Skip to main content
← Back to M Definitions

Moderne portfoliotheorie

What Is Moderne portfoliotheorie?

Moderne Portfoliotheorie (MPT), also known as Modern Portfolio Theory, is an investment theory that describes how rational investors can construct portfolios to optimize expected returns for a given level of market risk. A core concept within portfolio theory, MPT suggests that the risk and return of an individual asset should not be viewed in isolation, but rather in relation to how it affects the overall portfolio. The theory emphasizes the importance of diversification to reduce unsystematic risk.

History and Origin

Modern Portfolio Theory was introduced by American economist Harry Markowitz in his seminal 1952 paper, "Portfolio Selection," published in The Journal of Finance.14 Before Markowitz's work, investors often focused solely on maximizing returns from individual securities. Markowitz revolutionized this approach by demonstrating how to quantify the impact of asset correlation on overall portfolio risk and return. His groundbreaking work laid the foundation for modern financial economics and earned him a share of the Nobel Memorial Prize in Economic Sciences in 1990.13 This achievement solidified MPT's position as a cornerstone in the academic and practical application of investment management.

Key Takeaways

  • Moderne Portfoliotheorie aims to construct portfolios that maximize expected return for a given level of risk, or minimize risk for a given expected return.
  • It emphasizes that the overall portfolio's risk is not simply the sum of individual asset risks, but also depends on how assets move in relation to each other, known as covariance.
  • Diversification is a central tenet, suggesting that combining assets with low or negative correlations can reduce overall portfolio volatility.
  • The theory leads to the concept of the efficient frontier, representing the set of optimal portfolios.
  • MPT assumes investors are rational and risk-averse, seeking to maximize utility based on expected return and risk.

Formula and Calculation

Moderne Portfoliotheorie utilizes statistical measures to quantify portfolio risk and return. The expected return of a portfolio ((E(R_p))) is the weighted average of the expected returns of the individual assets within it:

E(Rp)=i=1NwiE(Ri)E(R_p) = \sum_{i=1}^{N} w_i \cdot E(R_i)

Where:

  • (E(R_p)) = Expected return of the portfolio
  • (w_i) = Weight (proportion) of asset i in the portfolio
  • (E(R_i)) = Expected return of asset i
  • (N) = Number of assets in the portfolio

The portfolio variance ((\sigma_p^2)), which measures portfolio risk, is more complex as it accounts for the correlation between assets:

σp2=i=1Nj=1NwiwjCov(Ri,Rj)\sigma_p^2 = \sum_{i=1}^{N} \sum_{j=1}^{N} w_i \cdot w_j \cdot Cov(R_i, R_j)

Or, alternatively, using standard deviation and correlation:

σp2=i=1Nwi2σi2+i=1Nj=1,ijNwiwjσiσjρij\sigma_p^2 = \sum_{i=1}^{N} w_i^2 \sigma_i^2 + \sum_{i=1}^{N} \sum_{j=1, i \neq j}^{N} w_i w_j \sigma_i \sigma_j \rho_{ij}

Where:

  • (\sigma_p^2) = Variance of the portfolio
  • (w_i), (w_j) = Weights of asset i and asset j in the portfolio
  • (Cov(R_i, R_j)) = Covariance between the returns of asset i and asset j
  • (\sigma_i), (\sigma_j) = Standard deviation (risk) of asset i and asset j
  • (\rho_{ij}) = Correlation coefficient between the returns of asset i and asset j

The standard deviation ((\sigma_p)), which is the square root of the variance, represents the volatility of the portfolio's returns.

Interpreting the Moderne Portfoliotheorie

Moderne Portfoliotheorie is interpreted through the lens of risk-return optimization. By calculating the expected return and variance for various combinations of assets, investors can identify portfolios that lie on the efficient frontier. The efficient frontier is a curve representing the set of optimal portfolios that offer the highest expected return for a defined level of risk, or the lowest risk for a given level of expected return.

An investor's individual risk tolerance then dictates where on this frontier they would choose to position their portfolio. A more risk-averse investor might choose a portfolio with lower risk and lower expected return, while a more aggressive investor might opt for a portfolio with higher expected return and consequently higher risk. The ultimate goal is to achieve an optimal balance, ensuring that any additional risk taken is adequately compensated by a higher expected return.

Hypothetical Example

Consider an investor, Anna, who wants to build a portfolio using two assets: Stock A and Stock B.

  • Stock A: Expected Return (E(RA)) = 10%, Standard Deviation (σA) = 15%
  • Stock B: Expected Return (E(RB)) = 8%, Standard Deviation (σB) = 10%
  • Correlation Coefficient (ρAB): 0.30

Anna decides to create a portfolio with 60% in Stock A and 40% in Stock B.

1. Calculate Expected Portfolio Return:
( E(R_p) = (0.60 \times 0.10) + (0.40 \times 0.08) = 0.06 + 0.032 = 0.092 = 9.2% )

2. Calculate Portfolio Variance:
First, calculate the covariance:
( Cov(R_A, R_B) = \rho_{AB} \cdot \sigma_A \cdot \sigma_B = 0.30 \cdot 0.15 \cdot 0.10 = 0.0045 )

Now, the portfolio variance:
( \sigma_p^2 = (0.60^2 \cdot 0.15^2) + (0.40^2 \cdot 0.10^2) + 2 \cdot (0.60 \cdot 0.40 \cdot 0.0045) )
( \sigma_p^2 = (0.36 \cdot 0.0225) + (0.16 \cdot 0.01) + 2 \cdot (0.24 \cdot 0.0045) )
( \sigma_p^2 = 0.0081 + 0.0016 + 0.00216 = 0.01186 )

3. Calculate Portfolio Standard Deviation:
( \sigma_p = \sqrt{0.01186} \approx 0.1089 = 10.89% )

In this hypothetical example, Anna's diversified portfolio has an expected return of 9.2% and a standard deviation (risk) of approximately 10.89%. This demonstrates how Moderne Portfoliotheorie allows for the quantification of both aspects when constructing a diversified portfolio, going beyond just individual asset metrics. Understanding asset allocation is crucial for this process.

Practical Applications

Moderne Portfoliotheorie is widely applied in various areas of finance. Financial advisors and institutional investors use its principles to construct and manage investment portfolios for their clients, aiming to achieve specific risk-adjusted returns. It forms the theoretical underpinning for concepts like the Capital Asset Pricing Model (CAPM) and helps define the concept of market efficiency.

Furthermore, MPT guides the development of mutual funds and exchange-traded funds (ETFs) that are designed to offer diversified exposure to various asset classes. Re12gulators, such as the U.S. Securities and Exchange Commission (SEC), also consider the principles of diversification, which stem from MPT, when issuing guidance to investors. Fo10, 11r example, the SEC's investor bulletins frequently highlight the benefits of diversification across international investments and various asset types to manage risk.

#8, 9# Limitations and Criticisms

Despite its widespread influence, Moderne Portfoliotheorie faces several limitations and criticisms. A primary critique is its reliance on historical data to predict future returns, volatilities, and correlations. Financial markets are dynamic, and past performance is not indicative of future results, which can make MPT's estimations less reliable during periods of significant market change or stress.

A6, 7nother major assumption of MPT is that investors are perfectly rational and risk-averse, always seeking to maximize utility based solely on expected return and variance. This assumption often clashes with observations from behavioral finance, which highlights that investor decisions can be influenced by psychological biases and irrational behaviors. Cr4, 5itics also point out that MPT assumes a normal distribution of returns, which may not hold true, particularly during extreme market events. Some modern extensions, such as Post-Modern Portfolio Theory, attempt to address some of these shortcomings by incorporating non-normal distributions and downside risk.

#3# Moderne portfoliotheorie vs. Post-Moderne Portfoliotheorie

Moderne Portfoliotheorie (MPT) and Post-Moderne Portfoliotheorie (PMPT) are both frameworks for portfolio construction, but they differ in their approach to risk. MPT defines risk primarily as volatility, measured by standard deviation, and assumes that investors are concerned with both upward and downward deviations from the expected return. It relies on the assumption of normally distributed returns.

In contrast, Post-Moderne Portfoliotheorie (PMPT) specifically focuses on downside risk, which is the risk of returns falling below a target or minimum acceptable return. PMPT uses measures like downside deviation (or Sortino Ratio) instead of standard deviation to quantify risk, arguing that investors are more concerned with negative deviations than positive ones. This aligns more closely with behavioral finance perspectives, which recognize that investors typically dislike losses more than they enjoy equivalent gains. PMPT aims to provide a more intuitive and practically relevant measure of risk for many investors.

FAQs

What is the main goal of Moderne Portfoliotheorie?

The main goal of Moderne Portfoliotheorie is to help investors build diversified portfolios that offer the highest possible expected return for a given level of risk, or the lowest possible risk for a given expected return. It aims to optimize the risk-return tradeoff.

Who developed Moderne Portfoliotheorie?

Moderne Portfoliotheorie was developed by American economist Harry Markowitz, who first introduced the concept in his 1952 paper, "Portfolio Selection." He later received the Nobel Memorial Prize in Economic Sciences for his work.

#2## How does diversification relate to Moderne Portfoliotheorie?
Diversification is a cornerstone of Moderne Portfoliotheorie. The theory demonstrates that by combining assets whose returns are not perfectly positively correlated, investors can reduce the overall portfolio risk without necessarily sacrificing expected returns. This is because the negative performance of one asset may be offset by the positive performance of another.

What are the key assumptions of Moderne Portfoliotheorie?

Key assumptions include that investors are rational and risk-averse, that markets are efficient, and that asset returns follow a normal distribution. It also assumes that investors base their decisions on expected returns and standard deviation (as a measure of risk).

#1## Why is Moderne Portfoliotheorie important?
Moderne Portfoliotheorie is important because it fundamentally changed how investors view and manage risk. It shifted the focus from individual securities to the entire portfolio, demonstrating how strategic asset correlation and diversification can lead to more efficient investment outcomes.