1, A2, ... An - these are factors that negatively or positively affect the attractiveness of an object for investing. As sources use statistics (the same Russian Rosstat) and information from rating agencies.
Risk Level Calculation Example
Government bonds of country N are available for sale. The following are factors of attractiveness and unattractiveness of debt securities of this country:
- GDP growth this year was 2%, although 3% was forecasted.
- Trade turnover for the current turnover grew by 7%.
- Farmers suffered losses due to the locust invasion this year. One tenth of the crop died.
- Inflation for basic consumer goods was only 2% instead of the estimated 6%.
- The stock price index 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 growth (decrease) that occurred or assign each factor a certain fraction of the value (at the discretion of the investor). The following is an example of calculation according to the first method, that is, percentages are added up, 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 a concrete example. In fact, investors have to deal with even more factors. They have to process a large amount of information and use various coefficients to determine the ratio of yield to maturity and the risk of buying a bond. But this is the only way to ensure reliable storage of capital.
The relationship between profitability and risk
As you know, there is no big income without risk. This applies to both entrepreneurial activity and investing in securities. Countries issuing OFZs with a high level of yield to maturity, as a rule, have problems in the economy. Such securities are cheap due to low demand from investors.
A high bond yield does not always mean a profitable deal. The most profitable and safe American, British and Japanese government bonds have low yield and high reliability.