Cost of risk. Methods for assessing market risk The essence of the var method is to determine

Value at Risk- one of the most common forms of measuring financial risks. Commonly referred to as “VaR”.

It is also often called "16:15", it received this name because 16:15 is the time at which it supposedly should lie on the table of the head of the bank’s board JPMorgan. (In this bank, this indicator was introduced for the first time in order to improve the efficiency of working with risks.)

Essentially, VaR reflects the amount of possible loss that will not be exceeded over a certain period of time with some probability ( which is also called the “tolerable risk level”"). Those. the largest expected loss that an investor can receive within n days with a given probability

The key VaR parameters are:

  1. Time horizon - the period of time for which the risk is calculated. (According to the Basel documents - 10 days, according to the Risk Metrics method - 1 day. Calculations with a time horizon of 1 day are more common. 10 days are used to calculate the amount of capital covering possible losses.)
  2. The level of acceptable risk is the probability that losses will not exceed a certain value (According to the Basel documents, the value is 99%, in the RiskMetrics system - 95%).
  3. Base currency - the currency in which VaR is calculated

Those. A VaR equal to X with a time horizon of n days, a risk tolerance level of 95% and the base currency of the US dollar would mean that there is a 95% chance that the loss will not exceed $X within n days.

  • The standard for broker-dealer reporting of OTC derivatives transactions to the US Securities and Exchange Commission is a 2-week period and a 99% confidence level.
  • The Bank of International Settlements To assess the adequacy of bank capital, I set the probability at 99% and a period of 10 days.
  • JP Morgan publishes its daily VaR values ​​at the 95% confidence level.
  • According to a study by New York University Stern School of Business, about 60% of US pension funds use VaR in their work

Example of VaR calculation in Excel:

Let's take the price history of the asset we are interested in, for example, ordinary shares of SberBank. In the example, I took EOD (EndOfDay) prices for 2010.

Let's calculate the standard deviation of the obtained return (the formula for calculating the standard deviation for a sample for Microsoft Excel will look like =STDEV.B(C3:C249)):

Assuming an acceptable risk level of 99%, we calculate the inverse normal distribution (quantile) for a probability of 1% (the formula for Excel in our case will look like =NORM.REV(1%, AVERAGE(C3:C249), C250)):

Well, now let’s directly calculate the value of VaR itself. To do this, subtract the estimated value obtained by multiplying by the quantile from the current value of the asset. Therefore, for Excel the formula will look like: =B249-(B249*(C251+1))

In total, we received the calculated value of VaR = 5.25 rubles. Taking into account our time horizon and the degree of acceptable risk, this means that SberBank shares will not fall in price by more than 5.25 rubles over the next day, with a 99% probability!

In recent decades, the world economy has regularly fallen into a whirlpool of financial crises. 1987, 1997, 2008 almost led to the collapse of the existing financial system, which is why leading experts began to develop methods that can be used to control the uncertainty that dominates the financial world. In the Nobel Prizes of recent years (received for the Black-Scholes model, VaR, etc.) there is a clear tendency towards mathematical modeling of economic processes, attempts to predict market behavior and assess its stability.

Today I will try to talk about the most widely used method for predicting losses - Value at Risk (VaR).

Concept of VaR

An economist's understanding of VaR is: “An estimate, expressed in monetary units, of the amount that losses expected to occur during a given period of time will not exceed with a given probability.” Essentially, VaR is the amount of loss on an investment portfolio over a fixed period of time, if some unfavorable event occurs. “Unfavorable events” can be understood as various crises, poorly predictable factors (changes in legislation, natural disasters, ...) that can affect the market. One, five or ten days are usually chosen as the time horizon, due to the fact that it is extremely difficult to predict market behavior over a longer period. The acceptable risk level (essentially a confidence interval) is taken to be 95% or 99%. Also, of course, the currency in which we will measure losses is fixed.
When calculating the value, it is assumed that the market will behave in a “normal” way. Graphically this value can be illustrated as follows:

VaR calculation methods

Let's consider the most commonly used methods for calculating VaR, as well as their advantages and disadvantages.
Historical modeling
In historical modeling, we take the values ​​of financial fluctuations for the portfolio already known from past measurements. For example, we have the performance of a portfolio over the previous 200 days, based on which we decide to calculate VaR. Let's assume that the next day the financial portfolio will behave the same as on one of the previous days. This way we will get 200 outcomes for the next day. Further, we assume that the random variable is distributed according to the normal law, based on this fact, we understand that VaR is one of the percentiles of the normal distribution. Depending on what level of acceptable risk we have taken, we select the appropriate percentile and, as a result, we obtain the values ​​that interest us.

The disadvantage of this method is the impossibility of making predictions for portfolios about which we have no information. A problem may also arise if the components of the portfolio change significantly in a short period of time.

A good example of calculations can be found at the following link.

Leading component method
For each financial portfolio, you can calculate a set of characteristics that help assess the potential of assets. These characteristics are called leading components and are usually a set of partial derivatives of the portfolio price. To calculate the value of a portfolio, the Black-Scholes model is usually used, which I will try to talk about next time. In a nutshell, the model represents the dependence of the valuation of a European option on time and on its current value. Based on the behavior of the model, we can evaluate the potential of the option by analyzing the function using classical methods of mathematical analysis (convexity/concavity, intervals of increasing/decreasing, etc.). Based on the analysis data, VaR is calculated for each of the components and the resulting value is constructed as a combination (usually a weighted sum) of each of the estimates.

Naturally, these are not the only methods for calculating VaR. There are both simple linear and quadratic price prediction models, as well as a rather complex variation-covariance method, which I did not talk about, but those interested can find a description of the methods in the books below.

Criticism of the technique

It is important to note that when calculating VaR, the hypothesis of normal market behavior is accepted, however, if this assumption were correct, crises would occur once every seven thousand years, but, as we see, this is absolutely not true. Nassim Taleb, a famous trader and mathematician, in his books “Fooled by Randomness” and “The Black Swan” severely criticizes the existing risk assessment system, and also proposes his solution in the form of using another risk calculation system based on the lognormal distribution.

Despite criticism, VaR is quite successfully used in all major financial institutions. It is worth noting that this approach is not always applicable, which is why other methods have been created with a similar idea, but with a different calculation method (for example, SVA).

In response to the criticism, modifications of VaR have been developed, based either on other distributions or on other techniques for calculating the peak of the Gaussian curve. But I will try to talk about this another time.

Let's consider methods for assessing risk, in particular market risk, using the VaR (Value at Risk) risk measure. To do this, let’s look at a practical example of risk assessment for a share in the company OJSC Gazprom.

Market risk. Definition

Market risk (EnglishMarketrisk) is the probability of an unfavorable change in the value of assets. Changes in value are influenced by many macro-, meso-, microeconomic factors, which include prices for raw materials (oil, steel, platinum, etc.); prices for precious metals (gold, silver); changes in sectoral production indices, national indicators (GDP, unemployment, key interest rate, inflation), levels of supply and demand, etc.

Market risks are included in the system of financial risks and the following types can be distinguished:

  • Equity risk is the probability of loss in the event of an unfavorable change in the value of securities on the stock market.
  • Interest rate risk – the probability of losses when bank interest rates change.
  • Commodity risk is the probability of unexpected losses in the event of changes in the value of goods.
  • Currency risk – the probability of losses due to changes in exchange rates.

Market risks are assessed by various investment companies, investment and hedge funds, private investors, banks, enterprises, financial agents, suppliers, etc. to minimize possible losses and create reserves. As we see, market risks affect a wide variety of financial market participants.

Risk assessment methods

In order to manage possible losses and determine reserves for loss insurance, a quantitative risk assessment is necessary. The basic axiom of any management is that you can only manage what can be measured quantitatively. All methods for assessing market risks can be divided into two groups:

  1. Statistical methods for risk assessment
    1. Standard deviation of returns (σ)
    2. Value at Risk (Var) method
    3. CVaR method
  2. Expert risk assessment methods
    1. Rating methods
    2. Ballroom methods
    3. Delphi method

The advantages of statistical methods include the ability to objectively assess the probability of unexpected losses and their absolute size. Expert assessment methods make it possible to take into account poorly formalized risk factors and develop various scenarios for its reduction.

G. Markowitz in the early 60s proposed assessing risk as the volatility of the value of securities on the stock market. That is, the more the price of an asset changes, the higher the risk of investing in it. The disadvantages of this method were the inability to predict the size and likelihood of future losses.

Method for assessing market risk. VaR (Value at Risk) risk measure. What is VaR?

In the 80s a new risk criterion – VaR (Value at Risk), which made it possible to comprehensively assess possible losses in the future with a selected probability and over a certain period of time. To calculate the VaR risk measure, several methods are used in practice:

  • Historical modeling method (“delta normal”, “manual method”).
  • Parametric model method.
  • Statistical (simulation) modeling using the Monte Carlo method.

VaR risk assessment based on historical modeling in Excel

Let's consider an example of assessing the risk of an asset in the stock market using the VaR model based on delta normal modeling of the probability and size of a loss. Let's take the stock quotes of OJSC Gazprom and calculate the possible losses for this type of asset. To do this, you need to download quotes from the finam.ru service (“Data Export”) or from the finance.yahoo.com website if you are assessing market risk for foreign companies. According to the recommendation of the Bank of International Settlements, at least 250 data on the share price must be used to calculate VaR. Daily quotes for OJSC Gazprom were taken for the period 01/31/2014 – 01/31/2015.

Market risk assessment using the Value at Risk (VaR) method

Return on shares of OJSC Gazprom=LN(B6/B5)

Calculation of profitability of shares of OJSC Gazprom

It should be noted that the correctness of using the delta normal method of risk assessment is achieved only when risk factors (profitability) are subject to the normal distribution law (Gaussian). To determine whether the profitability distribution belongs to the Gaussian distribution, you can use classical statistical tests - Kolomogorov-Smirnov or Pearson.

Expected value=AVERAGE(C5:C255)

Standard deviation=STDEV(C5:C255)

Calculation of parameters of the stock return distribution function

The next step in calculating the VaR risk measure is to determine the quantile of this normal distribution. In statistics, a quantile is understood as the value of a distribution function (Gaussian) according to given parameters (mathematical expectation and standard deviation) for which the function does not exceed a given value with a given probability. In our example, the probability level was taken at 99%.

Let us calculate in Excel the quantile value for the distribution of profitability of the shares of OJSC Gazprom.

Quantile=NORMBR(1%,E5,F5)

Quantile Estimation in Excel

Forecasting the future value of a stock based on the VaR method

Where:

P t +1 – minimum share price in the next time period t with a given quantile level.

To predict the future value of a stock (asset) for several periods in advance, you should use a modification of the formula:

Where:

q – quantile of distribution of stock returns;

P t – share price at time t;

P t +1 – minimum share price in the next time period t at a given quantile level;

n – depth of the forecast of the possible minimum share price.

The formula for calculating the future value of a stock in Excel will look like:

Minimum share price of OJSC Gazprom on the next day=(1+G5)*B255

Minimum share price of OJSC Gazprom in 5 days=B255*(1+G5*SQRT(5))

Forecasting the minimum stock price with a given probability

The value of P t +1 shows that with a probability of 99% the shares of OJSC Gazprom will not fall below the price of 137.38 rubles, and the value of P t +5 shows the possible minimum price of the share with a probability of 99% for the next 5 days. To calculate the absolute value of a possible loss, you must determine the percentage change in the value of the stock. The calculation formulas in Excel will be as follows:

Relative change in share price

Relative decline in stock price the next day=LN(F9/B255)

Relative decline in stock price over five days=LN(F10/B255)

Absolute change in share price

Absolute decline in stock price the next day = F9-B255

Absolute decline in stock price in five days=F10-B255

Thus, the economic meaning of the VaR indicator is as follows: over the next day, the price of a share of OAO Gazprom, with a 99% probability, will not be lower than 137.38 rubles. and absolute losses will not exceed RUB 6.44 (5%) per share. And similarly for estimating VaR for five days in advance: within five days, the price of the Gazprom share with a 99% probability will not fall below 129.42 rubles, and the loss of capital will not exceed 11% (14.4 rubles per share).

VaR risk assessment based on the “manual method” in Excel

The second method of calculating the VaR risk measure is called the “manual method”, since it allows you not to be tied to the distribution along which the value of the asset changes. This is one of its main advantages over the delta normal method. To assess market risks, we will use the same input data - quotes from OJSC Gazprom. The steps for calculating VaR are as follows:

Calculation of the maximum and minimum return on shares of OAO Gazprom

Based on the calculated profitability of OJSC Gazprom shares, we determine the maximum and minimum profitability. To do this, we use the formulas:

Maximum stock return=MAX(C5:C255)

Minimum share return=MIN(C5:C255)

Selecting the number of intervals for grouping stock returns/losses

For the manual method of risk assessment, it is necessary to take the number of intervals for dividing the grouping of returns. The quantity can be any, in our example we will take N=100.

Determining the width of the return grouping interval

The width of the interval or the group change step is necessary for constructing a histogram and is calculated as dividing the maximum spread of returns by the number of intervals. The formula for calculating the interval is as follows:

Interval size yields stock=(E5-F5)/H5

Manual VaR risk assessment

At the next stage, it is necessary to construct a histogram of the distribution of returns over selected intervals. To do this, we calculate the boundaries of all profitability groups (there are 100 in total). The calculation formula is as follows:

Stock return limit=H5+$E$11

Calculation of the yield boundary in Excel for the shares of OAO Gazprom

After determining the boundaries of the profitability groups, we build a cumulative histogram. To do this, go to the “Data” → “Data Analysis” → “Histogram” add-in.

In the window that opens, fill in the “Input intervals”, “Pocket intervals”, and also select the “Integral percentage” and “Graph output” option.

An example of constructing a histogram of profitability of OJSC Gazprom

As a result, a new worksheet will be generated with a graph and the frequency of profit/loss falling into a particular interval. The cumulative graph looks like this:

Cumulative return histogram in Excel

So, the first column of the resulting table is the quantile of the data for the distribution of returns/losses, the second is the frequency of returns falling into a particular interval, the third reflects the probability of losses occurring. In the table with the cumulative probability of falling into a particular interval, it is necessary to find a level of ~1%.

Determining the quantile of stock returns “manually”

The quantile value corresponds to -0.039, whereas with the delta normal method of risk assessment, the quantile was -0.045. To assess risks, we will use the assessment formulas already obtained and calculate the amount of losses. The figure below shows an estimate of possible losses for the next day and within five days with a 1% probability of 4 and 9%, respectively.

The result of manually assessing the VaR risk measure in Excel

Difficulty of using the VaR risk assessment method

The domestic stock market has a fairly high degree of volatility; the market experiences “heavy tails” – that is, the occurrence of frequent crises with large losses. As a result, the VaR model cannot accurately predict an investor's possible future losses. It should be noted that this model is well applicable to low-volatile commodity markets rather than stock markets.

Summary

In this article, we examined risk assessment methods using the example of the Gazprom OJSC stock; for this purpose, we examined step by step how a modern risk assessment Value at Risk (VaR) is constructed in Excel in two ways: delta using normal modeling and the “manual method”.

Price risk(price risk) - the likelihood of unexpected financial losses from changes in the level of prices for products or individual products in the upcoming period or purchase and sale transactions. Price risk can be insured by an enterprise by carrying out an operation.

The main types of price risks include:

  • increase in purchase prices for raw materials, materials, components;
  • the likelihood of competitors setting prices below market prices (for products sold by the enterprise);
  • changes in government pricing regulation;
  • the likelihood of introducing new taxes and other payments that are included in the price of products;
  • reduction in the level of goods on the market;
  • increase in prices and tariffs for services of other organizations (electricity, transport services, etc.).

Price risk is associated with determining the price of products and services sold by an enterprise, and also includes the risk in determining the price of necessary means of production, raw materials used, materials, fuel, energy, labor and capital (in the form of interest rates on loans). According to some calculations, a 1% error in the price of sold products leads to losses amounting to at least 1% of sales revenue. If the demand for a given product is elastic, then losses may amount to 2-3%. With product profitability of 10-12%, a 1% error in price could mean a 5-10% loss in profit. Price risk increases significantly in conditions.

Price risk is one of the most dangerous types of risk, since it directly and significantly affects the possibility of loss of income and profit of a commercial enterprise. Price risk constantly accompanies the economic activities of an enterprise.

Price risk is the risk of loss due to future changes in a commodity or financial instrument. There are three types of price risks: , and . Traditionally, the term “price risk” covers not only the possibility, but also the possibility of obtaining.

Price risk is the risk of changes in the price of a debt obligation due to an increase or decrease in the current level. Price risk is the risk that the value (or portfolio) will decline in the future. Also a type of mortgage period risk that arises in the production segment when establishing loan repayment terms for the borrower before establishing the terms for selling the security on the secondary market. With a general increase in the level of interest rates on loans during the production cycle, the lender may be forced to sell the loan issued at .

Regulatory price risk is the risk that arises when regulators limit what they can charge.