Theory of portfolio

Theory of portfolio
See also
Minimum variance portfolio Risk-return tradeoff Market Risk Premium Modigliani-Miller theorem Stochastic volatility Delta neutral Capital market theories Implementation Shortfall Unlevered beta

The Theory of Portfolio is a financial concept developed by Nobel Prize winner Harry Markowitz that suggests that investors can optimize their portfolios by diversifying them according to their individual risk and return preferences. The theory states that investors should focus on the expected return of the portfolio and the risk associated with it. It further suggests that investors should diversify their investments across different asset classes in order to reduce the overall risk of the portfolio while still maintaining an expected return. The main idea behind this theory is that investors can create a portfolio that is well balanced and contains both high-risk and low-risk investments in order to maximize their return while minimizing their risk.

The Theory of Portfolio is based on the following key principles:

• Diversification: This principle suggests that investors should diversify their investments across different asset classes in order to reduce the overall risk of the portfolio while still maintaining an expected return.
• Risk-return Tradeoff: This principle states that investors should focus on the expected return of the portfolio and the risk associated with it. In other words, investors should take into account both the risk and return of their investments when constructing a portfolio.
• Mean-Variance Optimization: Also known as modern portfolio theory, this principle states that investors can optimize their portfolio by minimizing the variance of the return while still maintaining an expected return. This can be done by combining assets with different levels of risk and return in order to create a portfolio that has the desired risk-return profile.

In summary, the Theory of Portfolio is a financial concept developed by Nobel Prize winner Harry Markowitz that suggests that investors can optimize their portfolios by diversifying them according to their individual risk and return preferences. The theory is based on the principles of diversification, risk-return tradeoff, and mean-variance optimization.

Example of portfolio

The Theory of Portfolio can be illustrated with an example. Suppose an investor has two assets, stock A and stock B, with expected returns of 8% and 12%, respectively, and standard deviations of 10% and 20%, respectively. The investor can create a portfolio that contains both stocks A and B in order to take advantage of the diversification benefits and reduce the risk of the portfolio while still maintaining an expected return of 10%. This can be done by combining the two stocks in a portfolio with the following weights:

• Stock A: 0.4
• Stock B: 0.6

The expected return of the portfolio is 10% with a standard deviation of 14%. This portfolio is well-balanced and contains both high-risk and low-risk investments in order to maximize the return while minimizing the risk.

In summary, the Theory of Portfolio can be illustrated with an example of an investor combining two assets with different levels of risk and return in order to create a portfolio that has the desired risk-return profile. The example demonstrates how investors can take advantage of the diversification benefits and reduce the risk of their portfolio while still maintaining an expected return.

Formula of portfolio

The Theory of Portfolio can be mathematically expressed through the following formula:

${\text{Portfolio Return}}=\sum _{i=1}^{n}w_{i}\cdot {\text{Asset Return}}_{i}$

Where n is the number of assets in the portfolio, w_i is the weight of each asset, and Asset Return_i is the return of each asset. This formula shows that the return of a portfolio is the sum of the returns of each asset weighted according to their respective weights.

When to use Theory of portfolio

The Theory of Portfolio can be used by investors to help them decide which investments to include in their portfolios. It can be used to help them create a well-diversified portfolio that is tailored to their individual risk and return preferences. The theory can also be used to evaluate the performance of a portfolio and to decide whether or not to make changes to the portfolio in order to optimize it. Finally, the theory can also be used to analyze the impact of market and economic conditions on the performance of a portfolio.

Types of Theory of portfolio

The Theory of Portfolio comes in two main forms:

• Passive Portfolio Theory: This theory states that investors should focus on the expected return of the portfolio and the risk associated with it. It suggests that investors should diversify their investments across different asset classes in order to reduce the overall risk of the portfolio while still maintaining an expected return.
• Active Portfolio Theory: This theory is based on the principle of mean-variance optimization, which suggests that investors can optimize their portfolio by minimizing the variance of the returns while still maintaining an expected return. This can be done by combining assets with different levels of risk and return in order to create a portfolio that has the desired risk-return profile.

Steps of creating portfolio

The Theory of Portfolio outlines the following steps for constructing an optimized portfolio:

• Step 1: Establish an Investment Objective: The first step in constructing an optimized portfolio is to establish an investment objective. This should include a clear understanding of the investor’s risk tolerance and desired return.
• Step 2: Estimate the Expected Returns of Each Asset: The next step is to estimate the expected returns of each asset in the portfolio. This can be done using a variety of methods, such as historical returns and analysis of financial trends.
• Step 3: Estimate the Risk of Each Asset: The third step is to estimate the risk of each asset in the portfolio. This can be done using a variety of methods, such as standard deviation and correlation analysis.
• Step 4: Calculate the Portfolio Variance: The fourth step is to calculate the portfolio variance using the expected returns and risk of each asset. This can be done using the following formula:

$Var(p)=\sum _{i=1}^{n}w_{i}^{2}Var(i)+\sum _{i=1}^{n}\sum _{j=1;j\neq i}^{n}w_{i}w_{j}Cov(i,j)$

Where Var(p) is the portfolio variance, w_i is the weight of asset i, Var(i) is the variance of asset i, and Cov(i,j) is the covariance between assets i and j.

Advantages of Theory of portfolio

The Theory of Portfolio has several advantages over traditional investing strategies. These benefits include:

• Lower Risk: By diversifying their investments across different asset classes, investors can reduce the overall risk of their portfolio.
• Higher Returns: By combining assets with different levels of risk and return, investors can maximize their expected return while minimizing their risk.
• Increased Efficiency: The mean-variance optimization principle allows investors to construct portfolios that are more efficient and have a higher expected return.

Limitations of Theory of portfolio

• Ignoring non-financial risks: The theory assumes that all investors have the same risk preferences and therefore ignores non-financial risks that could affect a portfolio’s performance.
• Ignoring market imperfections: The theory also assumes that markets are perfectly efficient, which is not always the case.
• Over-simplification: The theory is based on the assumption of mean-variance optimization, which is a relatively simple approach to portfolio management and may not be suitable for investors with more complex needs.

Other approaches related to Theory of portfolio

• Markowitz Efficient Frontier: This approach is based on the idea of mean-variance optimization and suggests that investors should focus on creating a portfolio that is on the efficient frontier, which is the curve that represents the optimal combination of expected return and risk.
• Capital Asset Pricing Model (CAPM): This approach suggests that investors should focus on the expected return of their investments when constructing a portfolio. The CAPM states that the expected return of an investment is equal to the risk-free rate of return plus a risk premium, which is a measure of the additional return an investor should expect to receive for taking on additional risk.
• Black-Litterman Model: This approach is an extension of the CAPM and suggests that investors should use their views on the expected return of different asset classes when constructing a portfolio. The model takes into account the investor's views on the expected return of different asset classes, as well as the market's views, when constructing a portfolio.

Suggested literature

• Constantinides, G. M., & Malliaris, A. G. (1995). Portfolio theory. Handbooks in operations research and management science, 9, 1-30.
• Sharifi, S., Crane, M., Shamaie, A., & Ruskin, H. (2004). Random matrix theory for portfolio optimization: a stability approach. Physica A: Statistical Mechanics and its Applications, 335(3-4), 629-643.