What is accumulated coupon income and how to calculate it

Accumulated coupon income on bonds

Investor interest in reliable debt securities is constantly growing in the modern world. This interest is fueled both by the growing in the Russian and global economies, and by the disappointment of investors who had to endure or lose on stock market.

The topic of investing in bonds has long been developed on the blog. Therefore, in this article I will not return to the definition of the instrument, the principles of its functioning and classification. For those who are not yet familiar with the history of analyzing and commenting on the issue, I recommend looking at previous articles about, and. Today I will talk about the accumulated coupon income when owning bonds.

• How does the accumulated coupon income on bonds arise;
• How to Calculate Accumulated Coupon Yield When Choosing an Issuer
• Pros and cons of coupon bonds

What is ACI and how it arises: starting with the basics

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Bonds, as you know, are divided into coupon and discount, purchased at a price below par. Today, almost all bonds traded on the Russian stock market (including OFZs) offer investors coupon income.

coupon bond is a bond whose terms of issue include an obligation to interest payments(coupons) until maturity. The coupon size has a fixed value and is already known before the start of the sale.

(ACI) - part of the coupon income on the bond. It is calculated based on the number of days that have passed since the date of the last coupon payment until the current day.

To present the dry definition more clearly, I made a diagram that shows all stages of a bond's life, from the initial issue to redemption.

The diagram also shows a segment during which the accumulated coupon income is formed, which is included in the cost of the bond and the buyer becomes the owner of it. Thus, the ACI is, as it were, transferred “by inheritance” from the seller to the buyer, who pays the accumulated coupon income.

On the day the coupon is paid, the accumulated amount falls into a brokerage account owned by the current owner of the bond. At the same time, ACI is reset to zero and begins to accumulate again.

To calculate ACI, we need pre-known initial indicators:

• Par value of the bond
• Issuer-Specific Coupon Interest Rate
• The number of days that have passed from the end of the last coupon period to the current (settlement) date.

Based on these data, we derive a simple formula:

• N is the face value of the bond
• C - coupon interest rate in annual terms
• t is the number of days after the end of the previous coupon period.

We substitute as values: 10% coupon yield and a 60-day holding period, and we get an example of a calculation, the result of which will be the amount of ACI we are interested in.

Unfortunately, you will not be able to find out the ACI directly and in finished form on the website or on the website of your broker. There we see the so-called "clean" price. To see the full price, accumulated income must be added to the net price. To do this, you need to use the trading terminal directly, where the indicator of interest to us is presented in a separate column.

You can also turn to partially paid specialized resources. For example, cbonds.ru or rusbonds.ru, the latter being a subsidiary of the Interfax agency. There the NKD is displayed on a separate line in the bond table. By the way, on the site you can freely use the bond yield calculator, even without registering.

Most of the other features on this service that help you get statistics and analyze bonds are unfortunately only available to paid subscribers.

Pros and Cons of Coupon Bonds

This type of payment on securities seems to be the most convenient and fair way to receive income from investments in debt securities. By selling a bond on any day, the investor receives on his brokerage account the entire amount of the accumulated coupon income for the holding period with an accuracy of one day, regardless of the frequency of payments (usually every 3 or 6 months). Thus, the price of the bond becomes fair for both parties to the transaction.

This is good news for an investor who has not previously dealt with coupon bonds and is accustomed to the conditions early closure which the depositor loses all accumulated interest income. On the bond, the investor, as well as the bank, daily accrues interest income, but, in the event of a sale of paper, he retains the entire ACI that was formed by the time of the transaction. The presence of ACI in the cost structure provides the secondary bond market with the necessary debt, otherwise the bidders would have to wait for the redemption date each time.

Coupon income received on the stock market, with the exception of OFZ, (IIA of the second type) and corporate bonds (2017-2020) . The same applies to the NKD. On January 1, 2012, Law No. 368-FZ came into force, according to which brokers received the status and obligations tax agents. Previously, investors had to fiddle with tax returns on one's own. The investor receives the coupon income to the account already in its pure form, minus the tax.

Conclusion

In conclusion, I propose to evaluate the attractiveness of coupon bonds with accumulated income. Involuntarily, a comparison arises with another conservative instrument more familiar to our citizens - a classic bank deposit. Not in favor of the latter - at least 4 characteristics:

• When exiting an exchange paper, unlike a deposit, you do not lose the coupon income accumulated on it.
• In addition to the ACI, you get a potentially higher rate of return, especially if you managed to purchase the bond before the next decline.
• Private investor receives a lower threshold for entering the bond market - from 1000 rubles.
• You are not limited by the term of investment, while the % rate in the bank directly depends on the term.

I think that the popularity of this tool among investors, and among the inhabitants, for whom it was originally created, will only grow. In the comments, I suggest that all investors working with bonds show off their income for the last year.

All profit!

For a long time I wanted to understand what yield to maturity is, but I still couldn’t get my hands on it. It's one thing when a quick / MICEX website shows you some number, like 5.25%, and it seems like it should be correct, but what are those behind it? And what does this mean in practice? There is on the Internet complex formulas returns, and (if you can figure it out) they seem to count about the same, but, again, why are they the way they are received? I would like this percentage, whatever it may be, to be directly compared with the rates bank deposits because it's simple and clear.

1. To see if she really is.
2. In order to take into account the tax on the coupon for corporate papers, as it is not taken into account in the quote.
3. To take into account the commission.
4. To calculate the yield for securities, for which there are no trades on the exchange (there are on the OTC), and therefore 0 is shown in the quick.
5. Can be calculated for any price or date.

I must say right away that the easiest way to calculate the yield is to use the INCOME function in Excel. For example, I will use the GAZPR-34 Eurobond on 01/10/18 with a price of 137.5 and ACI of 17.7292. In this case f-i INCOME gets 4.284% (tax is taken into account here), but at the same time it requires very few parameters:

INCOME(purchase date; maturity date; coupon rate; price; 100; 2; 0)*100.

NKD she considers herself. There is also a separate function for calculating ACI - NAKOPINCOME (). In addition, there are other functions in Excel that may be useful:
COUPONDATE/COUPONDATE AFTER – define the date of the previous/next coupon
COUPON NUMBER - the number of remaining coupons.

At first, I (probably, like many others) assumed that the whole focus here was capitalization and reinvestment of coupons, and even began to calculate profitability in Excel in this way. The figures turned out to be close to those shown by Quick, but still not the same, especially since for some securities they differed significantly.

Then I came up with an interval calculation method in which the entire period of time to maturity is divided into half-year intervals (between coupons), and the yield is calculated for each of them, and then the weighted average yield for the entire period is obtained. Here the assumption is made that the price from the moment of purchase to maturity evenly decreases (or increases) to par. Knowing the number of days to maturity and the current price, you can get the estimated price change for 1 day, and for any number of days, and therefore on the day of payment of each coupon. And knowing the latter, you can get for each interval:

• Amount at the beginning (price)
• Amount at the end (price at the end + coupon)
• difference, percentage and annual interest

For the 1st period itself, the situation is somewhat more complicated by the ACI, but this is not essential. Further, having received for each interval the annual percentage and knowing the price at its beginning, you can get the weighted average annual percentage for the entire time (using the price as a weight, since it changes all the time). The resulting value is already more similar to what the quick shows, but it is also slightly different. The problem is that it begins to noticeably change when there is little time left from the date of purchase to the first coupon, especially if you take into account the commission. The reason turns out to be that since the length of the interval in days is also different; it must also be taken into account as a weight. When you add it to the calculations, the result ceases to depend on the length of the first interval. In Excel, it all looks something like this (personal income tax is not taken into account here):

The problem with this method is that it is based on the assumption that the price goes to par evenly, but in reality this is not the case, and ideally, the definition of profitability should not depend on the price.

At some point I came across a post on this topic anatolyutkin"Eurobonds and deposits", who gave a hint. In fact, everything is written there, but because I don’t have an education in the financial field, so I couldn’t master it right away, especially since Newton’s Bean is used in the calculations, etc., but still I understood the main idea - the current value. It turns out that this is financial term, k-th means how much you need to invest today in order to receive a given amount after some time. The trick is that usually the calculation is done the other way around - we have an amount, for example, 1000 rubles, a percentage (8%), and in a year we get 1080 rubles. And here it is known how much it will be at the end and the percentage, but you need to find how much it was at the beginning.

Well, then the main brain trick is to understand that when you buy a bond (costs = current price + ACI), you kind of open many small deposits for different periods. As many deposits as you receive coupons + 1 more for face value. Each deposit closes when you receive a coupon on it, and all deposits have the same percentage.

But there is 1 nuance here - you need to count as if these deposits have capitalization. In fact, of course, there is none, but this must be done in order for the percentage received to correspond to some generally accepted guidelines. If we need to compare the yield with ordinary deposits, then we can use the annual capitalization. On the other side,

In a number of major markets (such as gilts) the convention is to quote annualised yields with semi-annual compounding

Which means that there is an agreement to indicate the yield with a semi-annual capitalization, so you can calculate it like that. It is clear that due to more frequent capitalization, the percentage of profitability will be slightly lower. In Quick, on the MICEX website and in the INCOME function, the yield is calculated in this way. The formula for calculating the initial amount of a separate contribution for annual capitalization looks like this:

Sum=EndSum / ((1+Rate/100)^Years) / (1+Rate/100*YearPart)

Here EndSum is the coupon or face value, Rate is the desired percentage, Years is the number of full years of the deposit, YearPart is the fractional part of years. For the semi-annual option:

Sum=EndSum / ((1+Rate/200)^YearHalves) / (1+Rate/100* YearHalfPart)

Here YearHalves is the number of full half-years, YearHalfPart is the fractional part of half-years. Further, if we sum up all the initial amounts of these contributions, then we should get a number equal to the initial costs, i.e. current price + ACI. In other words, here it is impossible to get a formula like Rate=… where the yield is calculated by one expression - you need to select different values ​​until the result differs from the required value by the value of the type 0.00001. In Excel, it looks like this (here personal income tax is already taken into account, while for simplicity it is also taken into account in the ACI):
Of course, it is not necessary to calculate the profitability in this way, it is just for understanding. On the Internet you can also find more simple formulas for calculating the yield without summation, in which there is the parameter "total number of coupon payments", but the ACI is not taken into account. In addition, on the MICEX website there is a document “Methodology for calculating ACI and profitability”A that contains a yield formula with the "number of days" parameter. This parameter is divided by the number of days in a year, i.e. the number of years is obtained, so this formula obtains a yield with an annual capitalization, and this not the one the value displayed on the same site for specific securities.

Once again I will say about the misconception about reinvestment - it is not taken into account in the calculation of DP:

A common misconception is that the coupons must be reinvested at the yield to maturity… making this assumption is a common mistake in financial literature and coupon reinvestment is not required for YTM formula to hold.
(Wiki)

It is a chronic error in that it persists in spite of continued attempts to correct it. For example, Renshaw addressed this error fifty years ago … but the reinvestment assumption continues to be replicated. … successive generations of financial professionals educated with the erroneous text have restated the claim in materials intended to educate investors….

Among the sites containing this claim are Bloomberg.com,… Investopedia.com, Morningstar.com, and even the popularly edited Wikipedia.org…
("Yield-to-Maturity and the Reinvestment of Coupon Payments")

The resulting value of DP, for example 4.3%, means only the interest, which is charged on the invested funds only while you own this security. As soon as you received the money (coupon) back, this interest ceases to accrue and his new investments have nothing to do with it. The only difference is that in the case ordinary deposit you get the whole amount back at once with interest, but here, as it were, there are many small deposits at the same percentage and you receive them one by one gradually.

Because we are more accustomed to the situation when the entire amount is returned immediately, we can try to calculate, and the so-called. real yield, taking into account the subsequent (re)investment of coupons (not necessarily in the same securities) to maturity. For each coupon, its reinvestment period is

ReinvDays=EndDate-CouponDate

where EndDate is the maturity date and CouponDate is the coupon payment date. The amount obtained as a result of coupon reinvestment is calculated by the formula:

ReinvSum = Coupon * ((1+ReinvRate/100)^ReinvYears) * (1+ReinvRate/100*ReinvYearPart)

(here it means annual capitalization). If you sum up all such amounts, as well as the last coupon and face value, you get the total amount for the entire period to maturity. Knowing the initial (Sum1=price + ACI) and final amount EndSum, as well as the term, you can choose a rate that will give the following result using the same formula:

EndSum = Sum1 * ((1+RealRate/100)^TotalYears) * (1+RealRate/100*TotalYearPart)

Obviously, in practice, reinvesting at the same rate will not work, so you can simply consider different variants for rate. For the same example with DP = 4.3263%:

• If ReinvRate=0 (coupons are not invested at all), then RealRate=2.96%
• If ReinvRate=3% then RealRate=3.876%
• If ReinvRate=Rate=4.3263%, then the real income will be the same
• If ReinvRate=5% then RealRate=4.567%

As you can see, the reinvestment rate affects the final real return.

Essentially, the yield to maturity is the internal rate of return ( English Internal Rate of Return) for an investor who bought the bond at the market price and intends to hold it until the maturity date ( English Maturity date). In other words, it is the discount rate, the use of which will bring all coupon payments and the face value of the bond to its present value ( market price) Today. Thus, yield to maturity can be found by solving the following equation.

Where P – market price(purchase price) bonds;

n- the number of coupon payments provided that the bond will be held until the maturity date;

C– the size of the coupon payment;

F- face value of the bond;

r- Yield to maturity.

Using this formula, it is necessary to take into account the frequency of coupon payments, which is determined by the terms of the issue. As a rule, these payments are made every six months, much less often annually or quarterly. Therefore, the received yield to maturity sometimes needs to be adjusted to annual terms. To better understand the situation, let's look at an example.

Example. The investor purchased 5 summer bond for 4875 c.u. At the same time, its nominal value is 5000 USD, and the coupon rate is 14% per annum, provided that coupon payments are made every six months. To use the above equation, we need to calculate the size and number of coupon payments. Since payments are made twice a year, and the maturity of the bond is 5 years, the number of coupon payments will be 10 (5 * 2). The coupon rate of 14% per annum assumes that the bond issuer must pay $700 to the investor annually. (5000 * 0.14). However, taking into account the fact that payments are made twice a year, the amount of the coupon payment will be 350 USD. Thus, we can substitute the obtained data into the equation and calculate the yield to maturity.

To solve this equation, you can use various financial calculators or use the "VSD" function of Microsoft Excel, for which the initial data must be presented as follows.

The cost of purchasing a bond, made at the 0-th point, must be recorded in a cell with a "-" sign. After 5 years, along with the last coupon payment, the investor will receive the nominal value of the bond, so the last cell should include their amount of 5350 USD. (5000+350). As a result, we will get a yield to maturity equal to 7.362%.

It should be noted that the resulting yield to maturity is expressed in semi-annual terms. Therefore, in order to present it in annual terms, it is necessary to adjust it taking into account compound interest. For the conditions of our example, it will be 15.266%.

YTM=((1+0.07362)2-1)*100%=15.266%

There is a definite relationship between the price of a bond and its yield to maturity.

1. If the yield to maturity is equal to the coupon rate, then the bond is traded at face value.

2. If yield to maturity is less coupon rate, then the market value of the bond will be higher than the face value, that is, it will be traded at a premium.

3. If the yield to maturity is greater than the coupon rate, then the market value of the bond will be below par, that is, it will be traded at a discount.

Let's illustrate these patterns based on the above example data.

Indeed, if the bond is purchased for 5000 USD, that is, for the face value, then the yield to maturity will be equal to the coupon rate. If the market value of a bond is below $5,000, then the yield to maturity will exceed the coupon rate, and vice versa.

Usage restrictions

The yield to maturity has the same drawback as the internal rate of return. Initially, it is assumed that all received coupon payments are reinvested at the rate of equal yield to maturity, which is extremely rare in practice. In other words, if coupon payments are reinvested at a lower rate, then the yield to maturity will be overstated, and if at a higher rate, then underestimated. Considering that the situation in the capital market is constantly changing, which leads to a constant change interest rates, the calculated results can only be used for a short period of time.

6-15% per annum- in this range is the yield of most bonds at the moment. This is a quick answer, and later in this article it will be written what it depends on. Reading this article is recommended to continue after reading the article.

In fact, the upper limit of bond yield is not limited, but we will not consider the yield of bonds of pre-bankrupt borrowers: the yield on such bonds can exceed 100% per annum, but who will pay them?

A more detailed answer to the question “what is the yield of bonds” might look like this:

• OFZ 25080, which is redeemed in 3.5 months, has a yield of +8.34% per annum.
• OFZ 25081, which matures in 1 year, has a yield of +8.58% per annum.
• OFZ 26219 with maturity in 9 years has a yield of +8.52% per annum.

2) 9-10% municipal bonds(bonds of regions) as of January 2016 Examples:

• Irkutsk region-34001 with maturity at the end of 2021 has a yield of +9.4% per annum.
• Mari El-34007 with maturity in a year and a half has a yield of +9.9% per annum.

3) 7-15% corporate bonds. Examples:

• Bonds of the truck manufacturer KAMAZ PAO BO-05 maturing in 2020 have a yield of +9.9% per annum.
• Bonds of the famous Russian company PJSC NK Rosneft BO-01 maturing in 2024 has a yield of +12% per annum.
• Bonds of "AKB Peresvet-BO-01" of the bank "Peresvet", which recently became the hero of the news (it found a hole) have a yield of + 500% per annum or more, which is typical only for pre-bankrupt borrowers.

Like bank deposit rates, bond yields can fluctuate. It may be unusual here that bond yields may fluctuate constantly, while deposit rates change 1-3 times a year.

Here, for example, as in Lately Sberbank deposit rates changed:

For a year and a half, deposit rates have changed 5 times.

For the most liquid, publicly traded bonds, profitability changes every day. Below you can see a graph of changes in the yield of the same bond for just 6 months:

Within six months, the yield could change from 9.1% to 7.8%.

As you can see, the yield on the horizon of several days does not change significantly, but on the horizon of several months it can fluctuate quite strongly.

In fact, there is a direct relationship between interest rates on deposits and interest rates on bonds - they change synchronously and always in the same direction.

It depends on macroeconomic indicators - key rate Central Bank. This mechanism will be discussed in more detail elsewhere. For now, it will suffice to understand that when rates go up bank deposits, then bond yields also increase., and vice versa.

This news is a little depressing for novice investors: after all, to be interested in alternative ways cautious investors start investing just when the profitability of bank deposits decreases. And if at the same time the yield of bonds decreases, then is it worth changing the needle for soap?

Bonds are more profitable than deposits

In fact, on average, bonds earn more than bank deposits. Anyone can conduct a curious experiment: compare the % yield on deposits of a bank and the % yield on its own bonds.

Take, for example, one of the largest banks - Rosselkhozbank, and its maximum rates by deposits:

"Golden Premium", opened through remote service channels, if the depositor has an "Ultra" or "Premium" service package (payment of interest at the end of the term):

+8,85% per annum for 4 years for amounts of 1.5-5 million rubles (as of February 1, 2017)

If we look for which bonds of this issuer are in circulation with a similar maturity (in 4 years), then we will stumble upon the RSHB-27-ob bond:

Yield +12,8% per annum! The income is almost half more than the income from the deposit in the same bank!

But that is not all. Coupons (interest) on this bond are paid every 3 months (i.e. 4 times a year), while we will receive interest on the deposit only at the end of the term (after 4 years in our example).

The difference between the yields of a bank deposit and interest on bonds is a natural phenomenon, which will be discussed in detail in other materials on this site. Now let's focus on:

• yields on bonds and bank deposits move in the same direction
• bonds can be more profitable than a deposit in the bank

Types of bond yields

Another difficulty in determining the yield of bonds may be that it is always necessary to clarify what yield we are talking about:

• Current (coupon) yield
• Yield to maturity
• Total yield (effective yield to maturity)

Thus, when choosing a bond, we only need to understand what bond yield we have in mind when deciding on this investment.

Current (coupon) yield is the coupon yield.

This type of yield does not take into account possible profits and losses from the revaluation of the value of the bond itself.

An analogy from real life can be connected with an apartment: when we buy an apartment for the purpose of renting it out and do not plan to sell it. We are only interested in the % return on the invested amount. Suppose we bought an apartment for 3 million rubles, and we receive rent payments for 200 thousand rubles. Thus, the “simple yield” of our apartment bond will be 0.2 million / 3 million = + 6.66% per annum.

Yield to maturity- takes into account income not only from coupons, but also from the difference between the purchase price of a bond and the redemption price. Those. Profits are made up of two components:

COUPONS + DIFFERENCE prices

This is the rate of return that an investor will receive if he holds the bond until maturity. Thus, he has the opportunity to earn also on the difference in the prices of the purchase and sale of the bond.

An analogy from real life with an apartment is as follows:

We bought an apartment for 3 years for 2.85 million rubles for the purpose of renting it out, and in three years it will be bought from us for 3 million rubles. Consequently, in three years we will receive rental payments in the amount of 200 * 3 = 600 thousand rubles + a profit of 150 thousand rubles from the difference in the prices of the purchase and sale of the apartment itself.

income will be 750 thousand rubles:

And the yield will be 26.3% over three years (0.75m/2.85m), which corresponds to an annual yield of about +8% per annum.

Effective (total) yield to maturity

This type of return implies that we use our money very efficiently and immediately reinvest all incoming income. To calculate this return, we need an additional parameter: the return on alternative investments.

In this capacity, a deposit in a bank usually acts, and the formula for the total profit takes something like this:

COUPONS + DIFFERENCE prices + REINVESTMENT coupons

Let's go back to our example with a rental apartment: now everything rent payments that we receive, we immediately put it on a bank deposit at 10% per annum (for example) and receive additional income from this, which in three years will amount to about 78 thousand rubles.

income will be 828 thousand rubles:

• 150 thousand from the difference in purchase and sale prices
• 600 thousand from coupon (lease) payments
• 78 thousand from reinvestment of income at a bank interest of 10% per annum

The total yield will be +29% over three years (0.828mn/2.85mn) or approximately +8.9% per annum.

Comparison of yield to maturity and effective (full) yield to maturity shows that, under the same initial conditions, the yield can increase significantly (8.9% instead of 8%) if we invest the proceeds from the bond in a timely manner.

When we find out the yield to maturity of bonds on the Internet, in most cases we will talk about just this type of yield - the effective (full) yield to maturity.

Bond Yield Calculation Example

Take for example a real bond - OFZ 26210. Here are its main characteristics:

• Current price: 97.199% (971.99 rubles)
• NKD: 9.5 rubles.
• Permanent coupon size: RUB 33.91
• Coupon frequency: 182 days
• Date of the next coupon payment: 06/14/2017
• Bond redemption: 12/11/2019 (approximately 3 years)

Current coupon yield:

33.91*2/971.99 = +6.97% per annum (sum of interest income for the year / bond price)

Yield to maturity:

Let's calculate the entire income from owning a bond until the very moment of redemption, for this we need to calculate how many coupon payments we will receive in total for this period. Let's create a payment schedule. For those who have previously taken loans, the phrase "payment schedule" has a somewhat uncomfortable meaning, but in this case the opposite is true: these payments are in our favor 🙂

We need to know the date of the next coupon payment and the frequency of its payment. We see that the next coupon will be paid on 06/14/2017, and the frequency of its payment is 182 days.

There are others. Each of them has its pros and cons. Some of the information may be provided for a fee, and the completeness or convenience of displaying the data also varies.

However, even the free information contained in the databases of these sites is more than enough to make investment decisions.

Here is an example of what you can see on a similar site for a bond of interest to us:

You also need to keep in mind that the methods and methods for calculating profitability may differ. For example, the opportunity return on investment (at what rate we reinvest our coupons) can affect the effective yield to maturity of a bond.

So, in this article we have covered the following questions:

• What is the yield on bonds
• What are the types of bond yields?
• How to find bond yields

To be continued.

I want to try investing in bonds, but I used to only use deposits. Everything is clear, the rate is specified in the contract.

In bonds, things are more complicated. Please tell me 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 by themselves securities more difficult. Let's figure out what types of returns 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 are coupon bonds. A coupon is an interest payment that occurs with 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: coupons are not paid on them, but the securities themselves are sold much cheaper than face value. Income can be received if the price rises or if the bond is redeemed at par at the end of the term.

Bonds with a coupon are more popular, so let's consider them using the example of a typical representative - OFZ -26217 with maturity on August 18, 2021. As of October 2, this bond is worth 99.3% of the face value, that is, 993 rubles.

coupon yield

This is the money that the issuer is obliged to periodically pay bondholders. The interest rate of a bond with a coupon is easy to calculate:

(Annual Coupons / Nominal) × 100%

The face value of the OFZ bond -26217 is 1,000 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 face value: their price fluctuates over time. Therefore, the calculation of 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 face value, but the net price, without accumulated coupon income. ACI is the part of the coupon that has been accumulated but not yet paid. When buying a bond, you need to pay its owner ACI - this is like compensation for the fact that he sells a security without receiving a coupon. But new owner will receive the entire coupon on the payout date.

The value of the current rate shows what cash flow yields a bond bought at a certain price.

The formula looks like this:

(Yearly Coupon / Net Price) × 100%

The yield of OFZ -26217 is equal to (74.8 / 993) × 100%, or 7.53% per annum.

This figure is higher than the coupon rate, as the price of OFZ -26217 is below par. If this OFZ were worth more than par, the current yield would be lower than the coupon yield.

Simple yield to maturity

Many hold bonds until their maturity date, when the investor receives face value along with the last coupon. But it is possible to calculate the yield of a bond at the time of redemption only when the size of all coupons is known.

The rate to maturity is calculated using a more complex formula:

((Denomination − Full price purchase + All coupons for holding period) / Total purchase price) × (365 / Number of days to maturity) × 100%

OFZ-26217 has a simple yield to maturity of ((1000 − 1001.2 + 224.4) / 1001.2) × (365 / 1051) × 100% = 7.74% per annum.

Effective yield to maturity

If you use the received coupons to buy additional securities, you can calculate the rate of return on bonds with coupon reinvestment - something like 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 buy additional securities. Having received 37.4 rubles in the form of a coupon for one OFZ -26217, part of the bond federal loan cannot be bought. But if you have 100 such securities, the coupon payment will be 3,740 rubles. This is enough for 3 additional securities - and more to come.

A simple and accurate way to find out the effective yield to maturity is to use the bond calculator on the Rusbonds website or on the Moscow Exchange website. For OFZ -26217, this figure was equal to 7.93% per annum as of October 2.

To calculate the yield using the bond calculator, you must select a security from the list, indicate the date of purchase and the net price without ACI. The calculator will also show the current and simple interest rates to maturity, so you don't have to calculate them manually. At the same time, 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 the rate, investors will want to have instruments with higher returns. They will start selling old papers with a permanent coupon, and they will fall in price. If the Central Bank lowers the rate, the demand for old bonds will increase and they will rise in price. The less time until the maturity date, the less sensitive the securities are to changes in the key rate. Deductible for contributions. Return of personal income tax will increase the return on investment by a few percentage points per year, and the deduction can be paid to IIA and buy additional assets.

It is good if the broker allows you to receive coupons to a bank account, and does not credit them to the IIS. Then the coupons can be independently deposited on the IIS and then receive a deduction from this money.