Calculation of the yield of a portfolio of bonds. Bond Portfolio Yield Calculation Calculate Bond Yield to Maturity Calculator

This is a system that, based on the price of a bond, allows you to calculate the indicators of yield, duration and other parameters that reflect the current market situation of a particular security. All this as a result makes it possible to make an informed decision regarding investments in these bonds.

There are two bond market websites where you can find bond yield calculator: rusbonds and cbonds. The second option is paid, so it's better to use rusbonds, the calculator itself.

The convenience of the calculator lies in the fact that with its help (as well as with the help of the issue questionnaire) you can make the final decision whether to invest in a particular bond or not. But here it is better to choose an object for study through.

How to do it? Building a quote table Current trades” in Quick and rank it by the column “ Yield”, we look for a bond with the level of income we are interested in, look at its market price, and then go to the calculator. Quick reflects only the effective yield, but the calculator calculates all types of yields, and also provides other useful information for a particular bond issue.

How to use the bond yield calculator

So, going to the calculator page, the first thing to do from the drop-down list " Name» You must select the bond that you selected in Quick by yield. Further in the field Price calculation» « net price"You need to drive in the market price that is currently available (the market price in Quick is reflected in the column" Last Traded Price"). Press the button " Calculate».

Information on this bond issue will appear below. The figure below shows the result of the calculation for bonds MTS 8th issue, the net price of which, as of the date of writing, was 100.5% of the face value.

Now I will explain separately each line and each figure shown in the table.

RELEASE PARAMETERS

• Maturity date – the day when the issuer will fully redeem this bond issue;
• Date of the next offer– the day when you can present the bond for redemption, i.e. in fact, this is the date of early repayment;
• Coupon type is variable, i.e. the coupon yield is known in advance only partially, (paragraph 3.2);
• Current rate, %– coupon size in this bond issue;
• Coupon payment – ​​the date of the next coupon payment redemption;
• Calculation basis - .

CALCULATION RESULTS

• Net price as a percentage of face value- the value that we drove into the bond yield calculator is the price excluding ACI;
• Full price in % of face value– price including ACI, the price that you will have to pay if you buy a bond today (on the coupon payment date, that part of the ACI that you paid to the seller will be fully compensated by the issuer);
• Net price in rubles;
• in rubles;
• Full price in rubles - net price in rubles. + ACI in rubles;
• Yield current modified in % per annum- reflects the annual income from coupon payments, taking into account purchases cheaper or more expensive than the face value (you can read more about it in the corresponding article);
• Yield current in % per annum- annual coupon income. This value actually means the same as the coupon, only in the case of a coupon of 10.75% it is assumed that the bond was purchased at 100% of the face value, if you buy at a different price, for example, as in my example, at 100, 5%, then the coupon yield will be slightly lower (i.e. 10.69%) due to the higher purchase price. If you buy for 90% of the face value, then this yield will be 11.94%.

• Effective yield, % per annum– takes into account all possible types of income from a bond: coupon payments, redemption at face value, as well as profit from reinvestment of coupon payments in the same bonds;
• Simple yield in % per annum– takes into account redemption at par and coupon yield;
• Duration in days - on the one hand, this is the payback period of investments, and on the other hand, the riskiness of this paper (more about);
• Modified duration in % - how much the price of the bond will change when the key interest rate changes by 1% (more about);
• , % is a measure of the sensitivity of the yield curve to changes in the interest rate. This indicator is not of great importance for a simple investor;
• PVBр in rubles – by how much the price of a bond in rubles will change if the yield changes by 0.01%.

The same calculations follow, only for DATE OF THE NEXT OFFER– the data is relevant if you plan to redeem the bond ahead of schedule on the date of the proposed offer.

Bond yield calculator - what points are important to consider?

Thus, we have examined in detail each item of the bond calculator. However, in order to get a complete picture of the selected bond, it is also necessary to study the questionnaire of this issue. There is a link to it in the header of the calculator (see above in figure No. 1). From the questionnaire you need to find out if there are bonds, if there is, then the yield will not be entirely correct, in reality it will be lower, because. Interest will be charged on the balance of the debt.

In addition, it is necessary to check in the questionnaire what type of coupon is available in this bond, if the coupon is floating, then it makes sense to analyze the bond yield calculator only in the section “ Settlements by the nearest offer date”, because calculations to maturity will be incorrect due to the fact that the coupon changes periodically and it is not known in advance.

It is also important to understand that if you want to hold a bond before the offer, then you need to not miss the moment when you can present the paper for early redemption, i.e. if you hold the bond to maturity, then at the end of the term everything will happen automatically: the broker will write off the bonds and credit the corresponding amount of money. If you want to sell the bond on the offer date, then you need to write an application addressed to the issuer with your broker, and if this is not done, the bond will remain in the portfolio until the maturity date.

So, bond yield calculator it is a useful tool in the arsenal of a reasonable investor, which makes it possible to understand what kind of return an investor will receive when buying a bond below or above par value. In addition, it allows you to assess the risk of investing in this bond, and get more information about the selected security (in the issue questionnaire).

To begin with, if you need to know the accumulated coupon income for the current date, you can always see it on the website of the Moscow Exchange moex.com or on the website of the Interfax agency rusbond.ru

Do not be surprised by the fact that the ACI values ​​on the Moscow Exchange website and the ACI values ​​on the Interfax website differ from each other. This is due to the mode of trading on the Moscow Exchange. Federal loan bonds are traded in the T+ mode, that is, with settlements postponed to the next trading day. Therefore, ACI on the website of the exchange for OFZ is always greater than the value on the website of the Interfax agency.

Important Afterword

The calculation method presented in the article is not suitable for all bonds. The number of days of the coupon period can be calculated in different bases. Recently, I came across a manual with a method for calculating bond yields and accumulated coupon income on the Moscow Exchange website. I don’t remember in which section of the exchange portal I found it, so I post it here for free download.

In the archive offered for download, in addition to the methodology, I have attached an Excel file with charting for stocks. Here is a link for download: Methodology for calculating ACI and profitability download

I welcome your opinions and personal experiences in the field of bonds when you share them in the comments on this article. I will also be happy with questions and will try to find answers to them, or maybe they are already known to me - ask questions in the comments to the article, do not be shy, I will answer everyone.

That's all for today, my dear readers.

The current yield of a bond is the ratio of periodic payments to the purchase price of the bond. Since coupon bonds are traded, as a rule, at a price higher than face value, the current yield will be lower than the coupon rate for this bond. If the bond is trading at a price below par, then the situation will be reversed. Accordingly, with the help of a financial calculator, having determined the current yield of a bond, you will get an idea of ​​what yield in % per annum you can expect on this bond.

Total: Bond current yield: enter the % per annum data.

Bond yield to maturity

A bond's yield-to-maturity calculator is an interest rate at a discount rate that equates the advertised coupon stream to the bond's current market value. This indicator is calculated on the assumption that you intend to hold the bonds to maturity. The more expensive you bought a bond, the lower the yield to maturity.

Total: Bond yield to maturity: enter the % per annum data.

Bond Yield to Sell

A bond's yield-to-sale calculator is an interest rate at a discount rate that equates the advertised coupon stream to the bond's current market value. The more expensive you bought a bond, the lower the yield to sell.

Total: Bond Yield to Sell: enter the % per annum data.

The current price of the bond

A financial calculator of the present (current, fair) value of a bond is an estimate of how much a bond, the parameters of which are known, should cost at the present (or current) moment.

Total: The current price of the bond: Enter RUR information.

Amount of coupon yield on a bond

The calculator allows you to calculate the amount of coupon payment for 1 bond, which you can count on, keeping it until the coupon payment date.

Total: Amount of coupon yield on a bond: Enter RUR information.

Accumulated coupon income

The calculator allows you to calculate the amount of accumulated coupon income on a given date for 1 bond, i.e. the amount that will have to be paid in addition when buying 1 bond on a given date.

Total: Accumulated coupon income: Enter RUR information.

Advantages

The main advantages of a bonded loan:

• investments of large amounts of money without the threat of interference of bondholders in the management of the organization;
• attracting funds from private investors (the public) and legal entities for a sufficiently long period and possibly on more favorable terms than shares and other securities;

compared to a loan low cost of borrowing, the term of attracting investments through the issuance of bonds exceeds the term of the loan, no need for surety or collateral, low degree of dependence on the creditor by attracting a wide range of buyers in the bond market, the possibility of attracting a significant amount of money.

AT difference from stock, which represents the equity capital of a joint-stock company, a bond is a representative of borrowed capital. Shares are issued only by joint-stock companies, bonds - by any commercial organizations and the state.

Bond face value- the amount of money indicated on a security that the issuer borrows and promises to repay after a certain maturity and under certain conditions of interest rate.

By deadline- there are urgent and indefinite.

Kinds

government bonds- securities issued to cover the budget deficit on behalf of the state or local authorities, but necessarily guaranteed by the government.

The state establishes issue rate - the price at which bonds are sold to banks. The market price is the price at which they are sold and bought on the loan capital market.

Corporate bonds- securities issued by corporations (legal entities) for investment in their activities. As a rule, they are long-term debt instruments with a maturity of more than a year.

coupon bonds- securities containing cut-off coupons, on which interest income is accrued and paid after a specified period.

Bond Calculator is a great tool for investors who use bonds in their work. With it, you can calculate your financial result from owning bonds both in nominal and percentage terms. At the same time, the calculator takes into account taxes and commissions of the broker, that is, you can immediately estimate your “net” income.

The calculator can also compare different bonds with each other to make it easier for you to make the best choice. And also calculate the price at which you need to buy a bond in order to get the desired yield. All you need is to enter the initial data.

Appearance:

The calculator consists of several blocks:

• Income
• Expenses
• Coupons and amortization
• Payment schedule
• Financial results
• Yield

Yellow fields are for data entry. All calculations are based on them.

How does the calculator work?

The calculator is an MS Excel file. In it you will find the calculator itself, detailed user instructions and examples. To calculate the yield, you need to enter the initial data in the yellow cells, it takes no more than 2 minutes of time (it is recommended to take the data from the Rusbonds.ru website):

• purchase costs (nominal value, price, date, ACI, number of securities);
• income from sale/redemption (date, price, ACI);
• coupon income (dates and bond coupon or depreciation of face value).

Calculations occur automatically as the cells are filled.

You can purchase four versions of the calculator to choose from: Lite, Full, Max and Ultra.

To order, enter in the payment form the price for the selected version of the calculator (Ultra version is selected by default), the type of payment (Yandex wallet, bank card) and click the Transfer button, specify your email. The calculator will be sent to your email within 24 hours.

Many investors seek to invest their money more profitably than in a bank deposit, but at the same time they do not want to go into the intricacies of exchange trading. Bonds are the ideal investment option in this case. It is these securities, in their essence, that represent exchange analogues of bank deposits, since they have a final maturity date and a regularly paid interest - a coupon (as a rule, either once a quarter or once a half year). In addition, they, like deposits, allow investors not to worry about sudden price changes (unlike stocks) and, by the way, can also be secured and guaranteed.

At the same time, it should be taken into account that, by investing in bank deposits, an investor a priori accepts the risk of the banking sector, which may increase from time to time. When investing in bonds, the investor himself chooses the industry and the issuer, that is, he gets the opportunity to diversify his bond portfolio much more widely. In other words, invest in the most reliable bonds of the Russian Federation (OFZ), and in various municipal securities, which have extremely high reliability and at the same time increased profitability, as well as in corporate bonds of various companies, the yield of which often overtakes bank deposit rates. In the process of such diversification, the investor collects a whole portfolio of bonds, and it is not always clear what profitability this portfolio will demonstrate.

Types of bond yields

Based on the fact that any portfolio consists of securities included in it, it is important to understand how the yield of the bonds themselves is calculated and what it happens to be. First of all, it should be noted that bonds are coupon (when cash is paid every period - interest) and discount (the paper is traded cheaper than its face value - the redemption price, in practice it is less common).

The method of calculating coupon and discount bonds is somewhat different. The formula for calculating the yield of discount type bonds is as follows:

D \u003d (N-C) / C * 365 / Dn * 100, where:

D is the yield of a discount bond,
. H - redemption price (sales),
. C - purchase price,
. Days - the number of days until maturity.

So, for example, if we buy a discount bond for 900 rubles. (90%), the face value of which is 1000 rubles, and in a year the paper is redeemed, then we will have:

(1000-900)/900* 365/365 *100 = 11.1% return.

It is worth noting that if, for example, the repayment of such a paper is not in a year, but in two years (730 days), then the yield of the paper will be less - 5.55%, since no intermediate payments are provided for discount papers.

With coupon bonds, the situation is a little more complicated. First, it is worth considering that a coupon bond can be purchased at a price different from the redemption price (that is, buying it, for example, at 980 rubles (98%) with a face value of 1000 rubles, we will earn 20 rubles, or 2.04% of the invested amount) and thereby earn more on the “body” of the bond. But in addition to the "body", in such bonds there are also coupon payments that are made with a certain period specified in days in the "Current Trades" table as "Coupon Duration" (as a rule, 70% - 182 days (half a year) and 30% - 91 days (quarter)). Also included in this table are:

Coupon sizes (in rubles) in the "Coupon size" column,
. coupon payment date in the same column in the format dd.mm.yyyy,
. accumulated coupon income in the column "ATC" in rubles (money received by the bondholder for the holding period of the last coupon period when selling before coupon payment),
. "Nominal" - the amount of money paid to holders upon redemption for one security,
. "Repayment date" - the date on which the face value will be paid,
. "Demand" - the best bid price (indicated in% of the nominal value),
. "Offer" - the best offer price (also indicated in % of the face value),
. lot (number of papers in a lot 99% - 1 paper - 1 lot),
. percentage change from the close of the previous session (same as in stocks),
. "Profitability", the calculation methods of which are discussed in this article.

Table.1 Current trades with parameters for bonds

Looking at these columns, you can determine the number of coupon payments per year by dividing 365 (the number of days in a year) by the value of the coupon duration (for example, 182). The resulting value will be two. Then we can multiply the value of the coupon size (for example, 65 rubles) by the number of payments per year (for example, 2), thereby obtaining the total amount of money paid to us on the bond for the year (65 * 2 = 130 rubles).

To understand what yield can be obtained in this case, it is necessary to correlate the money received on coupons to the purchase price of the bond - such a yield will be called the "current bond yield".

The formula for calculating the yield to maturity of a bond

Calculation of the current yield of bonds is made according to the formula:

D \u003d Kv / C * 100, where:

Kv - the amount of coupon payments,
. C - purchase price.

That is, buying a security for 1000 rubles. (100% of the face value) and having earned 130 rubles, we get the current yield equal to 13% (130/1000*100).

But it is worth considering that a bond can be bought at a different price than the face value, and held for more than one year (for example, 2 years or until maturity), and continue to receive coupon payments.

The calculation of such yield will be made according to the formula for calculating the yield to maturity of a bond:

D \u003d ((N-C) + Kv) / C) * 365 / Dn * 100, where:

H - face value (or subsequent sale price),
. C - paper price,
. Kv - the amount of coupon payments for the period of ownership of the paper,
. Days - the number of days of holding.

That is, if you take paper for 980 rubles. (98%), a total of 130 rubles is paid per year. coupons, and the planned holding period is 730 days, it will turn out: ((1000-980)+260)/980*365/730*100=14.28%.

Now, having knowledge of the methods for calculating the yield of bonds, we can talk about the calculation of the yield of a bond portfolio. The portfolio return is defined as the share of invested funds for the return on this share:

Dp \u003d ∑Share i * Di, where:

Dp - portfolio return,
. Sharei - the share of funds invested in the i-th security,
. Di - profitability of the i-th share.

That is, if the portfolio consists of two bonds - with a yield to maturity of 12% and 13%, respectively (maturity is 1 year), then it is necessary to determine the share of each paper in the portfolio (if there is free cash, then their share too). Let's say that 30% of cash was invested in paper No. 1 with a yield to maturity of 12%, and 60% of cash was invested in paper No. 2 with a yield to maturity of 13%. Another 10% is left in the form of cash. The formula for calculating the return on such a portfolio will be as follows: 0.3*12+0.6*13+0.1*0=11.4%. That is, the total return on a portfolio of bonds is the sum of the returns on the shares included in this portfolio.

Conclusion

The formula for calculating the return on a bond portfolio is the same as the formula for calculating the return on a portfolio in classical portfolio theory. The main difference between stock and bond portfolios in terms of determining returns is that the return on a stock is defined as the “direction vector of its price movement”, while in bonds, the return to maturity (or for the holding period) is determined.