Quantifying Risk in Finance With the Help of Dispersion
Risk – in its essence, is present everywhere around us. We generally seek to mitigate or manage it, and the same applies in the field of finance. Whether the objective is to eliminate risk entirely or to control it so that our financial decisions do not turn against us, the underlying goal remains the effective management of uncertainty.
In finance, risk can be defined as the possibility that actual returns will deviate from the expected returns, . While this deviation can occur in either direction—and most investors would certainly welcome a few extra percentage points of profit—the main focus usually lies in managing and mitigating downside risk. Investors are typically more concerned with protecting their portfolios from losses than with limiting unexpected gains.
1. Financial Risk
In the world of finance, there are many types of risks lurking around the corner. Some are quite apparent, while others may not be as obvious. In this section, we will classify and discuss the major groups of risks that an investor may encounter in a financial context.
In general, financial risk can be divided into two main categories: systematic risk and specific risk.
systematic risk represents the portion of total risk that is always present and cannot be eliminated, as will later be seen in the definition of market risk. The terms systematic risk and market risk are often used interchangeably, as many authors define market risk as a form of systematic risk.
Specific risk, on the other hand, refers to the portion of risk that can be mitigated—or in some cases, even eliminated entirely. Depending on the type of risk, various strategies can be employed to reduce it, with hedging and diversification being among the most common approaches.
1.1. Market risk
This type of risk usually arises from macroeconomic events, structural changes in the economy, political shifts, and similar factors. It represents the portion of total risk that while can be mitigated via hedging, or diversification, it cannot be eliminated by the investor entirely, which is why it is often also referred to as systematic risk. Two prominent examples of market risk are currency risk and interest rate risk.
Currency risk (often called foreign exchange or FX risk) is a classic example of systematic risk. While hedging strategies can help mitigate it, there will always remain an element of uncertainty that cannot be completely eliminated. Currency risk can be defined as the risk of a change in the value of an asset denominated in a currency different from the investor’s base currency, caused by fluctuations in exchange rates in the financial markets.
Interest rate risk is another important example, and it has become particularly relevant in recent years as central banks have adjusted their monetary policies. Although investors can mitigate this risk through hedging, it cannot be entirely removed, which again makes it a form of systematic risk. Interest rate risk can be defined as the risk of a change in an asset’s value resulting from shifts in interest rates driven by central bank policy decisions.
1.2. Credit Risk
Credit risk is a type of risk most commonly present in the capital markets, particularly when investing in money market instruments or debt securities. It represents the possibility that a borrower’s ability to repay the lender will deteriorate, or that the borrower may become unable to meet their obligations altogether. This type of risk depends on various factors, such as the borrower’s liquidity position, leverage, and overall financial health.
Credit risk can generally be assessed and partially mitigated by examining the borrower’s credit rating or by analyzing the credit spread—the difference between the yields of two bonds with similar characteristics (such as maturity and principal). The credit spread provides insight into how much additional risk the market attributes to a particular security relative to a risk-free benchmark.
1.3. Liquidity Risk
This type of risk represents the low ability—or even the inability—to liquidate a given asset. If an asset carries a high level of liquidity risk, it means the market for that asset is relatively illiquid, exposing the investor to potential complications when attempting to sell it. In such cases, one might have to wait for a buyer or sell the asset at a discount to its current market value in order to attract interest. This situation often arises when an investor needs to sell an asset abruptly or under unfavorable market conditions – which of itself is a very inconvenient time to sell anyway.
1.4. Operational Risk
Operational risk represents the possibility of incurring losses due to failures in internal processes, systems, or human error. It can also arise from indirect or external causes, such as natural disasters, cyberattacks, or other unforeseen events that disrupt normal business operations. Unlike market or credit risk, operational risk does not stem directly from market movements or counterparty default but rather from the way an organization conducts its daily activities.
Examples of operational risk include system outages that prevent transactions from being processed, accounting or data entry errors that lead to financial discrepancies, or breaches in internal controls that allow for fraud or unauthorized activity. It is important to note that well-established institutions might be exposed to operational risk, as complete prevention is virtually impossible. However, it can be effectively mitigated through strong internal controls, risk management frameworks and regular audits.
2. Quantifying Financial Risk
In the financial setting, we can use the mean expected return E[R]E[R] as an indicator of an expected return of our investment, and the standard deviation - also noted as sigma σσ to describe the risk of an asset or more often a portfolio of assets. We’ve discussed how to quantify the risk of a single asset in the previous article.
2.5. Measuring the Expected Return of a Portfolio
Before we can go and measure the risk of a portfolio, we first need to define a way to compute the expected return of that portfolio. Since risk is defined and measured as the standard deviation from this expected return, it represents a key metric we must know before doing anything else.
In the case of a single asset, we can compute the mean of the holding period returns simply by calculating its average return over time, as shown in the following equation.
3. Conclusion
Risk will always be part of the financial world—it’s what makes investing both challenging and worthwhile. Every choice we take in the financial markets carries a degree of uncertainty, and that’s what keeps markets alive. The real goal isn’t to remove risk completely but to understand it well enough to keep it from taking control or end up going against us. By recognizing the difference between risks we can manage and those we can’t, we give ourselves the ability to act with clarity instead of fear.
Strategies like diversification and hedging don’t make risk disappear, but they help keep it in check. They give investors a sense of direction when the market feels unpredictable. Still, managing risk isn’t just about using financial tools; it’s about judgment, awareness, and learning from experience. Markets change, new risks appear, and what worked yesterday might not work tomorrow.
In the end, risk is what makes finance dynamic—it’s the price of opportunity. To manage it wisely is to accept that uncertainty is part of progress, and that smart decision-making isn’t about avoiding losses entirely, but navigating them with purpose and understanding.