To calculate the profitability of a security, it is necessary to compare the income received on it (analogous to interest money) with the purchase price (initial investment). In the case when the full income for the entire storage period, received by the investor both in the form of dividends (d) and due to the difference in sales prices (C 1) and purchase prices (C 0), is taken into account, we speak of total profitability:

From the market position, the selling and purchasing prices mentioned in definition (1) by the investor coincide, respectively, with the purchasing and selling prices of the market, i.e., with the so-called market demand (ask-price) and market supply (bid-price) prices in stock market practice ). In reality they are not the same.

By buying securities from some and selling them to others, stock market through its professional traders (dealers, settlement firms, brokers, etc.), charges fees for intermediary services, extracting it from the excess of the sale price (ask-price) over the purchase price (bid-price), i.e. buys cheaper than sells. If we take into account the difference (spread) in these prices (bid-ask spread) for the same point in time, we arrive at a refined formula for efficiency (total profitability):

In contrast to this indicator, another characteristic is widely used by stock market participants - the current yield indicator, which takes into account only current income calculated at the current exchange rate:

It is assumed that the investor’s profit is formed only from current income (portion payments provided for the security for the period of their accrual), and there is no speculative income derived from possible resale.

Thus, for bonds purchased at a discount, for example for state bonds, the current income is determined by the difference between the par value and the current quote on the secondary market, in the case of coupon bonds - by the income paid on coupons; When determining current income on shares, only dividend payments are taken into account.

This meter is convenient for assessing the current market conditions of both securities traded on the market and those held by the investor (in the denominator calculation formula(2) it is not the purchase price that costs, but the current exchange rate).

When solving specific problems, the formulas for profitability indicators (1), (2) are specified both by type of securities (various types of bonds, shares, futures contracts, etc.), and depending on the dynamics of the exchange rate, the duration of the period taken into account, the flow of dividends . In the literature, simplified dependencies are often proposed for practitioners (employees of investment institutions, stock exchanges and other market participants), which lead to rough estimates, in particular without taking into account time and risk.

If necessary, you can take into account the impact of taxes by adjusting income by the amount of tax withdrawal. As a result, we arrive at profitability indicators taking into account taxation:

BONDS

These debt securities are characterized by:

• 1) nominal value;
• 2) maturity date;
• 3) coupon, i.e. interest payments that are made at certain intervals throughout the bond's circulation period.

The coupon rate on a bond is calculated in relation to the face value, regardless of the market rate of the bond:

Various types of bonds are used in practice:

• · zero-coupon, for which no coupon payments are made, but only the nominal value is paid at the time of redemption (for example, government papers-- GKO);
• · coupons that are purchased and redeemed at par (for example, OFZ-PK), etc.
• 1) Let us estimate the current return on investment in a zero-coupon bond with a par value of P and a market value of C = 95%, when purchased for the entire remaining period until maturity equal to T days - Here, according to the regulation stock exchanges, the bond rate is indicated as a percentage of its face value.

Obviously, to calculate the current yield to maturity at the simple interest rate, you should use the formula:

So, if there are 40 days left until maturity, then the current yield

The same formula is valid for the return on the placement price at the primary auction. The effective yield indicator used in the GKO market is based on the concept of an effective rate, calculated using the formula compound interest:

where S(O) is the amount issued;

S(T) - the amount received under any payment scheme;

T is the time (in years) for which the income was received.

For three-month GKOs, such a rate actually implies the possibility of quadruple reinvestment of C’s contribution in this market. So, with C = 80% of the ratio

2) A bond issued with a par value of 100,000 rubles, with coupon rate 8% for 5 years, sold at a 20% discount. Then for a bond holder who realizes his income in the form of a discount when it is repaid by the issuer according to (1, 2),

In this example, we can arrive at a more accurate estimate of the total return, which takes into account the disparity in the value of the money flowing to the bond owner in different years. To do this, it is necessary to calculate the income accrued by the investor by the end of the five-year period, which is formed by accruing interest on successive coupon receipts. Substituting the value found in this way as a component of five-year income, we arrive at a more precise description of this indicator. Let, for example, the interest rate on coupon payments be equal to the same 8%. Then, as is easy to understand, the increased amount of the flow of coupon payments

and therefore

In a situation where an investor receives income in the form of the difference between the purchase price and the sale price of a bond to another investor, it is correct to consider an increase in the market value as the investor’s income (and a decrease as a loss). Correlating this income with the purchase price, we arrive at the profitability indicator for such a transaction. For example, the yield on GKOs from the position of the seller at a secondary auction is calculated according to the so-called yield to auction indicator

Bonds without mandatory repayment with periodic (even once a year) payment of interest.

Income from this type of bond is received only in the form of interest, since the payment of the face value in the foreseeable future should not be taken into account.

Let g be declared annual rate bond yield,

N - nominal price (rub.),

C - purchase rate (%).

Let's determine the price of the bond (rubles) through its exchange rate (%):

Investment P provides the investor with an endless stream of income, i.e., a perpetual annuity with a term g x N.

STOCK

The profitability of operations with shares is determined by:

• a) the right to a portion of distributed profits joint stock company(dividend);
• b) the ability to resell shares at a price greater than the purchase price (additional income).

Dividend is a word of Latin origin meaning part of a division. In relation to a share, this is the share of the distributed profit of a joint-stock company attributable to one share in circulation, i.e., an outstanding share. Dividend, otherwise called current (dividend) income, is presented in absolute monetary units:

where I D is dividend income;

RP - the amount of distributed profit of the joint-stock company;

K size - the number of outstanding shares.

The number of dividends paid depends on the dividend policy of the joint-stock company (JSC), which in turn is determined by a number of factors: cash position, growth prospects, income stability, production capital needs, and the reputation of the joint-stock company.

The ratio of the dividend to the nominal price of the share, expressed as a percentage, is called the dividend rate:

Ratio of current income to invested funds, expressed as a coefficient or as a percentage, is called the current yield, or the current income rate, and characterizes the return on invested capital:

In translated literature on the securities market, the current income rate is sometimes called the rendit and is denoted by the letter R.

In addition to dividend important factor The return on a stock is the owner's expectation that the stock price will increase. By selling the share at the new price, the owner will receive additional income. By correlating the additional income with the purchase price of the stock, we obtain its percentage expression - additional profitability, or the interest rate of additional income:

Table 2 presents a system of indicators reflecting stock returns.

Table 2. System of indicators characterizing stock returns

The name of indicators
Dividend (current income)	The amount of distributed profit of a joint stock company per one share in circulation
Dividend rate	The interest rate of annual current income, calculated by the ratio of the annual dividend to the par price of the shares
Rendit (current yield, current income rate)	The interest rate of annual current income, calculated by the ratio of the annual dividend to the purchase price of shares (invested capital)
Additional (speculative) income, or exchange rate difference	The difference between the sale and purchase price of a stock
Additional (speculative) yield, or rate of additional (speculative) income	Interest rate of additional income, calculated by the ratio of exchange rate differences to invested capital
Total (final) income	Amount of dividends and exchange rate differences
Total (final) return (rate of total, or final, income)	Interest rate total income, calculated by the ratio of total income to invested capital
Net dividend	Dividend amount after tax withholding
Net additional income	The amount of additional income after paying income tax
Net comprehensive income	The amount of total income after withholding tax on dividends and income tax on additional income
Net current yield	The interest rate of net annual current income, calculated by the ratio of net annual dividends to invested capital
Net additional profitability	The interest rate of net additional income calculated by the ratio of net comprehensive income to invested capital
Net Total Return	The interest rate of net comprehensive income calculated by the ratio of net comprehensive income to invested capital
	dividend tax rate
	income tax rate

When deciding to buy a stock for a certain period of time, an investor needs to evaluate the profitability of the operation. Likewise, after a transaction is completed, its actual profitability should be assessed. The profitability of a stock transaction that takes several years can be calculated using the formula:

where is the sale price of the share;

Share purchase price;

Average dividend for n years (defined as the arithmetic mean);

n is the number of years from purchase to sale of shares.

An investor bought a share for 2 thousand rubles and sold it three years later for 3 thousand rubles; for the first year he was paid a dividend of 100 rubles, for the second - 150 rubles, for the third - 200 rubles. Determine the profitability of the investor's operation.

The average dividend for three years is:

If purchase and sale occur within a year, then profitability can be determined by the formula:

where t is the number of days from the moment of purchase to the moment of sale of the stock.

(If no dividend was paid during the past period, it is excluded from the formula). In the above formulas we did not take into account either tax payments, no commissions.

What would you like to achieve? investing in bonds? Save money and get extra income? Saving for an important goal? Or maybe you dream about how to gain financial freedom with the help of these investments? Whatever your goal, it's worth understanding how much income your bonds generate and being able to differentiate good investment from bad. There are several principles for assessing income, knowledge of which will help with this.

What types of income do bonds have?

Bond yield- this is the amount of income as a percentage received by an investor from investing in a debt security. Interest income according to them, it is formed from two sources. On the one hand, fixed coupon bonds, like deposits, have interest rate, which is charged on the face value. On the other hand, have bonds, like stocks, have a price, which may change depending on market factors and the situation in the company. True, changes in the price of bonds are less significant than those of stocks.

Total bond yield includes coupon yield and takes into account its acquisition price. In practice, different profitability estimates are used for different purposes. Some of them only show coupon yield, others additionally take into account purchase price, still others show return on investment depending on tenure- before sale on the market or before redemption by the issuer who issued the bond.

To make the right investment decisions, you need to understand what types of bond returns there are and what they show. There are three types of returns, the management of which turns an ordinary investor into a successful rentier. These are the current yield from interest on coupons, the yield on sale and the yield on securities to maturity.

What does the coupon rate indicate?

Coupon rate is the base percentage of the bond's face value, also called coupon yield . The issuer announces this rate in advance and pays it periodically fixed time. Coupon period for most Russian bonds - six months or a quarter. Important nuance is that the coupon yield on the bond is accrued daily, and the investor will not lose it even if he sells the paper ahead of schedule.

If a bond purchase and sale transaction occurs within the coupon period, then the buyer pays the seller the amount of interest accumulated from the date of the last coupon payments. The amount of this interest is called accumulated coupon income(NKD) and added to current market price of the bond. At the end of the coupon period, the buyer will receive the coupon in its entirety and thus compensate for his expenses associated with the refund of the tax return. to the previous owner bonds.

Exchange bond quotes from many brokers show the so-called net price of the bond, excluding NKD. However, when an investor orders a purchase, the NCD will be added to the net price, and the bond may suddenly be worth more than expected.

When comparing bond quotes in trading systems, online stores and applications of different brokers, find out what price they indicate: net or with income tax. After this, estimate the final costs of the purchase in one or another brokerage company, taking into account all costs, and find out how much money will be debited from your account if you purchase securities.

Coupon yield

As the accumulated coupon yield (ACY) increases, the value of the bond increases. After the coupon is paid, the cost is reduced by the amount of the NKD.

NKD- accumulated coupon income
WITH(coupon) - amount of coupon payments for the year, in rubles
t(time) - number of days from the beginning of the coupon period

Example: the investor bought a bond with a par value of 1000 rubles with a semi-annual coupon rate of 8% per year, which means a payment of 80 rubles per year, the transaction took place on the 90th day of the coupon period. His additional payment to the previous owner: NKD = 80 * 90 / 365 = 19.7 ₽

Is the coupon yield the investor's interest?

Not really. Every coupon period the investor receives a certain amount of interest in relation to face value bonds to the account that he indicated when concluding an agreement with the broker. However, the real interest that an investor receives on invested funds depends on bond purchase prices.

If the purchase price was higher or lower than face value, then profitability will differ from the base coupon rate set by the issuer in relation to the face value of the bond. The easiest way to evaluate real investment income- correlate the coupon rate with the purchase price of the bond using the current yield formula.

From the presented calculations using this formula, it can be seen that profitability and price are related to each other by inverse proportionality. An investor receives a lower yield to maturity than the coupon when he purchases a bond at a price higher than its face value.

C.Y.
C g (coupon) - coupon payments for the year, in rubles
P(price) - purchase price of the bond

Example: the investor bought a bond with a par value of 1000 rubles at a net price of 1050 rubles or 105% of the par value and a coupon rate of 8%, that is, 80 rubles per year. Current yield: CY = (80 / 1050) * 100% = 7.6% per annum.

Yields fell - prices rose. I'm not kidding?

This is true. However, for novice investors who do not clearly understand the difference between return to sale And yield to maturity, this is often a difficult moment. Considering bonds as a portfolio investment assets, then its profitability for sale in the event of a price increase, like that of shares, will, of course, increase. But the bond yield to maturity will change differently.

The whole point is that a bond is promissory note , which can be compared with a deposit. In both cases, when purchasing a bond or placing money on deposit, the investor actually acquires the right to a stream of payments with a certain yield to maturity.

As you know, interest rates on deposits rise for new depositors when money depreciates due to inflation. Also, the yield to maturity of a bond always rises when its price falls. The reverse is also true: the yield to maturity falls when the price rises.

Beginners who evaluate the benefits of bonds based on comparisons with stocks may come to another erroneous conclusion. For example: when the price of a bond has increased, say, to 105% and has become more than the face value, then it is not profitable to buy it, because when the principal is repaid, only 100% will be returned.

In fact, it is not the price that is important, but bond yield- a key parameter for assessing its attractiveness. Market participants, when bidding for a bond, agree only on its yield. Bond price is a derived parameter from profitability. In effect, it adjusts the fixed coupon rate to the rate of return that the buyer and seller have agreed upon.

See how the yield and price of a bond are related in the video of the Khan Academy, an educational project created with money from Google and the Bill and Melinda Gates Foundation.

What will be the yield when selling the bond?

The current yield shows the ratio of coupon payments to the market price of the bond. This indicator does not take into account the investor's income from changes in its price upon redemption or sale. To evaluate financial results, you need to calculate a simple yield, which includes a discount or premium to the face value when purchasing:

Y(yield) - simple yield to maturity/put
C.Y.(current yield) - current yield, from the coupon
N
P(price) - purchase price
t(time) - time from purchase to redemption/sale
365/t- multiplier for converting price changes into percentage per annum.

Example 1: an investor purchased a two-year bond with a par value of RUB 1,000 at a price of RUB 1,050 with a coupon rate of 8% per annum and a current coupon yield of 7.6%. Simple yield to maturity: Y 1 = 7.6% + ((1000-1050)/1050) * 365/730 * 100% = 5.2% per annum

Example 2: The issuer's rating was increased 90 days after purchasing the bond, after which the price of the security rose to 1,070 rubles, so the investor decided to sell it. In the formula, let's replace the par value of the bond with its sale price, and the maturity date with the holding period. We get simple return on sale: Y 2 7.6% + ((1070-1050)/1050) * 365/90 *100% = 15.3% per annum

Example 3: The buyer of a bond sold by a previous investor paid 1,070 rubles for it - more than it cost 90 days ago. Since the price of the bond has increased, the simple yield to maturity for the new investor will no longer be 5.2%, but less: Y 3 = 7.5% + ((1000-1070)/1070) * 365/640 * 100% = 3 .7% per annum

In our example, the bond price increased by 1.9% over 90 days. In terms of annual yield, this already amounted to a serious increase in interest payments on the coupon - 7.72% per annum. With a relatively small change in price, bonds over a short period of time can show a sharp jump in profit for the investor.

After selling the bond, the investor may not receive the same 1.9% return for every three months within a year. Nevertheless, profitability converted into annual percentages, is an important indicator characterizing current cash flow investor. With its help, you can make a decision on early sale of a bond.

Let's consider the opposite situation: as yields rise, the price of the bond decreases slightly. In this case, the investor may receive a loss upon early sale. However, the current yield from coupon payments, as can be seen in the above formula, will most likely cover this loss, and then the investor will still be in the black.

The lowest risk of losing invested funds during early sale is bonds of reliable companies with a short period until maturity or redemption under an offer. Strong fluctuations in them can be observed, as a rule, only during periods economic crisis. However, their exchange rate recovers fairly quickly as the economic situation improves or the maturity date approaches.

Transactions with safer bonds mean lower risks for the investor, but also yield to maturity or offer it will be lower on them. This general rule the relationship between risk and return, which also applies to the purchase and sale of bonds.

How to get the maximum benefit from a sale?

So, as the price rises, the bond's yield falls. Therefore, to get the maximum benefit from rising prices When selling early, you need to choose bonds whose yield may decrease the most. Such dynamics are usually shown by securities of issuers that have the potential to improve their financial situation and improving credit ratings.

Large changes in yield and price can also be seen in bonds with long term to maturity. In other words, long bonds are more volatile. The thing is that long bonds generate a larger cash flow for investors, which has a greater impact on price changes. It is easiest to illustrate how this happens using the same deposits as an example.

Suppose an investor a year ago deposited money at a rate of 10% per annum for three years. And now the bank accepts money for new deposits at 8%. If our depositor could assign the deposit, like a bond, to another investor, then the buyer would have to pay the difference of 2% for each remaining year of the deposit agreement. Additional payment in in this case would be 2 g * 2% = 4% on top of monetary amount in the contribution. For a bond purchased under the same conditions, the price would increase to approximately 104% of the par value. The longer the term, the higher the additional payment for the bond.

Thus, the investor will receive more profit from the sale of bonds if he chooses long papers with fixed coupon when rates in the economy decrease. If interest rates, on the contrary, rise, then holding long bonds becomes unprofitable. In this case, it is better to pay attention to securities with a fixed coupon that have short maturity, or bonds with floating rate .

What is the effective yield to maturity?

Effective yield to maturity- this is the investor’s total income from investments in bonds, taking into account the reinvestment of coupons at the rate of the initial investment. To estimate the full yield to maturity of a bond or its redemption under an offer, use the standard investment indicator - internal rate of return cash flow . She shows average annual return on investment taking into account payments to the investor over different periods of time. In other words, this return on investment in bonds.

You can independently calculate the estimated effective profitability using a simplified formula. The calculation error will be tenths of a percent. The exact yield will be slightly higher if the purchase price exceeded the par value, and slightly less if it was below the par value.

YTM OR (Yield to maturity) - yield to maturity, approximate
C g (coupon) - the amount of coupon payments for the year, in rubles
P(price) - current market price bonds
N(nominal) - bond face value
t(time) - years to maturity

Example 1: the investor purchased a two-year bond with a par value of 1000 at a price of 1050 rubles with a coupon rate of 8% per annum. Estimated effective yield to maturity: YTM 1 = ((1000 – 1050)/(730/365) + 80) / (1000 + 1050) / 2 * 100% = 5.4% per annum

Example 2: the issuer's rating was increased 90 days after purchasing the bond, and its price increased to 1,070 rubles, after which the investor decided to sell the bond. In the formula, let's replace the par value of the bond with its sale price, and the maturity date with the holding period. Let's get the approximate effective yield for sale (horizon yield): HY 2 = ((1070 – 1050)/(90/365) + 80) / (1000 + 1050) / 2 * 100% = 15.7% per annum

Example 3: The buyer of a bond sold by a previous investor paid 1,070 rubles for it - more than it cost 90 days ago. Since the price of the bond has increased, the effective yield to maturity for the new investor will no longer be 5.4%, but less: YTM 3 = ((1000 – 1070)/(640/365) + 80) / (1000 + 1050) / 2 * 100% = 3.9% per annum

The easiest way to find out the effective yield to maturity for a particular bond is to use bond calculator on the website Rusbonds.ru. An accurate calculation of effective profitability can also be obtained using financial calculator or Excel programs through the special function “ internal rate of return"and its varieties (XIRR). These calculators will calculate the rate effective yield according to the formula below. It is calculated approximately using the method of automatic selection of numbers.

How to find out the yield of a bond, watch the video from the Higher School of Economics with Professor Nikolai Berzon.

The most important!

✔ The key parameter of a bond is its yield, the price is a derived parameter from the yield.

✔ When a bond's yield falls, its price rises. And vice versa: when yields rise, the price of the bond falls.

✔ You can compare comparable things. For example, the net price without taking into account the accrued income - with the net price of the bond, and full price with NKD - with full. This comparison will help you make a decision when choosing a broker.

✔ Short one- and two-year bonds are more stable and less dependent on market fluctuations: investors can wait for the maturity date or repurchase by the issuer under an offer.

✔ Long bonds with a fixed coupon allow you to earn more by selling them when rates in the economy drop.

✔ A successful rentier can receive three types of income from bonds: from coupon payments, from changes in the market price upon sale, or from reimbursement of the face value upon redemption.

An intelligible dictionary of terms and definitions of the bond market. A reference base for Russian investors, depositors and rentiers.

Discount Bond- discount to the face value of the bond. A bond whose price is below par is said to be selling at a discount. This occurs if the seller and buyer of the bond have agreed on a higher rate of return than the coupon set by the issuer.

Coupon yield of bonds- this is the bet annual interest, which the issuer pays for the use of borrowed funds raised from investors through the issue of securities. Coupon income is accrued daily and calculated at a rate based on the face value of the bond. The coupon rate can be constant, fixed or floating.

Bond coupon period- the period of time after which investors receive interest accrued on the face value of the security. The coupon period of most Russian bonds is a quarter or six months, less often - a month or a year.

Bond Premium- an increase to the face value of the bond. A bond whose price is higher than its face value is said to sell at a premium. This occurs if the seller and buyer of the bond have agreed on a lower rate of return than the coupon set by the issuer.

Simple yield to maturity/offer- calculated as the sum of the current yield from the coupon and the yield from the discount or premium to the face value of the bond, as a percentage per annum. Simple yield shows an investor the return on an investment without reinvesting coupons.

Simple return to sale- calculated as the sum of the current yield from the coupon and the yield from the discount or premium to the sale price of the bond, as a percentage per annum. Since this yield depends on the price of the bond at sale, it can differ greatly from the yield to maturity.

Current yield, from coupon- is calculated by dividing the annual cash flow from coupons by the market price of the bond. If you use the purchase price of the bond, the resulting figure will show the investor the annual return on his cash flow from coupons on the investment.

Full bond price- the sum of the market price of the bond as a percentage of the nominal value and the accumulated coupon income (ACI). This is the price an investor will pay when purchasing the paper. The investor compensates for the costs of paying the NKD at the end of the coupon period, when he receives the coupon in full.

Bond price net- the market price of the bond as a percentage of the nominal value without taking into account the accumulated coupon income. It is this price that the investor sees in the trading terminal; it is used to calculate the return received by the investor on the invested funds.

Effective yield to maturity/put- average annual return on initial investments in bonds, taking into account all payments to the investor over different periods of time, redemption of par value and income from reinvestment of coupons at the rate of initial investments. To calculate profitability, the investment formula for the rate of internal return on cash flow is used.

Effective return on sale- average annual return on initial investments in bonds, taking into account all payments to the investor over different periods of time, proceeds from sales and income from reinvestment of coupons at the initial investment rate. The effective yield on sale shows the return on investment in bonds for a certain period.

Security as an object of the stock market

One of the segments of the financial market is the stock market. Its specific feature is economic object relationships between subjects. Such an object is a security. It has a dual nature. On the one hand, this financial instrument in itself does not carry value, but is subject to strict standards of registration, storage and transfer from one owner to another. In this case, the value is part of the capital or cash expressed by this instrument. That is, a security is determined by the means that it expresses, while itself being a commodity.

Thus, the stock market itself represents a certain set of economic relationships between its subjects in terms of the issue, sale and redistribution of securities.

In the function of this segment of the economy, based on the specifics of the object economic relations includes:

• redistribution of funds between industries and regions;
• formation of prices for financial instruments;
• creating an information field about changes in the market;
• regulation of relationships between market entities and the state;
• providing additional financing in times of deficit;
• optimization of the flow of funds into strategically important sectors of the national economy;
• distribution of risks between transaction participants.

Market entities purchase or issue stock instruments to effectively use their available cash and capital assets. The purpose of such activities is to obtain additional income from their own funds in the short and long term.

Note 1

To implement effective investments use investment portfolios. Their essence lies in the formation of a package of financial instruments that will allow not only to realize the goals of their owner, but also to reduce the risks of all ongoing transactions and operations with securities.

Investments in securities

To optimize portfolio risks, stock instruments of varying degrees of liquidity, as well as different expiration dates and principles of placement on the market are used. One of the most stable and frequently used methods is to use a deposit account at a bank. This account allows you to place free cash at a certain bank interest rate. This method is quite safe, but its profitability is not high. Over the past few years, the interest rate on deposit accounts has not exceeded the 7% threshold.

There are two types of such investments - on demand (implies that the period for withdrawing money is not specified, the owner of the deposit can use it at any time (savings or check books)); time deposit is an investment with a certain period for withdrawal of money by the investor.

Note 2

You can insure your deposit in case of bank bankruptcy.

If it is not possible to create a deposit account, you can purchase a bank draft. Its properties are more liquid, and it is much easier to open than a deposit account.

Highly liquid stock instruments are stocks, bonds and their derivatives.

Shares allow their owner to receive income in the form of periodic interest payments in addition, some types of shares give property law or the right to manage a business entity. This type of stock instruments can be used for speculation on the stock exchange in order to extract additional profit. Or a stock can act as a basis for derivative instruments that allow you to play on the difference in the value of a stock at different points in time. In order to place their shares on the stock exchange, their owner must go through the appropriate procedures giving the right to sell securities on the stock exchange.

Definition 1

A bond is a type of financial instrument that gives its owner the right to receive payment from the issuer within a certain period of time in the amount of the nominal price of the security plus the interest specified in the contract.

The risks associated with transactions with such instruments are relatively lower than with shares. They can be implemented over periods ranging from a year to several decades. The bond allows you to balance possible losses in the portfolio and bring a constant, albeit small, income to its owner.

By type of income, bonds can be:

• discount - their price on the market is lower than their nominal value, there are no interest payments on it;
• with a specific interest rate - interest is paid according to the amount established in the agreement;
• with a floating rate - interest payments depend on market conditions at the time of calculation.

Note 3

Important feature bond is the end of its existence after mutual settlements between the holder and the issuer.

Derivative instruments are designed to implement a hedging strategy for underlying securities, in addition, they allow you to carry out transactions and receive income in the short term.

Return on securities

A stock instrument is determined by the degree of its profitability. We must remember that the income on securities is directly proportional to the degree of risks associated with it. That is, the effectiveness of a portfolio is expressed in relation to its annual income to market value each instrument separately. The level of projected income can be determined according to the following principles:

• calculation interest rate taking into account the movement of financial instruments over a period of time;
• determination of annual income as a percentage;
• the level of income on the instrument until its maturity (for bonds);
• profitability at the current time.

The total return can be calculated using the following relationship:

$D = \frac(Sn-So)(So)$, where $D$ is income, $So$ is initial cost, $Sn$ is final cost.

This indicator allows you to analyze the potential of available financial instruments and determine the areas of their investment.

Income for the year is determined by the formula:

$D = (1+\frac(i)(n))\cdot n-1$, where $D$ is income, $i$ is the cost of compound interest for the year, $n$ is the number of time periods of the year.

Calculation of income on bonds in general view can be expressed by the formula:

$D = \frac(k+\frac(N-P)(t))(\frac(N+P)(2))$, $D$ – income, $k$ – coupon size, $t$ – repayment period, $N$ is the nominal value, $P$ is the market value.

Rating 4.6 out of 5. Votes: 5

Yield or Rate of Return (English) Rate of return) - 1. used in economics (in finance) a relative indicator of the effectiveness of investments in certain assets, financial instruments, projects or business as a whole. 2. Ability, ability to generate income. 3. Total ratio cash receipts that an asset brings to its price.

Profitability can often be estimated as a ratio of the absolute value income to some base, which usually represents the amount of the initial investment or investments that must be made to obtain this income.

Economic literacy - webinar about risk and profitability:

Where: r - profitability; V e - the final value of the financial asset; V b is the initial value of the financial asset.

Security yield

The yield of a security is a quantitative characteristic of a security that determines its value for an investor.
Profitability depends on the measure of risk. Generally, the higher the yield on a security, the higher the risk.
Profitability in general is calculated by the relation arrived received by the investor during the period of ownership of the security in addition to the costs of its acquisition.
Yield is usually determined as a percentage.

The following types of profitability are distinguished:

• Yield to maturity (for bonds)
• Current yield (for shares and bonds)
• Dividend yield (for stocks)
• Annual Percentage Yield
• Internal Return

Profitability and risk - The essence and methods of measuring profitability

To achieve its main goal - maximizing the wealth of the owners - the enterprise must constantly ensure the investment of available capital in assets that generate the greatest income. In its most general form, income can be defined as the increase in the well-being (wealth) of owners over a certain period of time:

Income for the period = Wealth at the end of the period – Welfare at the beginning of the period

The total amount of income received by the owner of capital consists of two parts: current income and capital gains. For example, having bought an apartment, you can rent it out and receive income in the form of rent. You can live in a purchased apartment and discover after a few years that its price has increased significantly compared to the time of purchase. In the first case, the apartment will generate current income, in the second, income will be received from the increase in the value of the apartment. The owner of an apartment who rented it out can sell it after a few years and thus realize both types of income - current and from the increase in value. Similarly, when purchasing a stock, an investor can expect to receive current income in the form of periodic dividend payments. However, if after some time the market price of the purchased share increases, then he will become even richer by the amount of the increase in value. Thus, the total income from owning the share will be equal to the amount of dividends received on it and the amount of increase in its market value. The income of the bond owner is formed in a similar way. If he purchased a coupon bond, he will receive current income in the form of periodic coupon payments. When purchasing a discount bond, the income is realized in the form of the difference between the sale and purchase prices. These two types of income (current and capital appreciation) can be realized jointly if during the holding period coupon bond there will be a reduction in interest rates. Coupon payments will remain unchanged, but the market price of the bond will increase, so along with the current income, its owner will also receive income from the increase in the value of the bond.

It is very important to understand that from a financial perspective, both of these types of income are equivalent for the owner and must be taken into account when making calculations. Often the concept of profitability is tied to some asset, financial transaction or enterprise. For example, you can talk about stock return or return on sales. This approach is justified for comparative assessment efficiency of various areas of capital investment: product A can provide more profit than product B, and investments V financial assets may turn out to be even more profitable. It should not be forgotten that it is not the assets themselves that generate income, but the capital invested in them. Therefore, it is more correct to talk about return on capital rather than on individual assets or operations. Capital can be simultaneously invested in both real and financial assets, which can generate both current income and increase (or decrease) in their value. Profitability individual transactions will rather reflect the effectiveness of the managers responsible for their implementation - the plant director or stock broker. Total return refers to the entire invested capital, that is, it must be calculated from the perspective of the owner of this capital.

Having capitalized 1 thousand rubles from total cost of his property, the owner has the right to hope for a subsequent increase in his total wealth. Let's assume that 500 rubles out of this thousand were invested in equity trading enterprise. The store director, having purchased goods with them, sold them for 750 rubles, that is, the marginal income was 50% (250/500). After deducting the main commercial and management expenses the profit from sales was 100 rubles, that is, the profitability of sales was 20% (100/500). Having covered other operating costs and paid income tax (50 rubles in total), the director reported net profit in the amount of 50 rubles. 20 rubles of this amount were returned to the owner in the form of dividends, and 30 rubles were reinvested in the enterprise.

The second half of the capital (500 rubles) was managed by the broker, who bought securities with this money. By the end of the year, the total income from owning these securities (both current and increase in their value) amounted to 500 rubles, that is, 100%. From this amount, the broker withheld commissions and other expenses, and also paid taxes in the amount of only 300 rubles. That is, the real increase in the wealth of the capital owner was 200 rubles (500 – 300). The total return on all invested capital will be 25% ((20 + 30 + 200) / 1000). As you can see, this value differs from both the return on sales and the return on securities. Evaluating the work of his agents (director and broker), the owner can conclude that the net profitability of the store was 10% (50/500), and the net profitability of financial speculation was 40% (200/500). But neither the first nor the second figures reflect the real total return on the capital invested by him. It is equal to 25%. It is this figure that he should focus on in his plans for the future.

So, speaking of profitability, we should mean the efficiency of using all capital invested by the owner and take into account all net income (in the form of both current payments and capital gains) received by the owner of the invested capital. For analysis, any indicators of profitability (profitability) of assets, operations, projects, etc. can be calculated, but it must be remembered that the most general financial indicator is the total return on invested capital. It is not the assets themselves or operations with them that bring income to the owner, but the capital invested in them.

Profitability is a derivative of total amount the total net income produced by capital over a certain period of time, and the amount of wealth of the owner of capital at the beginning of the period. Since welfare at the end of the period will be equal to the sum of its value at the beginning of the period plus the amount of total net income received by the owner for the entire period, the formula for calculating profitability can be presented as follows:

where indices 0 and 1 indicate the beginning and end of the time period, respectively.

The problem of accurately measuring the real value of all property owned by an investor is not directly related to financial management. Therefore, the amount of his wealth at the beginning of the period is taken to be equal to the amount of capital invested by him. The formula for determining the total return for the holding period (holding period return - HPR) can be presented as follows:

where CF is the flow of current income received by the owner from invested capital for the period;

I0 – initial amount of invested capital (investment at the beginning of the period);

I1 – final (accumulated) amount of invested capital (investment at the end of the period);

rC – current profitability;

rI – return on capital gains (capitalized return);

r – total return.

Profitability is one of the main indicators of investments, by which one can evaluate the profitability of investments, their feasibility and compare them with each other according to this indicator. Often, to assess the profitability of investing money, the risk-return relationship is used. The logic here is simple: indicators such as profitability and risk themselves are uninformative. What's the point of investing in tools with high level risk and low potential profitability? If the risk of loss is high, then the possible reward should be high.

Let us separate the concepts of income and profitability. Income is an absolute value, expressed, for example, in monetary units (Vasya invested 10,000 rubles and received an income of 2,000 rubles), while profitability is a relative value, expressed as a percentage or interest per annum, more on this later (Sasha invested his money to commercial real estate with a yield of 25% per annum).

Profitability calculation formula

Next there will be material with formulas, but don’t be afraid - anyone who studied at school will understand them - they are easy to understand. In addition, your browser must have images enabled, since the formulas are presented in the form of pictures.

The simplest formula for profitability is the ratio of the profit received to the amount of investment, multiplied by one hundred:

where sum1 is the initial amount,
sum2 - final sum.

However, these formulas do not take into account such an important indicator as time. Over what period is this profitability? In 100 years? Or in 3 months? To take into account the time during which investments have shown profitability, the following profitability formula is used:

where the period in months is the time during which the investment takes place.

The most common period for calculating profitability is 1 year (you don’t have to look far for examples - the same bank deposits calculated as a percentage per annum).

For example, the owner of an apartment worth $15,000 rented it out at the beginning of the year and received an annual fee from the tenant in the amount of $1,000. By the end of the year, the cost of the apartment increased and amounted to 17 thousand US dollars. The total return on owning an apartment for the year will be 20% (1 + (17 – 15) / 15), including the current return of 6.67% (1 / 15), capitalized return of 13.33% (2 / 15). More precisely, we should talk about the return on capital invested in the purchase of an apartment.

As follows from formula (5.1.1), the amount of profitability is influenced not only by the absolute amount of income received, but also by the amount of investment (I0). In other words, the same absolute amount of income of 1000 rubles will mean a different level of profitability for capital of 10 thousand and 10 million rubles. In the first case, the yield will be 10% (1,000 / 10,000), and in the second - 0.01% (1,000 / 10,000,000). The relative profitability indicator eliminates the influence of the scale factor and more accurately reflects the real financial and economic efficiency of using invested funds than the absolute value of the income received.

Returns always refer to a specific time period. For example, you can earn 1 thousand rubles in a month, or in a year. Even the calculation relative indicator profitability will not make these figures comparable. If we continue the example and assume that an investment of 10 million rubles brought an income of 1 thousand rubles in 1 week, and an investment of 10 thousand rubles provided the same income in 6 months, then the profitability values ​​​​obtained above will not be objective enough. To ensure comparability of these indicators, they must be brought to a single time base. In finance, profitability is usually annualized, that is, the original data is annulled. Comparing the formulas for calculating profitability and the formula for the annual interest rate (2.2.1), one can notice their identity. Both the return and the interest rate reflect the rate at which the initial investment grows. By calculating the yield, in essence, the value of the corresponding interest rate is determined.

Exist various ways interest accrual and, accordingly, different interest rates. Increase by simple and complex bets leads to different results. What specific rate should be used to determine the annual return? In finance, it is customary to use the effective compound interest rate as a measure of profitability, that is, an annual rate that assumes a one-time reinvestment of accrued interest during the year. However, for short-term financial transactions (lasting less than 1 year), a simple interest rate is allowed. So, for example, the yield on GKOs was calculated at the rate simple interest(formula 2.2.14) assuming that the length of the year is 365 days. Of course, such ambiguity complicates the life of a financier, but the difficulties that arise should not be taken into account as absolutes. First of all, it is necessary to understand that the method of annuity of profitability in no way affects the real parameters of the financial transaction under consideration. Profitability is an abstract indicator used to ensure comparability and comparative evaluation of different capital investments. Therefore, when comparing two investments in terms of their level of profitability, it is important to make sure that the methods for calculating these indicators are comparable. The question of which calculation method is better or “more correct” is not the most important. It is necessary that the same annuity method be used for both operations.