Financial risk refers to liquidity that changes due to changes in finance, markets, and the like. This refers to the possibility that ‘the future state may be different from what is currently expected.’ For example, suppose you bought one share of Samsung Electronics stock today for $50. You expect it to be worth $60 after one year. However, suppose a new product released by Samsung Electronics becomes a huge hit, causing the stock price to skyrocket to over $100 per share after one year. Although you made a better profit than expected, it also falls under financial risk.

There exists a principle called the Risk-Return Trade-off, which describes the trade-off between returns and risks. In essence, the greater the expected gain, the greater the risk, and this forms a perennial dilemma for human desire to minimize risks while maximizing profitability. Almost all issues in financial management involve researching ways to reduce risk and increase returns.

Units for measuring such risks include standard deviation and beta coefficients. Along with measuring returns, using expected values (means) and probability distribution models, we can describe the risk-return trade-off and establish simple models to mitigate risks.

On the other hand, risk can also denote the possibility of diminishing utility derived from what one possesses. In this case, there is a negative connotation akin to conventional ‘risk.’ Metrics like Value at Risk (VaR) focus more on this aspect of meaning. Management departments monitor how exposed the company or specific departments are to market volatility, thereby imposing limits on the funds that can be operated. Furthermore, they always manage the risk of default/loss associated with the transactions the company is pursuing. The concept of VaR, widely used in risk departments of financial institutions, originated from JP Morgan Chase’s risk department. An internationally recognized certification in this field is the International Financial Risk Manager (FRM).

People have a tendency to avoid uncertainty, termed as ‘risk aversion.’ Financial theorists often explain risk aversion through the law of diminishing marginal utility. For instance, given the choice between receiving $1 million with a 100% probability or receiving either $0 or $2 million each with a 50% probability, most people would choose the former because the utility of gaining $1 million is much greater than half the utility of gaining $2 million.

Mathematically, the Jensen’s Inequality is often cited. The graph of a utility function typically possesses characteristics where the first derivative is greater than 0 and the second derivative is less than 0. According to Jensen’s Inequality, for a convex function (a function where the second derivative value is less than or equal to 0), the value of the function’s arithmetic mean of the independent variable’s sum is always greater than or equal to the arithmetic mean of the value of the function. Thus, assuming the law of diminishing marginal utility holds, it is rational to prefer the option with less deviation when the expected values are the same.

Conversely, to be considered a rational investment, the expected value when there is risk must always be greater than the current value. If there is risk, but it does not guarantee a higher expected value than the current value, it would be closer to speculation or gambling rather than a rational investment.

In financial management, risk management generally focuses more on the first type of risk rather than the second, and in some sense, finding ‘how much return is adequate for the risk?’ constitutes the essence of the discipline of finance.

The fundamental logic explaining that ‘risks can be combined’ lies in the laws of probability and the central limit theorem. Consider throwing a dice. Whether thrown once or a thousand times, the expected value remains the same at 3.5, but the variance per trial in the latter case would likely be lower. Furthermore, aggregating the results of a thousand trials would likely follow the shape of a normal distribution.

In addition, the concept of correlation coefficient is applied. For example, if there are two stocks that move in opposite directions while providing a certain return, combining the two stocks can reduce risk to zero. According to the portfolio theory, the combination of assets with a correlation coefficient less than 1 reduces risk.

Therefore, it is more rational to diversify investments rather than invest in a single asset, and the reason for constructing a portfolio is to combine risks. This simple principle, first proved by Markowitz, earned him the Nobel Prize in Economics.

However, no matter how many risky assets are combined, there is ultimately unavoidable risk. This risk is called systematic risk, which refers to the risk of the entire market changing according to macroeconomic fluctuations. In other words, systematic risk is the risk that cannot be reduced further because the entire market has a certain directionality.

The compensation for this systematic risk is the market rate of return. Moreover, the Capital Asset Pricing Model (CAPM), which is still the most widely used model in practice, explains the returns of individual assets in relation to the market rate of return. When explaining financial theory, one cannot separate the concepts of risk and risk aggregation.

Professions related to finance must fundamentally understand theories regarding risk and returns.

For instance, a Quantitative Risk Analyst specializes in dealing with financial risk within the finance department. Their job is to develop computer systems tailored to financial engineering theories to minimize financial risks using computers. A good major for them to start with could be Statistics or Operations Research, with a good understanding of Quantitative Finance. Proficiency in scripting languages such as Python, Bash, Perl, JavaScript, regular expressions and knowledge of MySQL, Java, machine learning, and data mining is very important as well.