# A NEW APPROACH TO RISK IDENTIFICATION IN PORTFOLIO INVESTMENT

**DOI: https://doi.org/10.23670/IRJ.2022.119.5.138**

**НОВЫЙ ПОДХОД К ОПРЕДЕЛЕНИЮ РИСКОВ В ПОРТФЕЛЬНОМ ИНВЕСТИРОВАНИИ**

Научная статья

**Якупов Б.Т. ^{1, }*, Сафиуллин Л.Н.^{2}**

^{1 }ORCID: 0000-0001-8417-1971;

^{1 }Центр перспективных экономических исследований Академии наук Республики Татарстан, Казань, Россия;

^{2} Казанский федеральный университет, Казань, Россия

* Корреспондирующий автор (bulat.yakupov[at]mail.ru)

**Аннотация**

*Целью данной научной работы является попытка пересмотреть положения существующей портфельной теории инвестирования, в основе которой лежит принцип стремления к оптимальному соотношению доходности и риска инвестиционного портфеля. Где под риском понимается волатильность, которая выражается через стандартное отклонение. В статье анализируется портфельная теория Марковица, выделяются ее недостатки, среди которых, по мнению автора, основным является выражение риска в инвестировании через волатильность или стандартное отклонение. Автор статьи дает иную трактовку риска в инвестировании. Предлагаются понятия "риск волатильности" и "риск потери капитала", а также разграничение этих понятий и доказательство их нетождественности. Инструментами для доказательства положений статьи служат индекс S&P500 и индекс волатильности VIX 1985 года. Результаты исследования могут быть применены в практической деятельности частных инвесторов и портфельных управляющих.*

**Ключевые слова:** портфельная теория Марковица, волатильность, риск, стандартное отклонение, портфельные инвестиции.

**A NEW APPROACH TO RISK IDENTIFICATION IN PORTFOLIO INVESTMENT**

Research article

**Yakupov B.T. ^{1, }*, Safiullin L.N.^{2}**

^{1 }ORCID: 0000-0001-8417-1971;

^{1 }Center of Advanced Economic Research in the Academy of Sciences of the Republic of Tatarstan, Kazan, Russia;

^{2} Kazan Federal University, Kazan, Russia

* Corresponding author (bulat.yakupov[at]mail.ru)

**Abstract**

*The purpose of this research work is an attempt to revise the provisions of the existing portfolio theory of investing, which is based on the principle of striving for the optimal ratio of return and risk of an investment portfolio. Where risk is understood as volatility, which is expressed through the standard deviation. The article analyzes Markowitz's portfolio theory, highlighting its shortcomings, among which, in the author's opinion, the main is the expression of risk in investment through volatility or standard deviation. The author of the article gives a different interpretation of risk in investing. The concepts of "volatility risk" and "risk of capital loss" are proposed, as well as the distinction between these concepts and the proof of their non-identity. The S&P500 index and the VIX volatility index of 1985 are used as tools to prove the provisions of the article. The results of the study can be applied in the practical activities of private investors and portfolio managers.*

**Keywords: **Markowitz portfolio theory, volatility, risk, standard deviation, portfolio investments.

**Introduction**

Today, there are many theories aimed at improving investment outcomes through an optimal balance of return and risk.

Portfolio investment theory begins with the concept of value investing, suggested in the late 1920s by Benjamin Graham and David Dodd, professors at Columbia Business School. Value investing is an investment strategy based on identifying undervalued securities through fundamental analysis [4, P. 372]. Risk was practically not considered in such investing. The problem of the method of value investing consists in ambiguity of determination of "intrinsic value" of shares because there is no standard or generally accepted method of assessment of such value.

In 1930, Professor I. Fisher of Yale University published his book "The Theory of Interest" where he described a method of comparing two or more investment projects. In order to identify the more attractive investment project he suggests comparing the discounted difference between the benefits and costs of each project [3, P. 230].

In 1936 J. M. Keynes in his classic work "The General Theory of Employment, Interest and Money" introduced the concept of marginal efficiency of capital, suggesting to use it as a discount rate to calculate the net present value of an investment project [5, P. 125].

It is important to note the contribution of representatives of domestic science in the study of stock markets and modeling of investment portfolios. In particular, the modern stage of portfolio investment development is studied by I. A. Koch. Systematizing and supplementing classical methodological approaches to the formation of an investment portfolio, he singles out the following necessary elements of portfolio theory: portfolio construction methodology; methodology of evaluation of investment qualities of assets and portfolios; methodology of portfolio investment efficiency evaluation [9, P. 713].

However, the above considered methods of investment attractiveness analysis were not quite appropriate to the sphere of portfolio investments. When making investment decisions, the main emphasis was placed on profitability, while such parameter as risk and its measurement were actually ignored.

The key method for forming and evaluating investment portfolios today is Harry Markowitz's portfolio theory. Markowitz's theory had a revolutionary significance for the stock market, creating a basis for the formation and optimization of investment portfolios based on rigorous mathematical calculations, the proper use of which can reduce the risk of investing.

Markowitz argues that an investor should base his portfolio selection decision on expected returns and standard deviation. This means that an investor should evaluate the expected return and standard deviation of each portfolio and then choose the "best" portfolio based on the ratio of these two parameters. The expected return can be represented as a measure of the potential reward associated with a particular portfolio, and the standard deviation as a measure of the risk associated with that portfolio. Thus, after each portfolio has been examined in terms of potential reward and risk, the investor must choose the portfolio that is most appropriate for him [7, P. 79].

Thus, the object of this study is the portfolio theory of Markowitz as the main method of investment in the securities market.

The subject of the research is economic relations that develop in the process of investment activity on the securities market.

**Shortcomings of the Markowitz portfolio theory**

Markowitz's theory, like any other theory, has its limitations. According to the author, the main disadvantages of Markowitz's theory are:

- All portfolio theories, like all technical analysis theories, are based on historical stock price data. In the real world, past returns do not guarantee future returns.
- The basic premise of the model is efficient capital markets where rational agents operate, and thus there can be no prolonged irrational movements.
- The Markowitz approach is seen as a single period approach: at the beginning of the period an investor must decide which private securities to invest in and hold those securities until the end of the period. In reality, portfolio investments are not made at one time, but at regular intervals.
- The risk of a financial instrument is assessed by means of the standard deviation. However, a positive change in return above the average is not in fact a risk.
- The discrepancy also arises in the holistic definition of risk. Following Markowitz, all portfolio theories assess the degree of risk by the volatility of securities.

With numerous shortcomings, special attention should be paid to the latter shortcoming in the form of expressing risk to the investor as the volatility of a financial instrument. The reason for such a comparison is obvious - the volatility of financial instruments is quite easy to calculate using such indicators as standard deviation, dispersion, beta coefficient, Value at risk (VaR), etc. Mathematical calculation and numerical expression of volatility greatly facilitate the task of portfolio managers, if the volatility is taken as the risk of the portfolio. In this case there is an opportunity to justify numerically his/her point of view on the profitability and risk of certain financial instruments or investment portfolios to the client.

The expected return of a portfolio that is equally distributed between the stocks of two companies is equal to the average return of the stocks it contains, while the volatility of the portfolio is much less than the average volatility of the two stocks and much less than the volatility of the portfolio's constituents. This means that if you combine different assets in the same portfolio, the volatility to income ratio will improve. But will the risk-return ratio improve?

Figure 1 shows a typical chart of the volatility/return ratio of two assets. As can be seen from Figure 1, the dynamics of the two financial instruments have an inverse correlation with approximately the same rate of growth in value.

Fig. 1 – Reduced portfolio volatility when using assetswith negative correlation [8]

Common sense suggests that if two stocks fluctuate in opposite directions, these fluctuations cancel each other out. The total volatility of the portfolio decreases, but does the real investment risk decrease? The process of reciprocal damping of stock price fluctuations is shown in the figure above. You can easily see that the total return curve is much smoother than the return curves of individual securities.

**Methods**

The idea of this article is based on the distinction between risk and volatility and their non-identity. Volatility is a statistical financial indicator that characterizes the volatility of the price of something. Volatility is the most important financial indicator and concept in financial risk management today. To calculate the volatility, the statistical indicator of sample standard deviation is used.

Risk is a combination (in terms of calculation - product) of the probability and consequences of unfavorable events [11, P. 72].

Thus, high volatility indicates a high variability of the price relative to the average value. Risk is both the probability and the consequence of adverse events. Obviously, high price volatility does not increase the consequence of adverse events. For example, if an investor risks losing all his assets, then high volatility cannot increase these losses beyond his assets. This statement is also true for the probability of adverse events for the investor. Volatility does not affect the probability of their occurrence.

Based on the wording above, let us propose the concepts of "volatility risk" and "capital loss risk".

Volatility risk is the probability and consequences of unfavorable events due to sharp fluctuations of financial instrument prices in case of their realization by an investor himself.

Capital loss risk is the probability and consequences of adverse events due to multiple reasons, except for price fluctuations of a financial instrument, which lead to partial or complete loss of an investor's property regardless of their realization by an investor.

Thus, with volatility risk, there is no risk of capital loss as long as the investor has not realized them, i.e., has not recorded a paper loss on a sharp decline in prices. For example, the price of shares fluctuates a lot, but has a steady upward trend (which is typical of emerging markets as opposed to developed markets). In such a case, capital losses can only be sustained when the stock price is at the lower end of the trend.

On the contrary, even with low volatility of a financial instrument there is always a risk of capital loss as a result of incorrect evaluation of the real value of the company and its future profitability, as well as due to the influence of external for the stock market and little predictable factors: wars, disasters, natural calamities, government decisions, taxes, inflation, etc. In this case irrespective of the investor's actions the capital may be lost if an unfavorable event occurs.

"In fact, all investment textbooks define portfolio investment risk as the variability of returns as measured by the standard deviation (variance) of the portfolio return distribution.

If it is immediately apparent that the textbook definition of risk is quite far from the intuitive sense of risk, then why does the definition of risk as a "standard deviation" so often dominate investment research?

A direct answer to the first question is that standard deviation is much easier to calculate than any alternative measure. It is usually easier to formulate and research various principles of investment risk and return using standard deviation as a measure of risk" [10, P. 159].

For example, in the case of a normal distribution (or a bell-shaped curve). Both sides of the normal distribution curve are essentially risk according to modern portfolio investment theory, since each side is a deviation from the expected return. That's what Harry Markowitz also wrote. If an investor gets a much higher return than he expected, that deviation from the expected value is standard deviation, and therefore risk. But anyone would say that exceeding expected returns is not a risk, but rather a positive result and would be essentially right, because risk as understood by investors is the probability of losses in an investment, this follows from existing definitions of risk, as well as from the author's proposed definitions of risk above.

However, it follows from the author's proposed definitions that unrealized losses in investments expressed in volatility and negative standard deviation are also not risk. A return lower than expected is also a standard deviation, only at the other pole of the normal distribution scale. It cannot be considered a true risk as long as the decline in the value of the investment portfolio is caused by market volatility and losses are not fixed. The fact is that an investor usually chooses the most promising markets or invests at all in index funds of the largest countries according to diversification. In the long term, the capitalization of the market as a whole is growing due to the development of mankind, and therefore it is not quite correct to consider a temporary decrease in the value of securities in the portfolio as a risk.

Yes, it can be easily calculated using the standard deviation coefficient, but the true risk for the investor is the loss of capital, for example, when a certain company in the portfolio goes bankrupt, when a political regime changes in the country of investment, military actions, threats to humanity, nationalization of economies and even the risk of investment accounts theft or blocking them for some reason or other. It is impossible to calculate these types of risk mathematically due to the abstract nature of their origin and their independence from historical values.

In this vein, the risk of a temporary decline in assets, unrelated to the above examples, can instead be viewed as an opportunity to invest in assets at a better price, which increases the expected return on investment in the future, although under Markowitz theory any deviation of returns from expected returns (whether up or down) would be considered a "risk".

It follows from this that a high standard deviation is not a true risk for the investor, but acts as a tool to increase the potential return on investment in the future.

To confirm the conclusion that high volatility does not represent a real threat to an investor's investment capital and, therefore, is not a risk in the traditional sense of the concept of risk, let us compare the American S&P500 Index and the VIX Volatility Index.

The VIX (often called the fear index) provides a measure of expected market volatility on which to base expectations of further stock market volatility in the near future [6].

Figure 2 shows charts of the S&P500 and VIX indices since 1985. The blue chart with the right scale is the chart of the S&P500 index. The red chart with the scale on the left is a chart of the VIX index.

Fig. 2 – Comparison of the VIX Volatility Index and the S&P500 Index [12]

In Figure 2 we can observe an interesting pattern - the periods of maximum volatility on the VIX index coincide with the local minimum value of the S&P500 index: in 1991, 1994, 1998, 2002, 2003, 2008, 2010, 2011, 2020.

According to theory, the greater the volatility, the greater the risk. The graphs in Figure 2 show that it is much more profitable to invest in the periods of maximum volatility, than in the periods of minimum volatility, when the S&P500 index is at its maximum growth values. Thus, we can conclude that increased volatility does not increase the risk of real capital loss for the investor. Only "paper" profit is reduced, and when the economy recovers after the crisis, this "paper" profit returns to its previous values and continues to grow.

If the investor pursues long-term investment goals and does not take a loss at the peak of the crisis, the volatility and the minimum of the index, then there is no real threat to the capital, nor are there any real losses.

This is what the author wrote above when proposing new formulations of the concepts of volatility and risk in the form of "volatility risk", when there is no real threat to investor's capital if the investor does not realize this risk himself, and "capital loss risk", when there is a real threat of capital reduction and loss, regardless of the investor's will for external reasons.

**Conclusion**

Thus, in this article the problem of the risk-return ratio of the investment portfolio in conditions of long-term market volatility was considered. The author proposed the concepts of "volatility risk" and "risk of capital loss" in the framework of investment activity.

In addition to introducing the concepts of "volatility risk" and "risk of capital loss", the author proposed to distinguish these concepts and prove their non-identity due to the fact that the volatility risk does not pose a real threat of capital loss unless the investor fixes losses himself. And in the case of capital loss risk, unfavorable circumstances can deprive the investor of wealth regardless of his choice.

Finally, the author's contribution to the scientific field is an attempt to revise the existing provisions of portfolio theories based on the choice between profitability and risk, where risk is understood as the volatility of financial instruments in the form of a standard deviation.

The results of the study can be applied in the practical activities of private investors and portfolio managers in the highly volatile markets of developing countries such as Russia, Brazil, China, etc. Markets of such countries are more prone to crises, which often cause high volatility in the market due to low capitalization and low involvement of the population in the field of portfolio investment.

Конфликт интересов
Не указан. |
Conflict of Interest
None declared. |

**Список литературы / References**

- Belkina, T. A. Risk-Free Investments and Their Comparison with Simple Risky Strategies in Pension Insurance Model: Solving Singular Problems for Integro-Differential Equations / T. A. Belkina, N. B. Konyukhova, B. V. Slavko // Computational Mathematics and Mathematical Physics. – 2020. – Vol. 60. – No 10. – P. 1621-1641.
- Damodaran A. The big market delusion: Valuation and investment implications / A. Damodaran // Financial Analysts Journal. – 2020. – Vol. 76, Is. 2. – P. 15-25.
- Fisher I. The Theory of Interest / I. Fisher I. – Martino Fine Books, 2012. – 610 p.
- Graham B., Dodd D. Security Analysis / B. Graham, D. Dodd. – New York: McGraw Hill, 2008. – 700 p.
- Keynes J. M. The General Theory of Employment, Interest and Money / J. M. Keynes. – New York: Macmillan Cambridge University Press, for Royal Economic Society, 1936. – 472 p.
- Kuepper, J. CBOE Volatility Index (VIX) Definition. Investopedia [Electronic resource] URL: https://www.investopedia.com/terms/v/vix.asp (accessed: 15.02.2022).
- Markowitz H. Portfolio Selection / H. Markowitz // Journal of Finance. – 1952. – Vol. 7, no. 1. – P. 77–91.
- Nexus Financial Consulting. (2022). Diversification is the best way to reduce investment risks [Electronic resource] URL: https://www.nexus.ua/images/files/Diversification.pdf (accessed: 12.02.2022).
- Safiullin L.N. Possibilities of application of analytical methods on the present securities market / L.N. Safiullin, A. Kokh, R.G. Bodrov // Journal of Social Sciences Research. – 2018. – Vol. 4, Is.12. – P.711-717.
- Sharpe W.C. Investments / William C. Sharpe, Jeffrey W.Bailey, Gordon J.Alexander. – Prentice Hall, 1998. – 962 p.
- Tobin J. Liquidity Preference as Behavior Towards Risk / J. Tobin // The Review' of Economic Studies. – 1958. –25. No. 2. – P. 65-86.
- Comparison of the VIX Volatility Index and the S&P500 Index [Electronic resource] URL: https://ru.tradingview.com/chart/?symbol=SP%3ASPX(accessed: 15.02.2022).