Measuring investment performance is crucial for investors to evaluate the effectiveness of investment strategies and portfolios. There are several key formulas used by investors and financial professionals to quantify investment returns adjusted for risk. By applying these formulas, investors can better understand the risk-adjusted performance of individual assets and entire portfolios. This allows for more informed decision making when constructing optimal portfolios aligned with investment objectives. The most common investment performance measurement formulas include the Sharpe ratio, Treynor ratio, Jensen’s alpha, and information ratio. Each measures return per unit of risk, helping investors determine if investment performance is attributable to smart investment choices or excessive risk-taking.
Sharpe ratio for risk-adjusted return per unit of volatility
The Sharpe ratio is one of the most widely used investment performance measurement formulas. Developed by Nobel laureate William Sharpe, it measures the excess return per unit of volatility. The formula is: (Portfolio Return – Risk Free Rate) / Standard Deviation of Returns. A higher Sharpe ratio indicates superior risk-adjusted returns. By using standard deviation as the risk measure, the Sharpe ratio incorporates both systematic and unsystematic risk. This makes it best suited for comparing diversified portfolios or asset classes rather than individual assets.
Treynor ratio for excess return per beta
The Treynor ratio, developed by Jack Treynor, measures excess return generated per unit of systematic risk as measured by beta. The formula is: (Portfolio Return – Risk Free Rate) / Beta. For well-diversified portfolios, using beta as the risk factor isolates the impact of systemic market risk. A higher Treynor ratio indicates better risk-adjusted returns vs. the market benchmark. Since beta only measures systematic risk, the Treynor ratio is best suited for comparing diversified portfolios of individual assets.
Jensen’s alpha for absolute excess return vs. CAPM
Developed by Michael Jensen, Jensen’s alpha measures excess return generated above that predicted by the Capital Asset Pricing Model (CAPM). The formula subtracts the portfolio’s expected return based on CAPM from its actual return. A positive alpha indicates outperformance vs. CAPM expectations. Jensen’s alpha is useful for evaluating active portfolio managers since a consistently positive alpha signals skill in selecting mispriced assets.
Information ratio for excess return over a benchmark
The information ratio measures excess return generated relative to a benchmark, per unit of tracking error (active risk). The formula is: (Portfolio Return – Benchmark Return) / Tracking Error. It assesses a portfolio manager’s ability to beat a benchmark on a risk-adjusted basis. A higher information ratio indicates a greater excess return per unit of active risk taken.
Key investment performance measurement formulas like the Sharpe ratio, Treynor ratio, Jensen’s alpha, and information ratio allow investors to quantify risk-adjusted returns. By isolating different types of risk taken and excess return generated, these formulas provide valuable insights into the effectiveness of investment strategies.