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Theories of modern portfolio, Study notes of Corporate Finance

Modern Portfolio Theory (MPT) is an investment framework that aims to optimize investment portfolios by balancing risk and return. It emphasizes the importance of diversification and provides a tool for investors to evaluate the performance of their portfolios and make informed decisions. The key concept in MPT is the efficient frontier, which represents the optimal investment portfolios that offer the highest expected return for a given level of risk or the lowest risk for a given expected return. MPT also uses the Sharpe Ratio to measure the excess return per unit of risk and highlights the benefits of diversifying a portfolio across different asset classes to reduce overall risk while maintaining the potential for high returns.

Typology: Study notes

2022/2023

Available from 05/29/2024

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## Modern Portfolio Theory (MPT)
Modern Portfolio Theory (MPT), developed by Harry Markowitz in the
1950s, revolutionized the way investors think about portfolio construction.
It's a powerful framework that helps investors build portfolios that
maximize expected returns for a given level of risk. Here's a detailed
breakdown:
**1. Core Principles:**
* **Risk and Return are Inseparable:** MPT acknowledges that higher
returns typically come with higher risk. It doesn't aim to eliminate risk
entirely, but rather to manage it effectively.
* **Diversification is Key:** MPT emphasizes that diversifying across
different asset classes (stocks, bonds, real estate, etc.) reduces overall
portfolio risk without sacrificing returns.
* **Correlation Matters:** The relationship between different assets (how
they move together) is crucial. Assets with low or negative correlation can
further reduce portfolio risk.
* **Efficient Frontier:** MPT identifies the set of portfolios that offer the
highest expected return for each level of risk. This set of portfolios forms
the "efficient frontier."
**2. Key Concepts:**
* **Expected Return:** The average return an investor anticipates from an
asset or portfolio over a specific period.
* **Risk (Standard Deviation):** A measure of how much an asset's or
portfolio's returns are likely to deviate from the expected return. Higher
standard deviation indicates higher risk.
* **Correlation:** The statistical relationship between the movements of
two assets. A correlation of 1 means they move perfectly together, -1
means they move perfectly opposite, and 0 means no relationship.
* **Covariance:** A measure of how two assets move together, taking
into account their individual volatilities.
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Modern Portfolio Theory (MPT)

Modern Portfolio Theory (MPT), developed by Harry Markowitz in the 1950s, revolutionized the way investors think about portfolio construction. It's a powerful framework that helps investors build portfolios that maximize expected returns for a given level of risk. Here's a detailed breakdown: 1. Core Principles:

  • Risk and Return are Inseparable: MPT acknowledges that higher returns typically come with higher risk. It doesn't aim to eliminate risk entirely, but rather to manage it effectively.
  • Diversification is Key: MPT emphasizes that diversifying across different asset classes (stocks, bonds, real estate, etc.) reduces overall portfolio risk without sacrificing returns.
  • Correlation Matters: The relationship between different assets (how they move together) is crucial. Assets with low or negative correlation can further reduce portfolio risk.
  • Efficient Frontier: MPT identifies the set of portfolios that offer the highest expected return for each level of risk. This set of portfolios forms the "efficient frontier." 2. Key Concepts:
  • Expected Return: The average return an investor anticipates from an asset or portfolio over a specific period.
  • Risk (Standard Deviation): A measure of how much an asset's or portfolio's returns are likely to deviate from the expected return. Higher standard deviation indicates higher risk.
  • Correlation: The statistical relationship between the movements of two assets. A correlation of 1 means they move perfectly together, - means they move perfectly opposite, and 0 means no relationship.
  • Covariance: A measure of how two assets move together, taking into account their individual volatilities.
  • Portfolio Variance: A measure of the overall risk of a portfolio, considering the individual risks of each asset and their correlations. 3. Building an Efficient Portfolio:
  • Define Investment Goals: Determine your investment objectives (e.g., retirement, education, etc.) and risk tolerance.
  • Identify Asset Classes: Choose a range of asset classes that align with your goals (e.g., stocks, bonds, real estate, commodities).
  • Estimate Expected Returns and Risks: Research historical data and market forecasts to estimate the expected return and risk of each asset class.
  • Calculate Correlations: Determine the correlation between different asset classes.
  • Optimize Portfolio Weights: Use MPT tools (software or spreadsheets) to find the optimal allocation of assets that maximizes expected return for your desired level of risk. This will result in a portfolio on the efficient frontier.
  • Monitor and Rebalance: Regularly review your portfolio's performance and adjust asset allocations as needed to maintain your desired risk/return profile. 4. Benefits of MPT:
  • Improved Risk Management: MPT helps investors understand and manage risk more effectively by diversifying across asset classes.
  • Enhanced Returns: By optimizing portfolio weights, MPT can potentially increase returns for a given level of risk.
  • Data-Driven Decision Making: MPT relies on quantitative analysis and historical data to make informed investment decisions.
  • Tailored Portfolios: MPT allows investors to create portfolios that align with their individual goals, risk tolerance, and time horizon. 5. Limitations of MPT:

Imagine you're a young investor with a long-term investment horizon ( years) and a moderate risk tolerance. You have $100,000 to invest and are considering two asset classes:

  • Stocks (S): Historically, stocks have higher returns but also higher volatility (risk). Let's assume an expected annual return of 8% and a standard deviation of 15%.
  • Bonds (B): Bonds are generally considered less risky than stocks, with lower returns. Let's assume an expected annual return of 4% and a standard deviation of 5%. Step 1: Define Investment Goals and Risk Tolerance:
  • Goal: Long-term wealth accumulation for retirement.
  • Risk Tolerance: Moderate, meaning you're willing to take some risk for potentially higher returns, but not excessive risk. Step 2: Identify Asset Classes:
  • Stocks (S): Represent growth potential.
  • Bonds (B): Provide stability and diversification. Step 3: Estimate Expected Returns and Risks:
  • Stocks (S): Expected Return = 8%, Standard Deviation = 15%
  • Bonds (B): Expected Return = 4%, Standard Deviation = 5% Step 4: Calculate Correlation:
  • Correlation (S, B): Let's assume a correlation of -0.2, meaning stocks and bonds tend to move in opposite directions, which is beneficial for diversification.

Step 5: Optimize Portfolio Weights:

  • Using MPT Tools: We can use software or spreadsheets to calculate the optimal allocation of stocks and bonds that maximizes expected return for our desired level of risk.
  • Example: Let's say the optimal allocation is 70% in stocks (S) and 30% in bonds (B). Step 6: Calculate Portfolio Expected Return and Risk:
  • Portfolio Expected Return: (0.7 * 8%) + (0.3 * 4%) = 6.8%
  • Portfolio Standard Deviation: This requires a more complex calculation using the individual standard deviations and correlation. Let's assume the portfolio standard deviation is 10%. Step 7: Analyze the Efficient Frontier:
  • Efficient Frontier: The set of portfolios that offer the highest expected return for each level of risk.
  • Our Portfolio: Our 70/30 stock/bond portfolio would be a point on the efficient frontier, meaning it offers the highest expected return (6.8%) for its level of risk (10%). Step 8: Monitor and Rebalance:
  • Regular Review: We should periodically review our portfolio's performance and adjust asset allocations as needed.
  • Rebalancing: If the market moves significantly, our portfolio weights might deviate from the optimal allocation. Rebalancing ensures we maintain our desired risk/return profile. Comparison to a Non-Diversified Portfolio: