### 날짜 : 2024-04-15 15:28 ### 주제 : Modern portfolio theory (MPT) #economics #investment ---- Modern Portfolio Theory (MPT), introduced by Harry Markowitz in 1952, is a mathematical framework for assembling a portfolio of assets such that the expected risk-reward profile is optimized for a given level of risk. It relies on diversification to maximize returns for a given level of market risk or, alternatively, to minimize risk for a given level of expected return. MPT suggests that it's not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification, chiefly, a reduction in the riskiness of the portfolio. #### Key Concepts of MPT: 1. **Risk and Return**: MPT assumes that investors are risk-averse; they prefer a less risky portfolio to a riskier one if both portfolios offer the same expected return. Return is the reward for bearing risk, and risk is measured by the variance or standard deviation in returns of an asset or portfolio. 2. **Efficient Frontier**: This is a graph that plots 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. Portfolios that lie below the efficient frontier are considered sub-optimal because they do not provide enough return for the level of risk they carry. Portfolios that cluster to the left of the efficient frontier are considered optimal.   3. **Portfolio Diversification**: MPT encourages investment in different kinds of assets. Diversification reduces unsystematic risk, which is the risk associated with individual stocks (also known as idiosyncratic risk, or specific risk). Systematic risk, also known as market risk, cannot be diversified away and is the inherent risk that affects all investments. 4. **Correlation**: A key aspect of MPT is the correlation between assets, which measures how assets move in relation to one another. By investing in assets with low or negative correlations, investors can reduce the portfolio's overall risk. 5. **Capital Allocation Line (CAL)**: This line illustrates the risk-return tradeoff of portfolios, showing potential risk-reward combinations. The slope of the CAL is known as the Sharpe ratio, a measure for calculating risk-adjusted return.  #### Implications of MPT for Investors: - **Asset Allocation**: The primary application of MPT is in asset allocation. Portfolios are constructed by determining the mix of asset classes, rather than individual securities. - **Non-Concentration**: MPT suggests that holding a small number of securities increases the unsystematic risk of a portfolio. Diversification should spread risk across different sectors and securities. - **Investment Policy Statement (IPS)**: Financial advisors typically use MPT principles to draft an IPS for their clients, which outlines a targeted strategy for achieving returns while adhering to an agreed-upon level of risk tolerance. #### Limitations of MPT: While MPT provides a systematic framework for portfolio construction, it has some limitations: - **Historical Data**: MPT uses historical data to estimate returns and risks, which may not accurately predict future market behavior. - **Assumed Rationality**: MPT assumes investors are rational and markets are always efficient, which is often contradicted by the evidence from behavioral finance. - **Single-Period Model**: Traditional MPT models typically consider a single-period time horizon, which may not be suitable for long-term investors. - **Risk Simplification**: MPT equates risk directly with volatility, represented by the standard deviation of returns, which may not always be an appropriate measure of risk. - **Ignoring Skewness and Kurtosis**: MPT doesn't account for how the returns are distributed (which can be asymmetric or have fat tails), potentially understating the risk of investments that don't follow a normal distribution. Despite these limitations, MPT remains a cornerstone of investment strategy and portfolio management, challenging investors to think rigorously about the balance between risk and return in their investment choices. Its legacy endures in the concept of diversification, which is a fundamental strategy recommended for investors of all types. # Example Portfolio **Investor Profile:** - Risk tolerance: Moderate - Investment goal: Balanced growth with income generation - Time horizon: 10 years - Total investment capital: $100,000 For simplicity, we'll only consider three asset classes and use hypothetical rates of return and risk levels; in a real-world scenario, there would be many more assets and more complex calculations. **Assets Selected:** 1. Stock mutual fund: An index fund tracking the S&P 500 - Expected annual return: 8% - Standard deviation (risk measure): 15% 2. Corporate bond fund: Investment-grade bonds - Expected annual return: 4% - Standard deviation: 5% 3. Money market fund: High credit quality, very short-term debts - Expected annual return: 1.5% - Standard deviation: 1% **Correlations:** - Stocks and bonds have historically exhibited low correlation. For simplification, let's assume: - Stocks to bonds correlation: 0.3 - Stocks to money market correlation: 0 - Bonds to money market correlation: 0 **Portfolio Construction:** We want to combine these assets in a way that maximizes return for our given level of risk. Using the efficient frontier principle, we analyze different weightings of assets to determine the best mix. After analyzing different combinations, we find an optimal mix that fits our moderate risk profile and offers a reasonable expected return. **Optimal Portfolio Allocation:** - Stock mutual fund: 60% - Corporate bond fund: 30% - Money market fund: 10% **Analysis:** - Expected annual return (Portfolio) = (0.6 * 8%) + (0.3 * 4%) + (0.1 * 1.5%) = 6% - Approximate Portfolio Standard Deviation: Calculated using the formula for portfolio variance, which incorporates the standard deviations of the individual assets and their correlations. For this simplified example, we won't delve into that calculation, but this number would normally be lower than the 15% for stocks due to diversification. **Result:** - Our investor now holds a diversified portfolio expected to yield an average annual return of 6% with a lower risk profile than a portfolio invested 100% in stocks. Using real data, an investor or financial advisor would conduct a more rigorous analysis, often using software that can optimize the allocation to more precisely target the efficient frontier. The software uses historical returns, volatilities, and correlations to calculate expected returns and risks for thousands of possible portfolio combinations to identify the mix of assets that should theoretically give the best expected return for a given level of risk. Furthermore, in practice, investors and advisors may consider factors such as taxes, investment fees, liquidity needs, legal constraints, and personal preferences that can influence the final asset allocation. The output would also involve a range of possible scenarios based on different risk tolerance levels, from conservative to aggressive, allowing the investor to understand the trade-offs between risk and return more clearly and make an informed decision that is aligned with their individual investment goals and risk tolerance.