Annual rate of return on cash balances. How to calculate return on investment

Constantly and most importantly guaranteed, getting a certain income every month is the dream of any investor. Money works without your participation and any effort and brings even more money. How to achieve this? Answer - you need to know where to invest money. Of course, the amount of profit will directly depend on the amount of invested funds. And let's say, for novice investors, the profit received from their investments will be relatively small. But you need to start somewhere. After all, the very fact of generating very attractive. In order for income to grow, you need 2 things: periodically invest additional money and constant. In law - over time, even the most modest capital can turn into a rather impressive amount, the profit from which will give you a significant financial flow in the form of a monthly income from the placed funds.

Where can you invest money to get a constant monthly income?

We buy with different coupon dates. It is on these dates that you will accrue profit. You can build a portfolio of bonds in such a way that monthly profits will be credited to your account. Usually the duration of the coupon is 91 or 182 days. Every 3 months or half a year, the profit from the purchased bond will go to your account.

Advantages. Higher yield. Clearly predicted and fixed income. High (you can instantly sell bonds without losing accrued profits).

Flaws. Probability of bankruptcy of the issuer that issued the bonds. For blue chips, this probability is small. For OFZ (federal loan bonds) and municipal bonds, it is practically zero. Usually (although very rarely) the so-called third-tier companies (junk bonds) go bankrupt. Avoid buying them and you'll be fine.

4. Dividend shares . Buy, which consistently pay dividends. And not just dividends, but. On average, in the Russian market, this amount is 3-6% of the value of shares. There are companies (but there are few of them) whose dividends are slightly higher and amount to 8-10%. Judging by the latest payments, these are Surgutneftegaz, MTS and M-video.

Of course, the profitability is still small, but if you consider that you are buying a piece of a working (and successful) business, then with the further development of the company, the profit will also grow.

For example. The price of shares in the stock market is very volatile. They can "walk" within 20-30% during the year, both up and down. At the beginning of the year, the shares of SurgutNeftegazP cost almost 50 rubles apiece, then the price fell almost 2 times within six months, to 28 rubles. Considering that the yield on average is 10% per share (at a price of 45 rubles) or 4.5 rubles, buying at the “day” at 28 you would secure a future yield of 17% per annum. And if the company's profit continues to grow, then the annual yield will easily exceed 20%.

Advantages. Having bought a "piece of business" in the form of dividend shares, you will be entitled to count on a share of the company's profits. You can find, thereby obtaining even more annual profitability. With the development of the company, profits will increase, which means that dividends will also grow.

Flaws. Uneven distribution of dividends. The lion's share of payments occurs in the second quarter. Some companies pay dividends twice a year. High volatility in the stock market. Purchased shares can significantly fall in price. But if you are aiming (several years), then it will give you the opportunity to purchase additional shares at bargain prices.

Finally

It is possible (and even necessary) to receive passive income every month. There is nothing complicated about this. The listed methods are available to everyone. And don't forget. Divide your funds into several parts, and use them to make a profit in each way. So, of course, the overall profit will decrease, but you will greatly reduce the risks when investing.

Every economic activity has as its goal making a profit (or a positive return). And what is it from an economic point of view? The answer to this question will be discussed in the article. Also, besides this, it will be discussed what the rate of return is and how to calculate it.

What is yield?

Profitability in economic sciences means which shows the effectiveness of investments in individual assets, projects, financial instruments or in the whole business. From a mathematical point of view, this indicator can be viewed as the ratio of the total amount of funds received to a certain base. And what is meant by it?

The base is understood as the amount of initial investment or the amount of money that had to be invested in order to receive a given amount of money. Therefore, the entire performance evaluation system is also called the rate of return. Can this indicator be viewed from a negative side? Yes, returns can be positive or negative. Under the first one, they mean that the company returned the money spent and still has a plus. Negative returns mean that the invested funds did not pay off and there is no need to talk about net profit.

Rate of return

This indicator is necessary to assess the effectiveness of invested funds. The rate of return is a term that refers to the effectiveness of invested funds. So, if the word “internal” is in front, then this means that the current value of the investment is zero, and all the funds received, which go as profit from economic activity, are equal to the costs at the beginning of the business or project. With its help, you can determine the level of investment, which in any case will cost no loss for the owner of the money. With the help of the internal rate of return, the level of return on investment is shown, as well as the maximum amount that makes sense to invest in this enterprise.

Yield Ratings

If you buy shares, then how to find out their past, then how much they brought profit to their owners a month or a year ago? Especially for this, there are special profitability ratings. They select the best ones that provide the greatest benefit in the short term. The profitability rating, in addition to the amounts of profit, may also contain cost indicators. And if enterprises are listed on stock exchanges for a long time - years or decades, then it is possible to assess the trend of their development and better approach the decision whether to acquire them or not. Yield is a serious indicator and should be determined using as much information as possible.

Calculation

D \u003d (SFAKP - SFANP) / SFANP.

These abbreviations are deciphered as follows:

1. D - profitability.
2. FACF - the value of financial assets at the end of the period. Definitely what is being researched.
3. FFANP - the value of financial assets at the beginning of the period. Definitely what is being researched.

Forecast values ​​can also be used as values. So, you can know the value of the stock at the beginning of the year, see the expected value and decide whether to buy the security or not. But doing something with only projected returns in front of you is a thankless task. It does not hurt to know about the state of affairs in past years.

When rational investment strategies are compared, return and risk always move in the same direction with changes, all other things being equal. So, the higher the profit, the greater the risks.

To clarify, you can use an example: two people come to the bank. The first is a wealthy citizen who has a stable and well-paid job, a house and asks for a loan. The loan is issued at 20% per annum. The second person works odd jobs, abuses alcohol and has a number of other bad habits. He is given a loan at 40%. Further, the bank completes all the obligations of people like person No. 2 into one portfolio of securities and sells them at such a high level of profitability. But if you think about it: where can you earn more? With the second option, profitability is greater. With the first person, the yield is lower. But here it is also less likely that he will refuse to pay you money. Therefore, when considering investment proposals, it should be remembered that profitability is not the only parameter that should be considered.

Conclusion

Therefore, in the end, we can conclude: the higher the yield, the greater the risk. Excessively high opportunities for losing investments are not attractive to investors, so most people prefer to direct their money to something relatively safe and stable. Profitability is a mandatory parameter, because without it there is no point in investing your funds in something.

Evaluating the effectiveness of their investments and investments, many make the same mistake. This error consists in calculating the average annual return as the arithmetic mean. This is fundamentally wrong. At least by the fact that this approach does not take into account the time value of money, and money has it.

In order to close this question, I decided to post an article on the blog from the Investor's Notes website, which is called “Likbez: how to calculate profitability?”. Thanks to its author, Sergey Spirin, we will be able to easily understand everything.

The concept of interest

Before we start talking about profitability, let's define two concepts that often cause confusion. First, let's define what a "percentage" is? The word "percent" comes from the Latin "pro centrum" - "for a hundred". The main meaning of the word "percentage" is a hundredth of a number taken as a whole, one. Denoted by the sign "%".

If you enter any number in a cell in Excel without a percent sign (for example, "5"), and then change the format of this cell to "percentage", you will see the number 500.00% in the cell (i.e. one hundred times more) . If you enter a number in an Excel cell with a percent sign (for example, "8%"), and then change the cell format to "general" or "numeric", you will see the number "0.08" in the cell (i.e. in hundred times less). Further in the text, I will from time to time give values ​​both in percentage format and in numerical format.

If a number is followed by a % sign, then to convert it to a number format, you need to divide the number by 100. That is, 20% = 0.2. If, on the contrary, you want to convert the number to a percentage format, then you need to multiply it by 100. That is, 1.1 = 110%.

I also want to draw your attention to how the phrases “increased by x%” and “increased by y times” correlate with each other. A change of x% means a change of (1 + x) times. For example, the phrase "the index grew by 10%" means the same as "the index changed by 1.1 times".

Similarly, a change of y times is equivalent to a change of (y – 1)%. Moreover, if y > 1, then they speak of growth by (y - 1)%, and if y< 1, то говорят о падении на (y – 1)%. Например, изменение в 1,15 раз – это то же самое, что изменение на +15% (или рост на 15%). Изменение в 0,8 раз – это изменение на –20% (минус 20%) или падение на 20%.

If the price has increased by 100%, then it has increased by 2 times. A 25% fall in share price (-25% change) is equivalent to a 0.75 times price change.

Simple and compound interest

Let me briefly remind you of the difference between simple and compound interest. Let's assume that some asset grows by 10% per year (that is, it has a yield of 10% per annum). You invest 100 rubles in the specified asset. How much will you have in 2 years?

• Related link:

If you think that you will have 120 rubles, then you are certainly mistaken, forgetting about compound interest. In a year, you will have an amount of 110 rubles, but 10% in the second year of investment will be counted from the new amount of 110 rubles, so in two years you will already have 121 rubles.

Compound interest (or discounting) involves the reinvestment of capital, so capital increases exponentially when investing under the principle of compound interest. Simple interest does not involve the reinvestment of capital, so capital grows linearly.

However, the exponential increase in capital is observed not only in the case of the explicit calculation of "interest on interest", as in the case of . We observe exponential growth in value over long periods of time for any market asset.

For example, shares, commodities in the commodity markets (gold, silver, oil, grain), real estate, etc. over long periods of time also resembles an exhibitor, subject to the compound interest rule.

Arithmetic and average annual returns

Often you have to solve the reverse problem. It is known that the value of an asset has increased by 21% in 2 years. How to calculate the annual return that would achieve such a result? I think it's obvious from the example above that the obvious answer "divide 21 by 2" is wrong. 21/2 = 10.5%. And as we already know, the correct answer is 10.0%. In this example:

• 10.5% - arithmetic average yield.
  10.0% - average annual return (often also use the term "annualized average return" or "geometric average return").

As you can see, they are not the same. To make this quite clear, try answering the following question. Let's say that in the first year the value of an asset increased by 100% (change +100%), and in the second year it decreased by 50% (change -50%). What is the average return on investment in this asset over two years?

Obviously, the arithmetic mean of "25%" is the wrong answer. The correct answer is 0%. If at first the value of your assets increased by 2 times (+100%), and then fell by 2 times (-50%), then in the end it did not change.

Let's derive the formula for calculating the average annual yield, where:

• n is the number of years;
• x – annual return (in %).

The symbol "^" will denote exponentiation.

Result after 1 year: A(1) = A(0) * (1 + x)
Result after 2 years: A(2) = A(1) * (1 + x) = A(0) * (1 + x)^2
Result after 3 years: A(3) = A(2) * (1 + x) = A(0) * (1 + x)^3
Result after n years: A(n) = A(n-1) * (1 + x) = A(0) * (1 + x)^n

The units in the formulas are due to the fact that we used annual percentage returns, (x) in our calculations (i.e. we treat the change as +10% growth, x = 0.1). If instead we use the change per year in times (y) (i.e. we consider the change as a growth of 1.1 times, y = 1.1), then the units from the formulas will disappear:

• A(0) – initial amount of money;
• n is the number of years;
• A(n) - the amount of money in n years;
• y - annual change (in times).

Result after 1 year: A(1) = A(0) * y
Result after 2 years: A(2) = A(1) * y = A(0) * y^2
Result after 3 years: A(3) = A(2) * y = A(0) * y^3
Result after n years: A(n) = A(n-1) * y = A(0) * y^n

If for 2 years the result A(2) = 21% was shown, then the annual return x is calculated by the formula:

x = √((A(2)/A(0)) – 1. Or, equivalently, x = (A(2)/A(0))^(1/2) – 1.

Or, if we use changes in the formulas not “as a percentage”, but “in times”, then:

y = √(A(2)/A(0)). Or, which is the same, y = (A(2)/A(0))^(1/2).

Here √(number) is the square root of a number, (number)^(1/2) is a number raised to the power of 1/2. (Taking the square root of a number and raising a number to the power of 1/2 are the same thing.) Check: √(0.21 + 1) - 1 = √(1.21) - 1 = 1.1 - 1 = 0.1 = 10%

Example. You put 100,000 rubles on a bank deposit and after 4 years withdrew 150,000 rubles, i.e. the amount of your funds has grown by 50% in 4 years. What is the average annualized return?

Yield = 4√ (1 + 0.5) - 1 = (1 + 0.5)^(1/4) - 1 = 0.1067 = 10.67% per annum

4√(x) is the fourth root of x, (x)^(1/4) is x to the power of (1/4). Let me remind you that they are one and the same. Also (for those who have completely forgotten mathematics) let me remind you that 4√(x) = √ (√ (x)). To extract the fourth root on the calculator, you just need to press the "√" icon twice.

How to calculate the same in Excel? To extract the square root in Excel, there is a function =ROOT(number). For example, =SQRT(1.44) will give the value 1.2. But there is no function for extracting the root of an arbitrary degree in Excel. Therefore, instead, you will have to use the function =POWER(number; power). To take the 5th root of a number, write =POWER(number;1/5).

There is another way to calculate the annual average (geometric mean) profitability in Excel. If you have an array of data that represents changes "in times" (namely, "in times"!), Then you can use the Excel function = CPGEOM (number1; number2; ...).

In this function, number 1, number 2, ... - up to 30 arguments, for which the geometric mean is calculated. Instead of arguments separated by semicolons, you can also use a reference to an array of data. Instead of the list of arguments (number1; number2; ...), there can also be a reference to an array of cells, for example =СРГЭОМ(A1:A8).

The CPGEOM function calculates the result using the formula: CPGEOM(y1; y2; … ; yN) = N√(y1*y2*…*yN). Once again, I draw your attention to the fact that an attempt to use the CPGEOM function for percentage arguments gives incorrect results. Before using this function to calculate the average annual return, you need to convert the "percentage" into "times".

Example. For 2 years and 6 months, the value of a share in the investment fund increased by 42.7%. What is the average annual return of the fund?

On a regular accounting calculator (without the exponentiation function), you will not calculate this. Type in an Excel cell: \u003d POWER (1 + 42.7%; 1 / 2.5) -1. You get an answer: 15.28% per annum. Don't forget to set the cell format to "percentage", as well as display the desired number of decimal places. Otherwise, you will see the result 0.15 or 0.1528, which, in fact, is the same thing, however, it can mislead you.

Please note that in Excel you can mix percentage and number formats in formulas, you just need to remember where to put (or, conversely, not to put) the “%” sign. For example, the formula might be written like this: =POWER(1.427;1/2.5)-1. Or like this: \u003d POWER (100% + 42.7%; 1 / 2.5) -1. The result of this will not change.

Also pay attention to the fact that, unlike a bank deposit, the value of a mutual fund unit grows unevenly - in one period of time the value of the units increases, in others it falls. However, in order to compare different investment options with each other, we sometimes need to know what the annual return of an investment with a uniform growth schedule would have to be in order to give us the same result as an investment in an asset with uneven growth.

This return is called the average annual return (or average annualized return). Once again, I remind you that it should not be confused with the arithmetic mean yield.

The average annual return is the profit you have to earn each year to get the same result as different annual returns.

Example. The value of the MICEX index at the end of December 1997 was 85.05 points. The value of the MICEX index at the end of 2007 was 1888.86 points. What is the average annual return of the MICEX index for 10 years?

Solution: enter the following formula into the Excel cell: \u003d POWER (1888.86 / 85.05; 1/10) -1. We get the answer: the average annual return of the MICEX index for 1998-2007. = +36.35% per annum.

Example. According to the State Statistics Committee of the Russian Federation (gks.ru), consumer inflation in Russia was (by years):

2000 - 20.2%
2001 - 18.6%
2002 - 15.1%
2003 - 12.0%
2004 - 11.7%
2005 - 10.9%
2006 - 9.0%
2007 - 11.9%

What is the average annual consumer inflation in Russia for 8 years (2000-2007)?

We calculate the growth for 8 years as the product of changes for each year "in times". If in 2000 the consumer basket of Russians rose in price by 1.202 times, and in 2001 - by 1.186 times, then the total rise in price for two years was 1.202 * 1.186 = 1.426 times. Accordingly, in order to calculate the total growth of the consumer basket for 8 years, you need to multiply the changes in the cost of the consumer basket for each year:

The consumer basket for 8 years has risen in price by 2.777 times (or +177.7%, which is the same). This is equivalent to an average annual growth of 8√(2.777). To calculate this in Excel, you need to set the formula =POWER(2.777;1/8). We get an average annual growth of 1.1362 times, which corresponds to an average annual inflation of 13.62% per year.

There is another option. Enter the function =СРГЭУМ(1.202; 1.186; 1.151; 1.120; 1.117; 1.109; 1.090; 1.119) into the Excel cell. We get 1.1362, and then subtract one to get the percentage, and we get 13.62%.

To evaluate the effectiveness of investments, it is necessary to know what profitability they will bring (or have brought). And if there are many such investments? They need to be compared somehow. To understand what was more profitable. And in general, how can you calculate the return on a portfolio with various investments (bank deposits, bonds, stocks, etc.). For different amounts and different terms?

For example, which is more profitable? Invest 57 thousand for 3 months and earn 3 thousand. Or invest 75,000 for eight months and get 5,500?

How to find out the percentage of effective return on the portfolio, if during the year there was a constant withdrawal and deposit of funds?

So let's go!

We consider profit

The simplest and most basic formula for determining the "profitability" of investments.

The difference between the final amount and the initial amount forms the net profit.

To display as a percentage, use the formula:

Yield = (net profit) / investment amount * 100%.

Example.

We bought Gazprom shares for 10,000 rubles. A year later, everything was sold for 13,000 thousand.

Net profit amounted to 3 thousand rubles (13,000 - 10,000).

Return on investment 30% (3,000 / 10,000) * 100%).

This formula has one significant drawback. It allows you to calculate only the absolute return. Without reference to the period for which it was received.

We could earn 30% in 1 year. Or maybe in 5 years.

Annual return in percent

A more accurate estimate of the return on investment can be made using the annual return.

In simple terms, the annual return shows how much an investor earns for each ruble invested for the same period of time.

The generally accepted estimate of "the same period of time" is one year. All percentages of return received for different periods of time are reduced to the annual rate of return.

What does it look like in practice?

They invested in Sberbank shares - 30,000 rubles. And in the shares of Gazprom - 50,000 rubles

Six months later, after the growth of Sberbank quotes, they sold everything for 36 thousand rubles.

You held Gazprom for exactly a year and threw off the papers for 65 thousand.

Outcome: At Sberbank, you earned 6 thousand in six months. Gazprom has 15 thousand, but for a whole year.

• Sberbank - 6 thousand or 20%;
• Gazprom - 15 thousand or 30%.

To correctly assess the effectiveness of investments, you need to convert everything into annual percentages:

Yield (% per annum) = (profit in % * 365 days) / investment period in days.

Profitability of Sberbank = 20% x 365 days / 180 days = 40% per annum

Profitability of Gazprom = 30% x 365 / 365 = 30% per annum.

Investments in Sberbank shares turned out to be more profitable.

Profitability taking into account the movement of funds

And how to display the total result, for example, for a year?

Adding up all the yields is not very convenient and time consuming.

The simplest and most obvious option is to fix the value of the portfolio at the beginning and end of the year. And calculate the total profit.

Example. At the beginning of the year, the investor had a capital of 200 thousand rubles. Due to profitable investments, a year later his portfolio was estimated at 240 thousand.

Net profit 40,000 rubles or 20% per annum.

There is one significant disadvantage in this method of calculating profitability, which will distort the real figures. And in a simple way, doing them is not at all correct.

For the period under review, possible movements of funds on the account or portfolio are not taken into account.

What are these movements?

• input-output of funds;
• profit from outside. For example, coupon income on bonds or dividends on shares.

From the example above. If a month before the end of the annual period, the investor contributed an additional 40 thousand rubles. How will this affect the result? In absolute terms, we also have +40 thousand profit or 20% per annum. But in fact, the result is zero.

Another variant. After 1 month, the investor did not deposit, but withdrew 40 thousand. As a result, for almost a year he operated with an amount 20% less than the original one. And still earned 40 thousand profits.

Or during the year dividends, coupons were paid. There were constant deposits and withdrawals from the account. As then? How to determine the real return?

For the calculation, there is a special formula for calculating interest depending on the date and amount of the movement of funds. But I think most (probably all) will not use it. It is too complicated and cumbersome. I won't even bring it here.

Profitability calculation in Excel

There is a simpler option for calculating interest in an Excel spreadsheet. The CHISTVNDOH formula will help us.

All we need to know is the dates and amounts of the cash flows.

How to fill in the table?

We need 2 columns for cash flow:

1. sum of incoming and outgoing flows
2. Movement dates.

All receipts to the account must be with a plus sign. Withdrawals and other expenses must be with a minus sign. The final final amount (at the moment of which the profitability is calculated) on the account is also with a minus sign.

Here's what it looks like in an example:

How to do it in Excel?

We enter our own values ​​into the table (by analogy with the example above).

We call the CLEANOUT function.

In the fields "Value" and "Dates" we enter our conditions as in the picture below. Simply by right-clicking the required range.

The formula itself still needs to be multiplied by 100. In order to bring it to a more familiar form. By default, it is shown not as a percentage, but as a fraction of one. In our case, 0.16.

By the link, there is an Excel file with ready-made formulas listed in the article. Submit your data. Consider profit. Rejoice (or grieve) at the yield.

Successful investment!

"Today's investor does not profit from yesterday's growth" (Warren Edward Buffett)

Now I am summing up the results of the first year of my public project "Reasonable Investor". I’ll publish it soon, I’m not in a hurry, because I’m not going to do anything until the fall - neither buy nor sell ...

All year I determined profitability my portfolio according to the method used by mutual funds when calculating the value of shares. In principle, this is correct, but only for the unit price. The result of a particular investor will be quite different.

There is one nuance that complicates everything in terms of determining profitability. These are I/O operations!

Previously voiced mine result +17.89%, turned out to be incorrect (more precisely, this is not my profitability, but the change in the value of a share - if my portfolio were a mutual fund and I took money for management from shareholders).

Since I made regular investments, and also withdrew funds twice, then it is no longer possible to use this method, it distorts the actually obtained profitability. The real return is +23.78% per annum(just boring 24% per annum, which are on these weekend discussed on smart-lab)))

I think a lot of people will benefit from reading this post. Until recently, I did not even know this information, it seemed to me that the method used was quite acceptable.

« How to calculate yield?”, at first glance, this question should not cause the slightest difficulty. Many people know that in order to calculate the profitability, it is necessary to divide the result of the investment by the amount of invested funds and convert the resulting value into annual percentages.

The formula for calculating the yield (in percent per annum), if there were no deposits / withdrawals:

D = ((ΔS)/Sini) * 365/T * 100%, where

D is the desired return,

ΔS is the result of investment in absolute terms,

Snach - the amount of initial investment,

T is the number of days in the period under consideration.

But the task of calculating the profitability becomes much more complicated if during the period under review there were deposits or withdrawals of funds within the investment portfolio. In this form, it causes difficulties even for experienced investment professionals.

The solution to this problem was suggested to me by my colleagues from UK Arsager

A little theory:

Let's start by defining what deposits and withdrawals of funds are. The input of funds is the direction of money for investments. For example, you have purchased investment units of a fund or deposited money into a brokerage account - all this is a deposit of funds. Withdrawal of investment funds is a withdrawal, that is, within the scope of the examples, withdrawals occur when investment units are redeemed or money is withdrawn from a brokerage account.

Knowing what inputs / outputs are, let's consider a specific situation that will help to understand the logic of solving the problem of correctly determining profitability, taking into account inputs / outputs of funds.

A certain investor purchased shares in the amount of 1000 rubles ( Sstart).

After 3 months, he bought more shares for 500 rubles ( Svv).

After another 4 months, the investor urgently needed money, and he was forced to sell part of the shares in the amount of 300 rubles ( Sout).

One year after the initial acquisition, the share price was RUB 1,300 ( Total).

In the form of a graph, this situation can be represented as follows:

To correctly calculate the return on investment, we still need to divide the result of the investment by the amount of invested funds. It remains only to determine what is the result in the situation under consideration and what is the correct amount of invested funds.

first step will calculate the return on investment. It is intuitively clear that the return on investment is the difference between the funds that were received and those that were invested. That is, it is necessary to subtract the sum of the initial and subsequent inputs from the sum of the final cost of investments and all withdrawals.

The formula for determining the result of investing, taking into account inputs / outputs:

ΔS = (Stotal + ΣSout) – (Sini + ΣSin), where

ΔS is the result of investment for the period in absolute terms,

Stotal - final assessment of investments (1,300),

ΣSout - the sum of all withdrawals (300),

Snach - the amount of initial investment (1,000),

ΣSвв - the sum of all deposits (500).

Let's apply this formula to the considered situation: ΔS = (1300 + 300) - (1000 + 500) = 100. Thus, the investor earned 100 rubles.

Second step in the calculation of profitability is the most important: it is necessary to correctly determine with what amount to correlate the calculated investment result, that is, to correctly determine the amount of invested funds.

In each time sub-period (T1, T2, T3) the amount of invested funds was different. In the sub-period T1 - 1000 rubles, T2 - (1000+500) rubles, T3 - (1000+500-300) rubles. In addition, these time sub-periods themselves are not equal. T1 - 90 days, T2 - 120 days, T3 - 155 days. Therefore, it is necessary to reconcile the amount of invested funds with the number of days in the sub-period, thus determining the average "working" amount ( time-weighted average investment) for the period under review.

The formula for determining the weighted average amount of invested funds, taking into account inputs / outputs:

V = (T1*Sini+T2*(Sini+Sin)+T3*(Sini+Sin-Sout)+…+Tn*(Sin+ΣSin-ΣSout)/ ΣT, where

V is the weighted average amount of invested funds,

T1, T2, T3, Tn - the number of days in the sub-period,

ΣT is the total number of days in the considered time period.

Let's apply this formula to the considered situation: V = (90*1000 + 120*(1000+500) + 155*(1000+500-300))/365 = 1249.32.

The weighted average amount of funds invested by the investor amounted to 1249.32 rubles.

Now all the elements necessary for the direct calculation of profitability are known.

Third step– calculation of profitability from the obtained values. To do this, we divide the previously calculated investment result by the weighted average amount of invested funds and convert the result obtained into annual percentages.

The formula is: D = (ΔS/V) * 365/T * 100%

It turns out that in the considered situation, the yield is: (100/1249.32) * 365/365 * 100% = 8% per annum.

Conclusions:

Using these formulas, you will always be able to correctly evaluate the profitability of your investment portfolio and, using the obtained values, evaluate the effectiveness of your investments.

The considered algorithm is not simple, but when it comes to calculating profitability and profit, the main thing is accuracy. This algorithm allows you to take into account all the nuances associated with deposits / withdrawals of funds and get the correct calculation of profitability.

If you use trust management services, find out how the profit and return on your portfolio is calculated and, if it differs from the algorithm indicated above, then this is a reason to check the correctness of the algorithm used.

It is necessary to pay close attention to the calculation of the profitability of your investments, since this indicator is decisive in the analysis of the effectiveness of investment, and if it is calculated incorrectly, this will create an incorrect idea of ​​​​the effectiveness of your investments.

T Now a practical calculation for my portfolio.

As I wrote earlier, I calculated portfolio changes using the "mutual fund" method, i.e. when introducing new funds, I determined the new NAV and divided by the "value of the share" before the introduction of funds, thereby increasing the number of shares for a continuous continuation of the portfolio value graph.

In fact, I calculated the change "unit prices", but this is not real income my investment, since this method does not take into account the amount of deposit / withdrawal of funds. I could enter new money during drawdowns, and withdraw at peaks, and as a result, the “share price” chart could be at zero - and the result of investments in a good plus.

I will make calculations return on the portfolio according to the formula above, taking into account all deposits / withdrawals and dates of transactions, as well as the final financial result:

It turned out +23.78% per annum.

+21.76% for 334 days - in annual terms (for 365 days) it is +23.78%. So everything counted correctly.

Quite a significant distortion - 24% or 18% - there is a difference! If you manage assets and do not deposit or withdraw funds for a year, then the determination of profitability using the “mutual fund” method is suitable, but if you deposit and withdraw funds, then do not use this method - deceive yourself or your investor!

By the way, some cunning managers, showing their equity on history, they resort to such a trick - having a mega-result on a small amount, and later when investors enter more significant money - the result may worsen, but the equity will still be attractive to new investors.

For example, the growth of equity by 5 times in 2 years, of which in the first year the equity increased by 4.5 times with an initial capital of 100 thousand rubles, and then at the end of the first year another 50 million rubles were contributed, and the result for the second year was only +11%, but there will be a nice growth in equity over 2 years 5 times!

According to the method of determining the “share price”, everything will be fine, but in terms of real profitability for the investor, it will be much more modest. I advise you to be more attentive to such moments ...

What method are you using?

Both methods can and should be used - but for different purposes, you must understand this. If you are a mutual fund (or IMU) and take money into management, it is necessary to determine the value of the share, but in addition, you need to determine the profitability of each individual investor. It will vary depending on its deposit/withdrawal operations.

P.S. By the way, because of this nuance, sometimes there is an erroneous determination of the result of profitability for a particular investor, which leads to misconceptions because of this.

A striking example is Elvis Marlamov, which this spring contributed funds to buy stocks in a market failure. Was he even accused of it? Is the deposit/withdrawal of funds a bad thing for an investor?

I think that this is a plus for the manager - the ability to press the gas at the right time. Using the leverage - I'll leave it out of the box, this is everyone's business, I would not use it. But the introduction of funds for the purchase of inadequately cheap assets is buzzing.

He did everything right! Made money on this panic.

But his public account equity is still low. How can this be? They even write that Elvis leaked everything?! Is it really? Or is this a minus of the generally accepted system for determining profitability?

The trouble is that the public only determines the "price of a share" of each investor, and not the real return that a particular investor makes.

Elvis promised to send me the necessary data to calculate the real yield. To be continued!

Successful investment!