I want to try investing in bonds, but previously I only used deposits. Everything is clear there, the rate is specified in the contract.
In bonds, things look more complicated. Please tell us how to correctly calculate the yield on a bond. Does it depend only on the size of the coupon or not?
Bonds are a useful type of securities: the income on them is higher than on deposits. However, these securities themselves are more complex. Let's figure out what types of returns there are, what their value depends on, and how to calculate it all.
Evgeny Shepelev
private investor
Types of bonds by form of payment
The most common type is coupon bonds. A coupon is a payment of interest that occurs at a certain frequency: for example, once every six months. Payment dates are known in advance, but the size of coupons may change over time.
There are also discount securities: they do not pay coupons, but the securities themselves are sold significantly cheaper than their face value. Income can be obtained if the price rises or if the bond is redeemed at par at maturity.
Bonds with a coupon are more popular, so let's look at them using the example of a typical representative - OFZ -26217 with maturity on August 18, 2021. As of October 2, this bond costs 99.3% of its face value, that is, 993 rubles.
Coupon yield
This is money that the issuer is required to pay bondholders periodically. The interest rate of return on a bond with a coupon is easy to calculate:
(Annual coupons / Face value) × 100%
The par value of the OFZ bond is -26217 - 1000 rubles, payments are made every six months in the amount of 37.4 rubles. Coupon yield - 7.5% per year.
Bonds are not always sold at par: their prices change over time. Therefore, calculating the coupon yield does not allow you to know exactly how much an investor will earn on bonds.
Current yield
This is a more accurate indicator, the calculation of which uses not the nominal value, but the net price, without accumulated coupon income. NKD is the part of the coupon that has accumulated but has not yet been paid. When buying a bond, you need to pay its owner the NKD - this is like compensation for the fact that he sells the security without receiving the coupon. But the new owner will receive the entire coupon on the payment date.
The current rate shows how much cash flow a bond purchased at a certain price will generate.
The formula looks like this:
(Coupon income for the year / Net price) × 100%
The yield on OFZ -26217 is equal to (74.8 / 993) × 100%, or 7.53% per annum.
This figure is higher than the coupon rate, since the OFZ price -26217 is lower than the par value. If this OFZ were worth more than its face value, the current yield would be lower than the coupon.
Simple yield to maturity
Many people hold the bonds until their maturity date, when the investor receives the face value along with the final coupon. But it is possible to calculate the yield of a bond at the time of maturity only when the size of all coupons is known.
The repayment rate is calculated using a more complex formula:
((Denomination − Full purchase price + All coupons during the holding period) / Full purchase price) × (365 / Number of days until maturity) × 100%
For OFZ -26217, the simple yield to maturity will be ((1000 − 1001.2 + 224.4) / 1001.2) × (365 / 1051) × 100% = 7.74% per annum.
Effective yield to maturity
If you use the coupons received to purchase additional securities, you can calculate the rate of return on bonds with reinvestment of coupons - approximately the same as an investment with interest capitalization.
It is believed that coupons are invested in new securities at the current rate - the one that was originally. This is an assumption as the price changes over time and actual returns will vary.
You can reinvest a coupon if the income received from coupons is enough to purchase additional securities. Having received 37.4 rubles in the form of a coupon for one OFZ -26217, it will not be possible to buy part of the federal loan bond. But if you have 100 such securities, the coupon payment will be 3,740 rubles. This is enough for 3 additional securities - and there will be more left.
A simple and accurate way to find out the effective yield to maturity is to use a bond calculator on the Rusbonds website or on the Moscow Exchange website. For OFZ -26217, this figure as of October 2 was equal to 7.93% per annum.
To calculate the yield using a bond calculator, you must select a security from the list, indicate the date of acquisition and the net price without accrual. The calculator will also show the current and simple interest rates to maturity, meaning they do not have to be calculated manually. However, taxes, brokerage and depository commissions are not taken into account in the calculator.
The price of a bond depends, among other things, on interest rates in the economy. If the Central Bank raises rates, investors will want to have instruments with higher returns. They will start selling old papers with a constant coupon, and they will become cheaper. If the Central Bank lowers the rate, demand for old bonds will increase and they will rise in price. The shorter the time until the maturity date, the less sensitive the securities are to changes in the key rate. Deduction for contributions. A personal income tax return will increase the return on investment by several percentage points per year, and the deduction can be made to an IIS and the purchase of additional assets.
It’s good if the broker allows you to receive coupons to a bank account, and does not credit them to your IIS. Then you can deposit the coupons into your IIS yourself and then receive a deduction from this money.
ANC on bonds (or Accumulated Coupon Income) is a special parameter that allows you to pay interest income without reference to the maturity date of coupon payments. That is, if you sell a bond in the middle of the coupon period before the coupon payment date, then you will not lose interest for this period, because the person who buys this bond from you will pay you the cash flow accumulated for the specified period.
Surprisingly, NKD can be calculated in different ways; there are a huge number of different methods, but in this article I will give only seven, of which only two are the most significant (according to the list, these are the first and fourth).
The data is listed below methods for calculating NKD. Exactly how an individual issuer calculates the ACI is indicated in the bond prospectus (a special document that specifies the parameters of the bond issue). So, there are the following methods for calculating NKD.
1. 30/360 (one of the most common)
According to this method, there are only 360 days in a year, while each month has strictly 30 days, so the amount of accumulated coupon income will be the same every month. Here, the following formula calculates the difference in days (N) between the coupon payment date (D2/M2/Y2) and the current date (D1/M1/Y1):
N = D2 – D1 + 30 (M2 – M1) + 360 (G2 – G1)
However, there are some reservations about the days. So if D1 falls on the 31st number, then D1 is replaced by 30. When D2 falls on the 31st number, D2 changes to 30 only if D1 falls on the 30th or 31st.
2.30E/360
This method is similar to the previous one (calculated using the same formula), but the caveats are slightly different. So, if D1 falls on the 31st number, then D1 changes to 30. If D2 falls on the 31st number, D2 changes to 30.
3.30/360G
Similar to method No. 1, but the rules for adjusting D1 and D2 are slightly different:
- If D1 is equal to 31, then D1 is equal to 30;
- If D2 is equal to 31, then D2 is equal to 30;
- When D1 falls on the last day of February, then D1 is equal to 30;
- When D2 falls on the last day of February, then D2 is equal to 30.
Last date of February: February 29 in the case of a leap year, February 28 in the case of a non-leap year.
Methods for calculating NKD Actual
4. act/365 (most commonly used)
According to this method, it is believed that there are 365 days in a year, and it does not matter whether it is a leap year or not. For example, if the coupon payment for the whole year is 150 rubles, then per day we will receive 150 rubles/365 = 0.41 rubles. or 41 kopecks. And so every day, it will increase by 41 kopecks. If you hold the bond over the weekend, then on the first working day after the weekend, the NKD will increase by an amount corresponding to the number of days off. According to this type of calculation, the income tax in different months will not be the same, because The number of days in individual months varies.
5.act/360
Identical to method No. 4, but the calculation base is 360 days.
6.act/365L
Similar to method No. 4, but in a leap year the calculation basis is 366 days, in a non-leap year the calculation basis is 365 days.
7. act/act
Also similar to method No. 4, but the number of days between dates is determined by adding the share for a leap year and the share for a non-leap year.
So, we looked at the most commonly used methods for calculating NKD. What value does this information bring to a private investor? Nothing special! Only for a more nuanced understanding of the trading process. In general, this indicator is calculated automatically, and it is not necessary to know all these formulas.
If you are looking for this information in order to check how correctly the issuer calculates coupon payments and whether he is cheating you, then I can reassure you that he will not be able to deceive you, because the calculation of this indicator is controlled by the exchange, which always acts in the interests of the private investor. In addition, the accepted methods for calculating the income tax are prescribed in, violation of which threatens the issuer with damage to the reputation and, as a consequence, loss of business, so of course the issuer will not deceive its creditors.
Bond cash flow is a mechanism for paying interest income on debt securities. It makes it possible to sell them ahead of time without financial losses. To make it more clear, let’s cover the basic terms.
What is a bond
A bond (from the Latin obligation - “obligation”) is a debt security that secures the right to receive funds at par value. In fact, this is a promissory note with the only difference that it is “issued” (issued) by the economic regulator - the stock exchange.
The issue of securities is called an issue, and its owner is called the issuer.
The issuer applies to a registered exchange, which issues debt securities on the market with a certain par value - the value that must be returned at the time the bond expires.
Coupon bond
Investors typically buy securities on stock exchanges in order to make a profit. Or they want to save their capital in reliable financial instruments. Depending on the yield, bonds are divided into the following types:
- Coupons.
- Discount.
- Mixed.
- With a floating interest rate.
We will not describe each type in more detail here. We are only interested in the NKD for bonds. This concept directly applies only to the coupon type. What are these debt securities? 
A coupon bond is a debt security with a fixed interest rate on par. For example, an investor purchased a bond on the market with a par value of 1,000 rubles. for 1100 rub. The payment period for it is one year. At first glance, one might make the wrong conclusion that an investor is acquiring a deliberately unprofitable asset, but this is not the case. He is interested not in the cost of the security itself, but in the coupon on it - the payment of accrued interest for a certain period of time. For a bond of 1000 rubles, our investor will receive income every 3 months, for example, in the amount of 200 rubles. Now an obvious benefit emerges: in one year it will be 700 rubles: 800 rubles. according to the coupon minus 100 rubles. for loss from par value (purchase of 1000 rubles for 1100 rubles).
Now we come to the main concept of our article.
What is NKD on bonds
Our abstract example above is the standard of behavior in the investor market. However, the dynamics on it are such that only a small part of them waits until the end of the terms of payment at par and coupon. Traders, brokers, speculators, investors buy and sell various stocks, bonds, futures, forwards, etc. every day.
NKD on bonds is a recalculation of the coupon yield in the event of a security being sold ahead of schedule. This is reflected in the name itself - accumulated coupon income. That is, the amount that is already due to the investor, but it is still necessary to wait a certain time in order to receive it on schedule. Money, as you know, must constantly work and make a profit. That's why many people sell bonds ahead of time - after realizing that they can make more money on other investment products. The reasons for the sale, of course, may be other. We will not discuss this topic in detail, since it does not relate to ours.
Calculation formula
The NCD is usually located in a special section in the trading terminal. It is also published by various thematic sites, but we will talk about how to calculate the income tax yourself. To do this you need to know the initial data:
- Denomination
- Coupon size.
- Last payment date.
So, NKD is calculated using the formula:
NKD = NO x (C: 100) x T: 365, where:
- BUT is the par value of the bond.
- C - percentage per annum at the coupon rate.
- T - the number of days from the date of accrual of the last payments to the current date.
Let's give an example of calculation
Let's say we bought a coupon with a nominal value of 1000 rubles. The payment percentage is 10% per annum once a year. Let's assume that the previous coupon payments were on May 1, 2017, and we decided to sell the bond on May 10, 2017. We substitute all the initial data into the above formula and get:
1000 x 0.1 x 0.027 = 2.7 rubles.
It follows from this that our bond with a par value of 1000 rubles “earned” 2.7 rubles in 10 May days in 2017. With this in mind, we will sell securities on secondary markets. When purchasing coupon bonds, investors also make calculations to determine their yield.
Taxation
So, we have already said that the income tax on bonds is the income from a coupon bond when it is sold before the due date. Do not forget that the amount received from the NKD is subject to taxation. For ordinary citizens, the tax base when carrying out transactions with securities is subject to a 13 percent personal income tax. However, you need to remember that the purchase of securities along with the already accrued income tax is not subject to taxation.
Example
We bought a bond with a par value of 1000 rubles with the accumulated coupon on it - NKD - 50 rubles. At the time of sale, we received 100 rubles from the coupon. In total, we will pay 13% of 50 rubles earned as income tax.
Federal loan bonds for individuals
In 2017, an event occurred that excited the Russian public: the Ministry of Finance announced the sale of “people’s bonds.” Our citizens already at the genetic level perceive such statements with hostility, since the experience of previous eras showed that trusting our state is a rather risky proposition. Despite this, a new investment instrument has emerged - federal loan bonds for individuals, which, according to the department, is designed for “Russians with below-average income who do not have in-depth knowledge and understanding of the functioning of the financial market.”
Our citizens translated the above phrase into less beautiful words: “for poor fools.” However, the yield on them turned out to be slightly higher than that of a bank deposit and federal loan bonds on the exchanges. We'll talk more about this in the next section.
Yield of "people's bonds"
The yield on federal loan bonds for individuals will be 8.5%. They will not be able to be purchased by legal entities, nor can they be speculated on or resold for profit. In fact, “people's bonds” become an ordinary bank deposit. Many experts immediately questioned why they were needed. They are unlikely to fill the Russian budget, since the volume of emissions is negligible. In addition, the yield on federal loan bonds on the stock exchange is 0.5% lower than that of “public” bonds. 
So far, this has only led to the fact that applications are coming from large wealthy investors, and they have not yet reached ordinary citizens en masse. The head of the Ministry of Finance, A. Siluanov, hopes that such a measure will improve the financial literacy of the population and force them to pull out significant sums from under the pillow. Low inflation does not depreciate the value of this money, so there remains hope that the population itself will invest it in economic development. The concept of “Russian bonds” still remains incomprehensible to most citizens of our country.
NKD or Accumulated Coupon Income is a parameter with the help of which the mechanism for paying interest income is implemented in bonds, i.e. The presence of an NKD makes it possible to buy and sell bonds on the secondary market before the maturity date without losing coupon income.
In other words, the Accumulated Coupon Yield is the part of the coupon income on the bond, which is calculated based on the number of days from the date when the issuer last paid the coupon until the current day. To the concept NKD has become clearer, let's consider this parameter from the point of view of the buyer and the seller.
NCD from the buyer's side
Imagine that you want to buy a bond. You open the quote book and look at the prices, let's say the bond you are interested in is trading at 100% of the par value (bond prices are always expressed as a percentage of the par value). You decide to buy this bond, but to buy it, you will have to pay not 100%, i.e. not the price you see in the glass, but 100%+NKD, why?
Because the person who sells it to you does so in the middle of the coupon period. In other words, the previous owner held the bond for 2 months, during which he accumulated coupon income. The issuer pays the coupon for the security you have chosen once every six months, i.e. you, as a buyer, compensate your counterparty for the income that he has accumulated over 2 months, and when the full coupon period ends (i.e. in another 4 months), the issuer will pay you the coupon in full for 6 months. Thus, you will compensate for the 2 months of NKD that you paid when purchasing the bond, plus you will receive income for 4 months during which you held the bond.
NCD from the seller
Imagine that you have had a bond in your portfolio for 5 months, but you decide to sell it. However, there is still 1 month left until the end of the coupon period (i.e., until the day the issuer pays the coupon on the bond), but you need the money urgently. It turns out that you are selling the bond ahead of schedule, without waiting for the end of the coupon period. How will you generate income? And you will receive income at the expense of the buyer who will buy this bond from you, because your counterparty (or the buyer of your bond) will pay you the price of the bond, for example, 100% plus NKD for the 5 months during which you held this security.
How is NKD calculated?
NKD is always calculated based on the coupon. For example, if an investor buys a one-year with a 10% coupon for 90% of the par value, then in fact he has a simple yield to maturity of 20% per annum (because at the end of the year he will receive a 10% coupon plus 10% income from the exchange rate difference, since he bought at 90%, and repayment will take place at 100%). But if the investor sells the bond without waiting for maturity, then the NKD will be calculated based on the coupon yield of 10%, and not on the yield to maturity of 20%.
The opposite is also true: if the coupon on a bond is 20% of the par value, and the paper was purchased for 110%, then the simple yield to maturity will be equal to 10% (+20% coupon -10% difference in price), however, with an early sale, the income tax will be calculated based on a coupon yield of 20%, not 10%.
Thus, the NKD is always less than the coupon. On the day when the ACI equals the coupon, a coupon payment will occur from the issuer, after which the ACI will be reset to zero and will be calculated again from the new coupon period.
How to find out the size of the income tax before buying a bond
The size of the tax accreditation can be found out in two ways: first, look on the RusBonds website in the “General Information” section in the Questionnaire for the issue of the security you are interested in.
Second, look in the QUIK trading terminal; the necessary information will be reflected in the “NKD” column.
NKD and taxes
The tax agent for income in the form of a coupon is the issuer, i.e. coupon payments are transferred to the investor's account already cleared of tax. If you bought a bond at the beginning of the coupon period and decided not to wait for the coupon to be paid by the issuer, but sold it to someone else (i.e., in fact, this new owner of the bond transferred the NKD to you), in this case the tax on the NKD is withheld broker.
Deposits and interest VS bonds and NKD
The profitability of a bank deposit directly depends on the period for which you “lock” your money; the shorter the period, the lower the profitability. Of course, there are deposits for which money can be withdrawn ahead of schedule, but the interest rate will be significantly lower than the market one.
In bonds, the situation is different, you have the opportunity to choose an acceptable return (market, so that it is minimal, or even higher), while the investment period will not in any way affect the interest rate. In other words, you can keep money in bonds for only 2 weeks, and get the return at the market level. A bank deposit for two weeks will give a return at best two times lower than the market one, or even less. This advantage in bonds is possible precisely due to the presence NKD, allowing you to sell securities ahead of schedule without losing interest income.
A bond coupon is a regular cash payment due to the bondholder that does not reduce* the par value of the securities.
Along with the concept of coupon. Use the concept Coupon rate– this is the total amount of coupon payments for the year calculated as a percentage of the face value.
For example, we bought a bond with a face value of 1000 rubles, on which an income of 25 rubles is paid every three months. We get the coupon size to be 25 rubles. Let's calculate the bet. Income is paid 4 times a year, 25 rubles each. Total 100 rubles per year. As a percentage, it is 10%. Thus, the coupon rate is equal to 10 percent of the face value.
The coupon rate is not necessarily fixed. The rate may be floating and be tied to some publicly announced interest rate (Key Rate, Interbank Lending Rate).
In case of a floating rate. The coupon value is also set in monetary terms. And the bond issuer is obliged to announce the size of coupons for several future coupon periods.
* not reducing because there may be regular payments that reduce the face value of the securities, I call them amortization payments, and the papers are bonds with amortization of the face value.
Who is the coupon paid to?
This logical question arises if we remember that bonds can be bought and sold, i.e. owners constantly change.
At a certain point in time (for example, at the end of the day preceding payment), a list of bondholders is compiled. Payments are made to persons from this list.
However, if this were the entire payment mechanism, it would not be fair, or it would greatly affect the price of the securities. Therefore, there is a mechanism for calculation and accrual.
Legislation
The Federal Law “On the Securities Market” recognizes delay in fulfillment of the obligation to pay the next interest income on bonds for a period of more than ten working days significant violations conditions for fulfilling obligations under bonds. What entails the holder's right to present bonds for early redemption.
Payment schedule
There are no uniform requirements for publication, rules for determining the period and amount of payments.
In general, it can be said that the Issue Decision document will indicate how the size of each coupon will be determined. If the rate is floating, then the method for determining the rate. The payment date can be specified as a specific date (usually for OFZs) or as the i-th day from the start of placement.
The law also requires that such information be publicly available and comply with disclosure standards. Thus, information is published on the issuer's website and the information disclosure page in the news feed (for example, Interfax).
Story
Why is a regular payment called a coupon? The word coupon comes from the French coupon - cut, in turn from couper - to cut. This meant the cut portion of the bond. On the appointed date of the next payment, the holder came to the issuer. A part of the bond (the next coupon) was cut off and the corresponding amount was issued.
The picture just shows a bond, with a cut-off part. Attention question! What total amount of coupons on this bond has already been received by its holder, provided that he (the owner) has not changed since the date of placement? Write in the comments.