Gesamtrisiko

What Is Gesamtrisiko?

Gesamtrisiko, or total risk, refers to the overall uncertainty or variability of an investment's or portfolio's returns. Within the field of Portfoliotheorie, Gesamtrisiko encompasses all sources of unpredictability that can affect an asset's value, reflecting both market-wide fluctuations and specific factors related to the individual investment. Investors and financial professionals employ various measures to quantify this risk, aiming to understand the potential range of outcomes for their Rendite. Effective Risikomanagement strategies often begin with an assessment of Gesamtrisiko.

History and Origin

The concept of Gesamtrisiko as a quantifiable metric gained prominence with the advent of Modern Portfolio Theory (MPT), largely attributed to Harry Markowitz's seminal work "Portfolio Selection," published in 1952. Markowitz's framework revolutionized investing by demonstrating how the combination of assets within a Portfoliooptimierung could reduce overall risk without necessarily sacrificing returns. Before MPT, investors often focused solely on the risk of individual assets. Markowitz introduced the idea that the total risk of a portfolio is not merely the sum of the risks of its components but also depends on how those components move in relation to each other, a concept central to Diversifikation. His work laid the foundation for understanding how diversification can lead to an Effizienzgrenze, maximizing return for a given level of total risk. The Yale University Library provides an overview of Harry Markowitz's contribution to finance and his Nobel Memorial Prize in Economic Sciences.

Key Takeaways

• Gesamtrisiko represents the total variability of returns for an investment or portfolio.
• It is typically measured by the Standardabweichung of returns.
• Gesamtrisiko can be divided into systematic risk (market risk) and unsystematic risk (specific risk).
• Diversification strategies aim to reduce unsystematic risk, thereby impacting the overall Gesamtrisiko of a portfolio.
• Understanding Gesamtrisiko is crucial for effective portfolio construction and risk assessment.

Formula and Calculation

The most common measure for Gesamtrisiko is the statistical concept of Standardabweichung ((\sigma)) of an asset's or portfolio's returns. It quantifies the degree of dispersion of returns around the average return. A higher standard deviation indicates greater Volatilität and, consequently, higher Gesamtrisiko.

For a series of historical returns, the standard deviation is calculated as follows:

Where:

• (\sigma) = Standard deviation (Gesamtrisiko)
• (R_i) = Individual return in the series
• (\bar{R}) = Average (mean) return of the series
• (n) = Number of observations in the series
• (\sum) = Summation

For a portfolio, the calculation involves considering the weights of each asset and the covariance between them.

Interpreting the Gesamtrisiko

Interpreting Gesamtrisiko involves understanding that a higher standard deviation implies a wider range of potential returns, meaning the actual return is more likely to deviate significantly from the average expected return. For instance, an investment with a 15% average annual return and a Standardabweichung of 20% carries more Gesamtrisiko than an investment with the same average return but a 5% standard deviation.

Investors use this measure to align their portfolio's risk profile with their individual Anlagehorizont and risk tolerance. A higher Gesamtrisiko might be acceptable for investors with a longer time horizon who can withstand greater short-term Volatilität, while those with shorter horizons or lower risk tolerance typically seek investments with lower total risk. Effective Risikomanagement involves choosing assets that offer an acceptable level of Gesamtrisiko relative to their potential returns.

Hypothetical Example

Consider two hypothetical portfolios, Portfolio A and Portfolio B, over a five-year period, with the following annual returns:

Step 1: Calculate the average return ((\bar{R})) for each portfolio.

• Portfolio A: ((12 + 18 - 5 + 20 + 10) / 5 = 55 / 5 = 11%)
• Portfolio B: ((8 + 15 + 10 + 12 + 9) / 5 = 54 / 5 = 10.8%)

Step 2: Calculate the variance (square of the standard deviation) for each portfolio.

• Portfolio A:

  • Differences from mean: ((12-11)^2=1), ((18-11)^2=49), ((-5-11)^2=256), ((20-11)^2=81), ((10-11)^2=1)
  • Sum of squared differences = (1 + 49 + 256 + 81 + 1 = 388)
  • Variance = (388 / (5-1) = 388 / 4 = 97)

• Portfolio B:

  • Differences from mean: ((8-10.8)^2=7.84), ((15-10.8)^2=17.64), ((10-10.8)^2=0.64), ((12-10.8)^2=1.44), ((9-10.8)^2=3.24)
  • Sum of squared differences = (7.84 + 17.64 + 0.64 + 1.44 + 3.24 = 30.8)
  • Variance = (30.8 / (5-1) = 30.8 / 4 = 7.7)

Step 3: Calculate the Standardabweichung ((\sigma)) for each portfolio (square root of variance).

• Portfolio A Gesamtrisiko: (\sqrt{97} \approx 9.85%)
• Portfolio B Gesamtrisiko: (\sqrt{7.7} \approx 2.77%)

Despite Portfolio A having a slightly higher average Rendite, its Gesamtrisiko (9.85%) is significantly higher than that of Portfolio B (2.77%). This example demonstrates that Portfolio B offers more consistent returns with less overall variability.

Practical Applications

Gesamtrisiko is a fundamental concept across various aspects of finance and investing. In Asset-Allokation and portfolio construction, investors analyze the Gesamtrisiko of different asset classes and individual Wertpapier to build portfolios that align with specific risk-return objectives. It is a key input for performance measures like the Sharpe-Verhältnis, which evaluates risk-adjusted returns by comparing excess returns to the total risk taken.

Furthermore, Gesamtrisiko assessment is vital for regulatory bodies and financial stability oversight. Regulators, such as the U.S. Securities and Exchange Commission (SEC), require investment companies to disclose the risks associated with their offerings to protect investors. Understanding the total risk exposure across financial markets is also critical for central banks and organizations like the Federal Reserve, which publishes a Financial Stability Report to monitor potential threats to the financial system. This broad oversight helps identify systemic vulnerabilities that could impact the Gesamtrisiko for a wide range of investments.

Limitations and Criticisms

While standard deviation is widely used to measure Gesamtrisiko, it has limitations. A primary criticism is that it treats all volatility equally, meaning it doesn't distinguish between upside volatility (positive price movements) and downside volatility (negative price movements). Investors generally welcome positive volatility but are concerned about negative fluctuations. Some alternative risk measures, such as downside deviation, attempt to address this by focusing only on returns below a certain threshold.

Another limitation is that the calculation of Gesamtrisiko assumes that asset returns follow a normal distribution. However, real-world financial returns often exhibit "fat tails," meaning extreme events (both positive and negative) occur more frequently than a normal distribution would predict. This can lead to an underestimation of potential large losses. Critics of traditional Portfoliotheorie argue that reliance on standard deviation alone may not fully capture the true risk profile of an investment, especially during periods of market stress or for assets with non-linear return patterns. The CFA Institute has published articles discussing the limitations of Modern Portfolio Theory, including its assumptions about risk measurement. Measures like Beta, while related to risk, focus specifically on systemic risk rather than Gesamtrisiko.

Gesamtrisiko vs. Systematisches Risiko

It is crucial to differentiate between Gesamtrisiko and Systematisches Risiko. Gesamtrisiko is the total, overall risk of an investment or portfolio. It comprises two main components:

1. Systematisches Risiko (Systematic Risk) / Marktrisiko: This is the risk inherent to the entire market or market segment. It is broadly undiversifiable, meaning it cannot be eliminated through Diversifikation across different assets or industries. Examples include economic recessions, interest rate changes, political instability, or major global events. Investors are compensated for bearing systematic risk.

2. Unsystematisches Risiko (Unsystematic Risk) / Spezifisches Risiko: This is the risk specific to a particular company, industry, or asset. It can include factors like management changes, product recalls, labor strikes, or regulatory changes affecting a single company. Unsystematic risk is considered diversifiable, as combining various assets in a portfolio can mitigate the impact of adverse events affecting any single holding.

In essence, Gesamtrisiko = Systematisches Risiko + Unsystematisches Risiko. While diversification can significantly reduce the Unsystematisches Risiko component of total risk, the systematic portion, or Marktrisiko, will always remain.

FAQs

What is the primary measure of Gesamtrisiko?
The primary measure of Gesamtrisiko is the Standardabweichung of returns, which quantifies how much an investment's returns typically deviate from its average return. A higher standard deviation indicates greater total risk.

Can Gesamtrisiko be completely eliminated?
No, Gesamtrisiko cannot be completely eliminated. While Diversifikation can significantly reduce the unsystematic portion of risk, the systematic risk (market risk) remains present in all market-based investments and cannot be diversified away.

Why is understanding Gesamtrisiko important for investors?
Understanding Gesamtrisiko helps investors make informed decisions that align with their personal risk tolerance and financial goals. It enables them to assess the overall variability of their portfolio's Rendite and implement appropriate Risikomanagement strategies to manage potential losses.

Does Gesamtrisiko only refer to negative outcomes?
No, Gesamtrisiko, as measured by standard deviation, refers to the overall variability of returns, whether positive or negative. It indicates the likelihood of returns deviating from the average in either direction. While investors are typically more concerned with downside risk, standard deviation doesn't distinguish between favorable and unfavorable volatility.

How does diversification affect Gesamtrisiko?
Diversification primarily reduces the unsystematic component of Gesamtrisiko by combining various assets whose individual risks are not perfectly correlated. This strategy smooths out portfolio returns, making the overall portfolio less susceptible to the specific risks of any single Wertpapier.

References

Yale University Library. "Portfolio Selection". Yale University Library Guides, Harry M. Markowitz. https://guides.library.yale.edu/c.php?g=296062&p=1974175
Investor.gov. "Mutual Fund Risks". Investor.gov, U.S. Securities and Exchange Commission. https://www.investor.gov/introduction-investing/investing-basics/investment-products/mutual-funds/mutual-fund-risks
Federal Reserve. "Financial Stability Report". Board of Governors of the Federal Reserve System. https://www.federalreserve.gov/publications/financial-stability-report.htm
CFA Institute. "The Limitations of Modern Portfolio Theory". CFA Institute Investor Insights. https://blogs.cfainstitute.org/investor/2021/04/27/the-limitations-of-modern-portfolio-theory/