Being able to measure and quantify risk/return is a top priority when evaluating investment portfolios. There are many sophisticated tools that help investors assess risk-adjusted portfolio performance. These tools are also useful for comparing investment strategies, indices, or the historical performance of different money managers and hedge funds.

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Combining Risk and Return into a Single Comparable Value

There are two main investing goals: (i) achieve the highest annual return, and (ii) minimize the chances of losing money. By combining risk and return into a single value, investors can compare the true performance of different portfolios. This measure is called risk-adjusted portfolio performance. This analysis includes the following risk-adjusted performance ratios:

1️⃣ Sharpe Ratio

2️⃣ Sortino Ratio

3️⃣ Treynor Measure or Treynor Ratio

4️⃣ Jensen Measure or Jensen Alpha

5️⃣ Calmar Ratio

6️⃣ MAR Ratio

7️⃣ Omega Ratio

8️⃣ Information Ratio or Appraisal Ratio

🏁 Key Takeaways from Our Analysis

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Three Fundamental Investment Concepts to Understand Before Advancing

Before moving on to the ratios that measure risk-adjusted performance, it is important to understand some basic concepts. These include the risk-free rate of return, standard deviation (SD), and maximum drawdown. Most of the performance ratios are partially based on these three components.

① The Risk-Free Rate of Return

The risk-free rate is the annual return an investor can earn without taking any risk. It is generally based on the annualized interest of a 3-month Treasury bill. Any investment expected to deliver less than the risk-free rate is considered unacceptable.

• In the US, you can use the annualized return of the 3-month Treasury Bill. 🔗 Treasury Bills (T-Bills)

• In the EU, the 3-month Euribor is commonly used.

② The Standard Deviation (SD)

The standard deviation (SD), or Sigma (σ), measures the amount of variation or dispersion in a set of values.

• A higher SD means values are spread out; a lower SD means values are closer to the mean (expected value).

• This is important because investors want to ensure a portfolio’s historical positive performance is consistent and repeatable.

☑ Key points:

• Lower SD is better.

• Lower SD means returns are more consistent and predictable over time.

• SD rises as returns become more volatile; a portfolio with lower SD is preferable to one with higher SD.

• SD is typically calculated monthly or yearly.

③ Maximum Drawdown

Maximum drawdown measures the largest loss a portfolio experiences from its peak value. It is calculated by subtracting the portfolio’s lowest value from its peak value, then dividing by the peak value.

🧮 Maximum drawdown (%) = (Peak value($) − Lowest value($)) / Peak value($)

👉 Example: If a portfolio peaks at $120,000 and falls to $85,000, the drawdown is: ($120,000 − $85,000) / $120,000 = 37.5%

☑ Key points:

• Lower maximum drawdown is better for the portfolio.

• Time is important when calculating maximum drawdown.

• Portfolios with low maximum drawdown over long periods are considered very reliable.

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The Key Measuring Performance Tools

As mentioned earlier, by combining risk and return into a single value, we can reliably compare different portfolios. Keep in mind that a portfolio with the highest return is not necessarily the best one to invest in.

(1️⃣) Sharpe Ratio

☑️ Use: All Portfolios | Strategies | Assets

☑️ Alternatives: Sortino Ratio | Omega Ratio

Developed by William F. Sharpe in 1966, the Sharpe ratio (or Sharpe index) is one of the most widely used tools in portfolio management. A Sharpe ratio above 1.0 is considered very good. For example, the ‘Amundi ETF Nasdaq 100’ delivered an average annual growth of 16.4% between mid-2007 and mid-2022, with a Sharpe ratio of 0.93.

Unlike other ratios, the Sharpe ratio measures portfolio quality not only based on performance but also on diversification, using standard deviation.

The Sharpe ratio calculates a portfolio’s excess return over the risk-free rate (explained above) and divides it by the standard deviation of that excess return. The formula is:

🧮 Sharpe ratio = { (PR − RFR) / SD(p) }

​where:

PR = Return of the Portfolio

RFR = Risk-Free Rate (such as a US Treasury security)

SD(p) = Standard Deviation of the portfolio’s excess return

☑ Key Points

• The Sharpe ratio provides an easy way to measure the risk-adjusted returns of any portfolio
• The Sharpe ratio requires data collected over a sufficiently long period.
• The higher the ratio, the greater the investment return, relative to the risk taken
• The ratio illustrates how much excess return is received for the additional risk
• The Sharpe ratio considers unsystematic risk and can be used to compare both well-diversified and less-diversified portfolios

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(2️⃣) Sortino Ratio

☑️ Use: Risk-Averse Portfolios | Strategies | Assets

☑️ Alternatives: Sharpe ratio

Developed by Frank A. Sortino, the Sortino ratio measures a portfolio’s risk-adjusted return by penalizing only returns that fall below a user-specified target. In contrast, the Sharpe ratio penalizes both positive and negative deviations equally.

🧮 Sortino Ratio= ( PR - R(f) ) / SD(d)

where:

PR = Portfolio Return (actual or expected)

R(f) = Free Rate of Return

SD(d) = Standard deviation of Negative Portfolio Returns

📊 Interpreting Sortino Ratio

A negative Sortino ratio means the portfolio return can’t even beat the risk-free rate.

• Below 0 is completely unacceptable
• Below 1.0 is considered low
• Between 1.0 and 2.0 is considered promising
• Between 2.0 and 3.0 is considered very promising
• Higher than 3.0 is considered excellent

☑ Key Points

• The Sortino ratio measures a portfolio’s risk-adjusted return—the higher, the better
• The Sortino ratio is similar to the Sharpe ratio, except for the fact that it incorporates a downside deviation for the denominator, instead of a standard deviation
• It penalizes returns that fall below the specified target rate
• By focusing on negative returns, it is useful for evaluating risk-oriented portfolio performance
• A Sortino ratio above 1.0 is generally considered acceptable

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(3️⃣) Treynor Measure or Treynor Ratio

☑️ Use: well-diversified Portfolios / Hedge Funds

☑️ Alternatives: Jensen Alpha

Developed by Jack Treynor in 1965, the Treynor ratio is similar to the Sharpe ratio, but it uses relative volatility (beta) in the denominator instead of standard deviation. The beta coefficient (β) measures a portfolio’s volatility relative to the overall market.

🧮 Treynor Measure = { (PR − RFR) / β }

​where:

PR = Return of the Portfolio

RFR = Risk-Free Rate

β = beta

☑ Key Points

• The Treynor Measure is the ratio of a portfolio’s excess return to its systematic risk
• The higher the Treynor Measure, the better the portfolio has performed
• It is similar to the Sharpe ratio but uses beta (β) in the denominator instead of standard deviation
• Beta (β) measures the relative volatility between the portfolio and the overall market
• The Treynor Measure adjusts for systematic risk but ignores unsystematic risk, so it should only be used to compare well-diversified portfolios.

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(4️⃣) Jensen Measure or Jensen Alpha

☑️ Use: well-diversified Portfolios / Hedge Funds

☑️ Alternatives: Treynor Measure

Developed by Michael C. Jensen in 1968, Jensen Alpha is similar to the Treynor Measure but incorporates the Capital Asset Pricing Model (CAPM). It measures a portfolio’s ability to deliver above-average returns after adjusting for market risk.

🧮 Jenson's Alpha = PR – { R(f) + β * ( R(m) - R(f) ) }

where:

PR = Return of the Portfolio

R(f) = Risk-Free Rate

β = beta

R(m) = Return of Market Risk

☑ Key Points

• The higher the Jensen Alpha, the better the risk-adjusted returns
• Jensen Alpha shows a portfolio’s excess return compared to its expected return
• It is calculated using the CAPM model, which shows the relationship between systematic risk and expected return for an asset
• In investing, alpha (α) measures a portfolio’s ability to outperform the market
• A portfolio with positive excess returns will have a positive alpha, while negative excess returns result in a negative alpha
• Positive alpha indicates outperformance, negative alpha indicates underperformance, and zero alpha indicates performance in line with the benchmark
• Jensen Alpha considers only systematic risk, so it should be used to compare well-diversified portfolios

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(5️⃣) Calmar Ratio

☑️ Use: Portfolios | Hedge/Mutual Funds

☑️ Alternatives: MAR Ratio

The Calmar ratio measures a portfolio’s or fund’s performance relative to its risk. Performance is calculated as the average annual return minus the annual risk-free rate, while risk is measured by the maximum drawdown over a period of three years or more.

🧮 Calmar ratio = { PR – R(f) } / max(drawdown)

where:

PR = Average Annual Portfolio Return (3 years or more)

R(f) = Risk-Free Rate

max(drawdown) = the maximum drawdown (3 years or more)

👉 Example:

As mentioned above, the maximum drawdown measures the maximum loss of a portfolio from its peak value. For example, the portfolio’s maximum drawdown is 37.5%, the average annual return is 45%, and the risk-free rate is 3.5%. Now, let’s calculate the Calmar ratio:

• Calmar ratio = { 45% – 3.5% } / 37.5% = 1.11

☑ Key Points

• The Calmar ratio measures a portfolio’s performance on a risk-adjusted basis, typically over three years
• The higher the Calmar ratio, the better; a ratio above 3.0 is considered very good
• Performance is based on the average annual return, while risk is measured by the maximum drawdown
• A low Calmar ratio indicates the portfolio is exposed to large drawdowns, whereas a high ratio signals low drawdown risk
• When comparing two portfolios with similar annual returns, the Calmar ratio is useful for identifying the better risk-adjusted portfolio

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(6️⃣) MAR Ratio

☑️ Use: Hedge Funds | Strategies

☑️ Alternatives: Calmar Ratio

Developed in 1978 by Leon Rose, the MAR ratio measures the risk-adjusted returns of a hedge fund or investment strategy. The higher the MAR ratio, the better the risk-adjusted performance. The ratio is calculated by dividing the compound annual growth rate (CAGR) by the maximum drawdown over a specific period.

🧮 MAR Ratio = CAGR / max(drawdown)

where:

• CAGR is the Compound Annual Growth Rate (It measures the annual growth rate of an investment, assuming all profits are reinvested at the end of each period)
• max(drawdown) is the maximum drawdown of the portfolio for a particular period

☑ Key Points

• MAR stands for “Managed Account Reports Ratio”
• The MAR ratio is useful for measuring the risk-adjusted returns of hedge funds and investment strategies
• Return is calculated using the Compound Annual Growth Rate (CAGR), and risk is measured by the maximum drawdown
• Over longer periods, the MAR ratio tends to produce lower values, as it is very sensitive to the portfolio’s maximum drawdown
• The MAR ratio is similar to the Calmar ratio, but the two can give very different results over long periods

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(7️⃣) Omega Ratio

☑️ Best Use: Complex Portfolios | Hedge Funds | Strategies | Assets

☑️ Alternatives: Sharpe ratio | Information Ratio

Developed by Con Keating and William Shadwick in 2002 in the article “A Universal Performance Measure,” the Omega ratio is a risk-return performance metric. It is considered a useful alternative to the Sharpe ratio.

The ratio is calculated as the ratio of probability-weighted profits and losses. To calculate the ratio, we need to know the cumulative excess return of the portfolio:

🧮 Omega Ratio = { Σ(Winning) – Benchmarking } / { Σ(Benchmarking) – Losing }

☑ Key Points

• The Omega ratio is a versatile risk-return performance measure and an alternative to the Sharpe ratio
• A higher Omega ratio indicates a higher probability of gains relative to losses
• Unlike the Sharpe ratio, the Omega ratio focuses on excess returns rather than absolute returns
• It incorporates all distribution moments and risk-return characteristics, including standard deviation, mean, kurtosis, and skewness
• The Omega ratio is especially useful for evaluating portfolios or funds with non-normal return distributions over time

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(8️⃣) The Information Ratio or Appraisal Ratio

☑️ Use: Portfolio Relative Returns (benchmark-based)

☑️ Alternatives: Sharpe Ratio | Omega Ratio

The Information Ratio, also called the Appraisal Ratio, measures a portfolio’s risk-adjusted return relative to a benchmark index. It calculates the excess return a manager achieves over the benchmark, divided by the additional risk taken to achieve that return. This excess return is known as the ‘active return’.

🧮 Information ratio = { R(P) -R(b) } / SD

where:

R(P) = Portfolio returns

R(b) = Benchmark Index returns (i.e. S&P 500)

SD = Standard Deviation of return

The Information Ratio is similar to the Sharpe ratio, but it uses a benchmark index instead of the risk-free rate.

☑ Key Points

• The Information Ratio is the ratio of a portfolio’s active return divided by the tracking error (standard deviation) of that return.
• Active return is the difference between a portfolio’s return and the return of a benchmark index (e.g., S&P 500).
• The Information Ratio works similarly to the Sharpe ratio.

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🏁 Key Takeaways from Our Analysis

Here are some key takeaways from our analysis:

• Risk matters as much as return, so investment performance should be evaluated on a risk-adjusted basis.

• A portfolio with the highest return is not necessarily the best investment.

• Combining risk and return into a single value allows investors to easily compare portfolio performance.

• Lower standard deviation is better, as it indicates more consistent and predictable returns.

• A portfolio with lower standard deviation is preferable to one with higher standard deviation.

• The risk-free rate of return is the annual return an investor can earn without taking any risk. Investments expected to deliver less than the risk-free rate are considered unacceptable.

• The risk-free rate is generally based on the annualized interest of a 3-month Treasury bill.

• Maximum drawdown measures the largest loss from a portfolio’s peak value. It is calculated as the difference between the peak and the lowest values divided by the peak value.

• CAGR (Compound Annual Growth Rate) measures the annual growth rate of an investment assuming all profits are reinvested.

• The Sharpe ratio is one of the most widely used portfolio management tools. It accounts for unsystematic risk and can be used for both well-diversified and less-diversified portfolios.

• The Sortino ratio is similar to the Sharpe ratio but focuses only on negative returns, making it useful for evaluating risk-oriented performance.

• The Treynor Ratio adjusts for systematic risk but ignores unsystematic risk, so it should only be used for well-diversified portfolios.

• Jensen’s alpha also considers only systematic risk and is best used to compare well-diversified portfolios.

• When comparing portfolios with similar annual returns, the Calmar ratio is useful for identifying the better risk-adjusted portfolio. A higher Calmar ratio indicates lower drawdown risk.

• The MAR ratio is similar to the Calmar ratio, but the two may produce very different results over long periods.

• The Omega ratio is especially useful for evaluating complex portfolios or funds with non-normal return distributions. Unlike the Sharpe ratio, it focuses on excess returns relative to a benchmark rather than absolute returns.

• The Information Ratio is similar to the Sharpe ratio but uses a benchmark index instead of the risk-free rate. Its active return is the difference between a portfolio’s return and the benchmark return (e.g., S&P 500).

 

■ Essential Tools for Measuring Portfolio Performance

Giorgos Protonotarios, Investment Analyst

for Tradingcenter.org (c) -July 2022