Total risk

What Is Total Risk?

Total risk, in the realm of portfolio theory, refers to the overall uncertainty or variability associated with an investment or a portfolio of investments. It quantifies the potential for actual returns to deviate from expected returns. This comprehensive measure encompasses all sources of risk an investor faces, whether they are specific to a particular asset or broadly impact the entire market. Understanding total risk is fundamental to effective portfolio management as it informs decisions about asset allocation and diversification. Total risk is composed of two primary elements: systematic risk and unsystematic risk.⁵

History and Origin

The concept of total risk, and its decomposition into distinct components, gained prominence with the advent of Modern Portfolio Theory (MPT). Developed by economist Harry Markowitz, MPT was introduced in his seminal 1952 paper, "Portfolio Selection." Markowitz's groundbreaking work revolutionized investment thinking by demonstrating that investors should not evaluate individual assets solely on their standalone risk and return characteristics. Instead, he proposed that an asset's contribution to the overall risk and return of an entire portfolio is what truly matters. His framework provided a mathematical approach to constructing portfolios that maximize expected return for a given level of total risk, or minimize total risk for a given expected return, laying the foundation for modern quantitative finance.

Key Takeaways

Total risk measures the complete variability of returns for an investment or portfolio.
It comprises two main components: systematic risk (non-diversifiable) and unsystematic risk (diversifiable).
Quantitative tools like standard deviation and variance are commonly used to calculate total risk.
Effective diversification can reduce unsystematic risk, but not systematic risk, within a portfolio.
Assessing total risk is crucial for investors to align their investment strategy with their risk tolerance.

Formula and Calculation

Total risk is typically measured using the standard deviation of an investment's or portfolio's returns. Standard deviation quantifies the dispersion of data points around the mean, indicating how much the actual returns are likely to vary from the average expected return.

For a single asset, the formula for standard deviation ($\sigma$) is:

\sigma = \sqrt{\frac{\sum_{i=1}^{n} (R_i - \bar{R})^2}{n-1}}

Where:

$R_i$ = Individual return in period (i)
$\bar{R}$ = Average (mean) return
$n$ = Number of periods

For a portfolio, the calculation of total risk (portfolio standard deviation) involves considering the weighted average of the standard deviations of individual assets, as well as the correlation between those assets. The correlation coefficients play a critical role in determining the overall portfolio risk, as they capture how the returns of different assets move in relation to each other.

For a two-asset portfolio (Assets A and B):

\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B}

Where:

$\sigma_p$ = Portfolio standard deviation
$w_A, w_B$ = Weights of Asset A and Asset B in the portfolio
$\sigma_A, \sigma_B$ = Standard deviations of Asset A and Asset B
$\rho_{AB}$ = Correlation coefficient between Asset A and Asset B

This formula highlights how combining assets with low or negative correlation can significantly reduce a portfolio's total risk through the benefits of diversification.

Interpreting Total Risk

Interpreting total risk involves understanding the implications of the calculated standard deviation or variance. A higher total risk (larger standard deviation) indicates greater volatility and a wider range of potential returns, meaning the actual return is more likely to deviate significantly from the expected return. Conversely, a lower total risk suggests less volatility and a tighter distribution of returns around the mean.

Investors use total risk metrics to gauge the uncertainty of an investment. For example, a stock with a high standard deviation implies its price can swing wildly, offering both higher potential gains and higher potential losses. When evaluating total risk, it is important to consider the investor's time horizon and financial objectives. Short-term investors might be more sensitive to high total risk, as they have less time to recover from adverse market movements. Long-term investors, with a longer investment horizon, might be more comfortable with higher total risk, especially if it comes with the potential for greater long-term returns. Investors often balance total risk against their desired expected return when constructing their portfolios on the efficient frontier.

Hypothetical Example

Consider an investor, Alex, who is evaluating two hypothetical portfolios: Portfolio X and Portfolio Y. Both portfolios have an expected annual return of 8%.

Portfolio X: Consists primarily of highly volatile technology stocks. Historical data shows its annual returns have varied significantly, resulting in a standard deviation of 20%.
Portfolio Y: Is a diversified portfolio comprising a mix of stable dividend stocks, bonds, and real estate investment trusts. Its historical returns have been much steadier, with a standard deviation of 10%.

Even though both portfolios have the same expected return, Portfolio X carries a higher total risk than Portfolio Y. This means Alex can expect Portfolio X's actual returns to fluctuate much more widely around the 8% average. In some years, Portfolio X might yield 30% or -15%, while Portfolio Y might consistently stay within a tighter range, perhaps between 2% and 14%. If Alex is a conservative investor with a low risk tolerance, Portfolio Y, despite having the same expected return, would be the more suitable choice due to its significantly lower total risk. This scenario underscores that total risk is a critical factor in investment selection beyond just expected returns.

Practical Applications

Total risk is a cornerstone concept with numerous practical applications across finance and investing:

Portfolio Construction: Investors utilize total risk measurements to build diversified portfolios. By understanding the total risk of individual assets and their correlations, investors can combine them to achieve a desired overall portfolio risk level.
Performance Evaluation: Fund managers and analysts assess the total risk of investment funds to evaluate their risk-adjusted returns. A fund that delivers strong returns but exhibits extremely high total risk might not be considered superior to one with slightly lower returns and significantly less total risk.
Regulatory Compliance: Regulatory bodies, such as the U.S. Securities and Exchange Commission (SEC), emphasize transparent disclosure of investment risks. Mutual funds and other investment companies are required to provide clear information about the principal risks associated with their offerings, which inherently relates to their total risk profile.⁴ For instance, the SEC's disclosure requirements aim to ensure investors are fully informed about the potential variability of returns.
Risk Management: Financial institutions employ sophisticated models to quantify and manage the total risk exposure across their various asset classes, from credit portfolios to trading books.
Investment Suitability: Financial advisors assess a client's risk tolerance and financial goals to recommend investments whose total risk profiles align with the client's capacity for losses.

Limitations and Criticisms

While total risk, often measured by standard deviation, is a widely accepted metric in finance, it has certain limitations and has faced criticisms:

Symmetry Assumption: Standard deviation treats upside volatility (positive deviations from the mean) the same as downside volatility (negative deviations). However, investors typically view positive fluctuations as desirable and negative ones as undesirable. Critics argue that this symmetry can lead to a misrepresentation of true risk, as it penalizes investments for performing unexpectedly well.³
Historical Data Dependence: Total risk calculations rely on historical data, which may not accurately predict future volatility. Market conditions, economic cycles, and other unforeseen events can drastically alter an investment's risk profile going forward.
Normal Distribution Assumption: Many financial models that use standard deviation implicitly assume that returns are normally distributed. In reality, financial market returns often exhibit "fat tails," meaning extreme positive or negative events occur more frequently than a normal distribution would predict. This can lead to an underestimation of tail risk, the risk of rare, high-impact events.
Lack of Context: A standalone total risk figure does not provide insights into the sources of risk. Two portfolios might have the same total risk, but one might be heavily exposed to market risk, while the other is more susceptible to company-specific risk.

Despite these criticisms, standard deviation remains a fundamental and broadly understood measure of total risk when used in conjunction with other analytical tools and qualitative assessments.

Total Risk vs. Systematic Risk

Total risk and systematic risk are distinct but related concepts in investment analysis. Total risk, as discussed, is the overall variability of an investment's returns, encompassing all factors that can cause returns to deviate from expectations. It is the sum of systematic risk and unsystematic risk.²

Systematic risk, also known as market risk or non-diversifiable risk, refers to the portion of total risk that is inherent to the overall market or economic system. It cannot be eliminated or reduced through diversification because it affects all investments to some degree. Examples of systematic risk include changes in interest rates, inflation, recessions, or political instability. Investors are compensated for bearing systematic risk through the risk premium. The capital asset pricing model (CAPM) uses beta to measure an asset's sensitivity to systematic risk.

In contrast, the other component of total risk is unsystematic risk, also known as specific risk or diversifiable risk. This portion of total risk is unique to a specific company, industry, or asset. It can be reduced or largely eliminated by holding a well-diversified portfolio across various assets, sectors, and geographies. Examples include a company-specific product recall, a labor strike, or a change in management.

Therefore, while systematic risk is a component of total risk that cannot be diversified away, total risk is the aggregate measure of all risks, both diversifiable and non-diversifiable, that affect an investment's returns.

FAQs

What are the two main components of total risk?

The two main components of total risk are systematic risk (also known as market risk or non-diversifiable risk) and unsystematic risk (also known as specific risk or diversifiable risk).¹

How is total risk typically measured?

Total risk is commonly measured using the standard deviation of an investment's or portfolio's returns. A higher standard deviation indicates greater total risk, meaning the returns are more volatile.

Can diversification eliminate total risk?

No, diversification cannot eliminate total risk entirely. Diversification can significantly reduce or eliminate unsystematic risk, which is unique to individual assets. However, it cannot mitigate systematic risk, which affects the entire market. Therefore, some level of total risk will always remain in a diversified portfolio.

Why is understanding total risk important for investors?

Understanding total risk is crucial for investors because it helps them make informed decisions that align with their financial goals and risk tolerance. It provides a comprehensive view of an investment's potential for variability, allowing investors to select appropriate assets, construct suitable portfolios, and manage their overall exposure to market fluctuations.