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15.4 Applications in Performance Measurement

3 min read•june 18, 2024

Performance measurement techniques are crucial for evaluating investment strategies. These tools help investors assess risk-adjusted returns, compare portfolios with different risk levels, and gauge manager skill. Understanding these metrics is essential for making informed investment decisions.

The , , and are key performance indicators. These metrics provide insights into risk-adjusted returns, exposure, and excess returns. Additional metrics like and further refine performance analysis.

Performance Measurement Techniques

Sharpe ratio for risk-adjusted performance

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  • Measures of an investment by comparing to ()
    • Excess return represents the return above the risk-free rate ()
    • Volatility quantifies the variability of returns over time
  • Calculated using the formula: [Sharpe](https://www.fiveableKeyTerm:Sharpe) ratio=Rp−Rfσp[Sharpe](https://www.fiveableKeyTerm:Sharpe)\ ratio = \frac{R_p - R_f}{\sigma_p}
    • RpR_p represents the average return of the portfolio
    • RfR_f denotes the risk-free rate
    • σp\sigma_p signifies the of the portfolio's returns
  • Higher indicates better , as investors prefer investments with higher risk-adjusted returns (, )
  • Enables comparison of investments with different risk levels (bonds vs stocks) to determine if higher returns result from superior investment decisions or increased risk

Treynor measure vs systematic risk

  • Evaluates a portfolio's risk-adjusted return relative to its , which cannot be diversified away (, )
  • Calculated using the formula: Treynor measure=Rp−RfβpTreynor\ measure = \frac{R_p - R_f}{\beta_p}
    • RpR_p represents the average return of the portfolio
    • RfR_f denotes the risk-free rate
    • βp\beta_p signifies the of the portfolio, measuring its systematic risk
  • Higher Treynor measure indicates better risk-adjusted performance relative to systematic risk, as it compares excess returns to the portfolio's sensitivity to market movements
  • Useful for comparing portfolios with different levels of systematic risk (aggressive vs conservative) to assess if a portfolio manager generates higher returns by taking on more market risk

Jensen's alpha for excess returns

  • Measures a portfolio manager's ability to generate excess returns above the expected return based on the portfolio's systematic risk ()
    • Excess returns represent the returns above the market's expected return given the portfolio's beta
  • Calculated using the formula: Jensen′s alpha=Rp−[Rf+βp(Rm−Rf)]Jensen's\ alpha = R_p - [R_f + \beta_p(R_m - R_f)]
    • RpR_p represents the average return of the portfolio
    • RfR_f denotes the risk-free rate
    • βp\beta_p signifies the beta of the portfolio
    • RmR_m represents the average return of the market (S&P 500)
  • Positive Jensen's alpha indicates the portfolio manager has generated excess returns above what is expected given the portfolio's systematic risk, suggesting skill in selecting investments or timing the market (Warren Buffett, Peter Lynch)
  • Negative Jensen's alpha suggests the manager has underperformed relative to the market, considering the portfolio's systematic risk ()
  • Evaluates the performance of actively managed portfolios and compares the skills of different portfolio managers to determine if they add value beyond

Additional Performance Metrics

  • Tracking error measures the deviation of a portfolio's returns from its , indicating how closely the portfolio follows the benchmark's performance
  • Information ratio evaluates a portfolio manager's ability to generate excess returns relative to a benchmark, considering the consistency of outperformance
  • analyzes the sources of a portfolio's returns, breaking down performance into factors such as asset allocation and security selection
  • Risk-adjusted performance metrics (e.g., Sharpe ratio) help investors compare investments with different risk levels on an equal footing
  • Benchmarks (e.g., S&P 500) serve as reference points for evaluating a portfolio's performance and risk characteristics

Key Terms to Review (35)

Actively Managed Mutual Funds: Actively managed mutual funds are investment vehicles where a professional fund manager actively selects and manages a portfolio of securities with the goal of outperforming a specific benchmark or index. The fund manager uses their expertise, research, and market analysis to make decisions about which securities to buy, hold, or sell within the fund.
Benchmark: A benchmark is a standard or point of reference against which things may be measured or compared. In the context of performance measurement, a benchmark serves as a point of comparison to evaluate the performance of an investment, portfolio, or strategy.
Berkshire Hathaway: Berkshire Hathaway is a multinational conglomerate holding company founded by Warren Buffett and Charlie Munger. It is known for its successful long-term investment strategy and diversified portfolio of subsidiaries across various industries, making it highly relevant in the context of performance measurement applications.
Beta: Beta measures the volatility or systematic risk of a security or portfolio relative to the overall market. A beta greater than 1 indicates more volatility than the market, while a beta less than 1 indicates less volatility.
Beta: Beta is a measure of the volatility or systematic risk of a financial asset or portfolio in relation to the overall market. It represents the sensitivity of an asset's returns to changes in the market's returns, providing a quantitative assessment of an investment's risk profile.
Capital Asset Pricing Model: The Capital Asset Pricing Model (CAPM) is a financial model that describes the relationship between the expected return of an asset and its risk. It provides a framework for understanding how the market values an asset based on its systematic risk, which is measured by the asset's beta. CAPM is a fundamental concept in finance that is widely used in investment analysis, portfolio management, and corporate finance decision-making.
Excess Return: Excess return refers to the investment performance that exceeds the expected or benchmark return. It represents the additional return an investor earns above the market or a specified benchmark, providing a measure of the value added by an investment strategy or manager.
Information Ratio: The information ratio is a risk-adjusted measure of active portfolio management that quantifies the active return of a portfolio relative to the active risk taken. It is used to evaluate the skill of an investment manager in generating excess returns over a benchmark index, while accounting for the risk taken to achieve those excess returns.
Interest rate risk: Interest rate risk is the potential for investment losses due to fluctuations in interest rates. It primarily affects bonds and other fixed-income securities, as their values are inversely related to interest rate changes.
Interest Rate Risk: Interest rate risk refers to the potential for financial losses due to changes in the prevailing market interest rates. It is a critical concept in the context of various financial topics, including bond characteristics, bond valuation, yield curve analysis, interest rate and default risks, performance measurement, optimal capital structure, and interest rate risk management.
Jack Treynor: Jack Treynor is a renowned American financial economist who made significant contributions to the field of portfolio theory and performance measurement. He is best known for his work on the Treynor ratio, a metric used to evaluate the risk-adjusted performance of investment portfolios.
Jensen’s alpha: Jensen's alpha is a risk-adjusted performance measure that represents the average return of a portfolio or investment above what would be predicted by the Capital Asset Pricing Model (CAPM), given the portfolio’s beta and the market’s excess return. It is used to determine if an investment manager has added value through their stock-picking skills.
Jensen's Alpha: Jensen's alpha is a measure of a portfolio's or investment's risk-adjusted performance. It represents the average return of a portfolio or investment above or below what is predicted by the capital asset pricing model (CAPM) given the portfolio's or investment's beta and the average market return.
Lower-volatility investments: Lower-volatility investments are financial assets that exhibit smaller price fluctuations over time compared to higher-volatility investments. These assets are often considered safer and more stable, making them attractive for risk-averse investors.
Market Risk: Market risk, also known as systematic risk, is the risk associated with the overall fluctuations in the financial markets. It is the uncertainty inherent in the performance of the market as a whole, which can impact the value of an investment or a portfolio of investments. Market risk arises from factors such as changes in interest rates, economic conditions, political events, and other macroeconomic factors that affect the entire market.
McKinley Investment Management: McKinley Investment Management is a firm specializing in the management of investment portfolios for institutions and high-net-worth individuals. It focuses on delivering customized investment solutions based on rigorous performance measurement and analysis.
Passive Market Exposure: Passive market exposure refers to an investment approach that aims to track or replicate the performance of a specific market index or benchmark, rather than actively trying to outperform it. This strategy involves investing in a diversified portfolio that mirrors the composition and weightings of a selected market index, providing investors with broad exposure to the overall market.
Performance Attribution: Performance attribution is a methodology used to analyze and understand the drivers of investment portfolio performance. It aims to break down the overall portfolio return into various components, such as asset allocation, security selection, and other factors, in order to identify the sources of value added or lost by the portfolio manager.
Risk-Adjusted Performance: Risk-adjusted performance is a method of evaluating the returns of an investment or portfolio in relation to the amount of risk taken. It allows investors to compare the risk-return profile of different investments or portfolios to make more informed decisions.
Risk-adjusted return: Risk-adjusted return is a measure of the return on an investment or portfolio, adjusted for the amount of risk taken to achieve that return. It allows for a more meaningful comparison of investments with different risk profiles by accounting for the level of risk inherent in each investment.
S&P 500: The S&P 500 is a stock market index that tracks the performance of the 500 largest publicly traded companies in the United States. It is widely regarded as one of the best representations of the overall U.S. stock market and is a key benchmark for evaluating the performance of various investment portfolios and strategies.
Sharpe: The Sharpe Ratio is a measure used to evaluate the risk-adjusted return of an investment portfolio. It is calculated by subtracting the risk-free rate from the portfolio's return and dividing the result by the portfolio's standard deviation.
Sharpe ratio: The Sharpe ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. It is calculated by subtracting the risk-free rate from the investment return and then dividing the result by the standard deviation of the investment's excess return.
Sharpe Ratio: The Sharpe ratio is a measure of the risk-adjusted return of an investment or portfolio. It is calculated by dividing the average return of an investment by its standard deviation, providing a metric to evaluate the performance of an asset relative to the risk taken.
Standard deviation: Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. It is used to assess the risk and volatility of an investment's returns in finance.
Standard Deviation: Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data values around the mean or average. It provides a way to understand how spread out a group of numbers is from the central tendency.
Systematic risk: Systematic risk is the risk inherent to the entire market or a market segment. It cannot be eliminated through diversification and is influenced by factors such as economic changes, political events, and natural disasters.
Systematic Risk: Systematic risk, also known as market risk or undiversifiable risk, is the risk inherent to the entire market or market segment, which cannot be mitigated through diversification. It is the risk that affects all assets and cannot be eliminated by holding a diversified portfolio.
Tracking Error: Tracking error is a measure of the difference between the performance of a portfolio or fund and the performance of the benchmark or index it is designed to track. It quantifies how closely a portfolio follows the returns of its underlying benchmark, providing insight into the effectiveness of an investment strategy.
Treasury Bills: Treasury bills (T-bills) are short-term debt securities issued by the U.S. government with maturities of one year or less. They are considered one of the safest investments due to the full faith and credit backing of the U.S. government, and they play a crucial role in the functioning of financial markets and the broader economy.
Treasury bills (T-bills): Treasury bills (T-bills) are short-term debt securities issued by the U.S. Department of the Treasury with maturities ranging from a few days to 52 weeks. They are sold at a discount to their face value and do not pay periodic interest.
Treynor Measure: The Treynor measure, also known as the Treynor ratio, is a performance metric used to evaluate the risk-adjusted return of an investment or portfolio. It measures the excess return of an investment over the risk-free rate, divided by the investment's systematic risk, as measured by its beta.
Treynor ratio: The Treynor ratio measures the risk-adjusted return of an investment portfolio by comparing its excess return over the risk-free rate to its beta. It helps investors evaluate how well they are compensated for taking on market risk.
Volatility: Volatility refers to the degree of variation in the price or value of a financial asset, economic indicator, or market over time. It is a measure of the uncertainty or risk associated with the size of changes in a variable's value. Volatility is a crucial concept in finance, economics, and risk management, as it helps understand the stability and predictability of various financial and economic phenomena.
William Sharpe: William Sharpe is a renowned American economist and professor who made significant contributions to the field of finance, particularly in the area of performance measurement. Sharpe is best known for developing the Sharpe ratio, a metric that evaluates the risk-adjusted performance of an investment or portfolio.
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15.5 Using Excel to Make Investment Decisions