# Performance Metrics

Analyzing investment performance can help quantify the overall quality of investments in a portfolio, identify successful strategies, or highlight areas that need improvement. Performance metrics can be viewed individually or holistically to create robust systems and strategies.

The win rate divides the total number of winning trades by total trades. For example, if an investor has placed 200 trades and has realized a profit on 120 of them, the win rate is 60% (120/200).

While the win rate can identify how successful trades are at generating profit, it is not as important as the profit factor, or how much is gained or lost on each trade. For example, an investor may have a 60% win rate, but if they lose 3x as much when they lose than they make when they win, they will lose capital over time.

The profit factor divides the total amount of money gained by the total amount of money lost. Profit factor is important when used in conjunction with the win rate because it creates a more complete view of trading performance.

For example, if an investor has placed 200 trades with a win rate of 60% and averages $50 per winning trade and $50 per losing trade, their profit factor will be 1.5 with a net profit of $2000 ((120 x $50 = $6,000) / (80 x $50 = $4,000)).

Compare this with an investor who has a 60% win rate on 200 trades but a profit factor of .5 because they average $50 per winning trade, but $150 per losing trade ((120 x $50 = $6,000) / (80 x $150 = $12,000)). They will have a net loss of -$6,000, despite the same win rate.

Return on investment measures the effectiveness of an investment relative to its initial cost of entry. ROI divides the return of an investment by the cost of the investment.

For example, if an investment cost $5,000 to purchase and is now worth $6,000, the ROI for the investment is 20% ($6,000-$5,000 = $1,000 / $5,000).

Return on margin is the net gain or loss of an investment relative to the required margin to initiate the trade. The return on margin is calculated by dividing the realized return by the initial margin.

For example, if a security cost $50,000 to purchase, and $25,000 of margin was used, a $5,000 return would have an ROI of 10% and a return on margin of 20%.

Return on margin can also take into account the interest rate paid on the borrowed capital.

Compounded annual growth rate measures the rate an investment would grow if it increased at the same rate every year, and the profits were reinvested at the end of each year. This is not typically realistic because investments generally do not have identical returns every year.

For example, if an investment returned $3,000, $500, and $6,500 over three years, the cumulative return would be $10,000, or $3,333 per year.

Let’s assume a starting capital of $10,000. The three-year return would be 100%; the average annual return would be 33%.

The CAGR is calculated by dividing the ending capital by the starting capital, raising that value to 1 divided by the number of years, and subtracting that total by 1.

For this example, the CAGR would be 25.99%, or less than the annual return of 33%. ($20,000/$10,000)1/3 = $21/3 = 1.2599 -1 = 25.99%).

CAGR helps compare two uncorrelated investments and smooths out the returns over multiple years, despite the fact the year-to-year returns may vary significantly.

The Sharpe ratio, created by William Sharpe, helps an investor measure the return of an investment relative to its risk. The Sharpe ratio is calculated by subtracting the risk-free rate of return from the portfolio’s return and dividing the value by the portfolio’s standard deviation of returns.

The numerator is known as the portfolio's excess return. Excess return refers to any gains earned beyond the risk-free rate of return. The risk-free rate is typically represented by Treasury bills.

The Sharpe ratio helps to determine if returns are the result of sound investing or a product of taking on too much risk and can be used to evaluate past performance. The higher the Sharpe ratio’s value, the better the performance is relative to the risk required to generate the returns. Increasing the diversification of a portfolio often results in a higher Sharpe ratio.

The Treynor ratio, developed by Jack Treynor, is a risk to reward measurement that investors can use to calculate and adjust a portfolio’s exposure to the unavoidable, systematic risk involved with investing.

The Treynor ratio uses a portfolio’s beta to determine its risk exposure. The Treynor ratio is calculated by subtracting the risk-free rate from the portfolio’s return and then dividing it by the portfolio’s beta. Treasury bills typically represent the risk-free rate.

The Treynor ratio is similar to the Sharpe ratio but uses beta instead of the standard deviation. Both the Treynor and Sharpe ratios are used to evaluate performance and are often used to compare a portfolio’s performance relative to a benchmark.

Jensen’s alpha measures the excess returns earned by a portfolio compared to the projected returns of the capital asset pricing model (CAPM). Jensen’s alpha takes into account the risk-free rate of return for a specified time period and measures a portfolio’s performance relative to the broad market or index.

When evaluating a portfolio, Jensen’s alpha helps to determine if the returns generated were consistent with the risk taken to achieve the results. The “alpha” in Jensen’s alpha is the amount by which the portfolio outperformed the benchmark. A Jensen’s alpha of 0 means the portfolio earned no excess return.

The information ratio measures a portfolio’s alpha divided by its tracking error.

To calculate the information ratio, subtract the benchmark’s return from the portfolio return, and divide by the difference in the standard deviation between the two. The difference between a portfolio’s volatility and the benchmark’s volatility is known as tracking error.

The information ratio is the portfolio’s alpha divided by its tracking error. A higher IR signifies that a portfolio is outperforming the benchmark index relative to the risk taken to achieve the returns.

The Calmar ratio uses a portfolio’s maximum drawdown as a measure of its risk and compares it to the compounded annual rate of return. The Calmar ratio uses a three year lookback period and is updated monthly.

A high Calmar ratio equates to a low risk of large drawdowns while a low Calmar ratio indicates a higher risk of a large drawdown.

The Sortino ratio is similar to the Sharpe ratio but focuses primarily on negative volatility in a portfolio. In calculating the standard deviation for the Sortino ratio, only the returns that lie below the mean are used. Therefore, the Sortino ratio gives investors a way to evaluate the return of investment based on its return for downside risk only.

For example, funds with high levels of performance tend to have higher standard deviation of returns. However, if the returns are +10%, +30%, +15%, and +50%, the high standard deviation of returns is misrepresentative because the volatility has all been to the upside.

### How is the win rate calculated?

To calculate the win rate, divide the total number of winning trades by total trades. For example, if an investor has placed 200 trades and has realized a profit on 120 of them, the win rate is 60% (120/200).

### What is a good profit factor?

Profit factor is important when used in conjunction with win rate because it creates a more complete view of trading performance. Profit factor is calculated by dividing gross profit by gross loss for a trading period.

A profit factor of 1 means that all profits and losses added together break even, so any profit factor over 1 would indicate a profitable investing approach.

### What is the formula for return on investment?

Return on investment measures the effectiveness of an investment relative to its initial cost of entry. ROI divides the return of an investment by the initial cost of the investment. For example, if an investment cost $5,000 to purchase and is now worth $6,000, the ROI for the investment is 20% ($6,000-$5,000 = $1,000 / $5,000).

### What is a good ROI?

A good return on investment is subjective and varies depending on each individual investor’s profit target and account size. ROI varies from industry to industry, and different strategies will produce different returns. ROI is often analyzed over several periods to determine if performance is improving or declining.

### What is the difference between profit margin and ROI?

Profit margin is net income divided by sales and measures the percentage of sales that reach a company’s bottom line.

Return on investment measures the effectiveness of an investment relative to its initial cost of entry. ROI divides the return of an investment by the cost of the investment.

### What does the CAGR tell you?

Compounded annual growth rate (CAGR) measures the rate an investment would grow if it increased at the same rate every year and the profits were reinvested at the end of each year.

### How do you calculate CAGR in Excel?

The “RRI” function in Excel calculates the compounded return for an investment. Enter the number of periods, the starting value, and the ending value into Excel.

For example, if an investment has grown from $1,000 t0 $2,000 over 5 years, enter =RRI(5,1000,2000). The calculated value in Excel is 14.87%.

### What is a good Sharpe ratio?

The Sharpe ratio measures the return of an investment relative to its risk. The Sharpe ratio helps to determine if returns are the result of sound investing or a product of taking on too much risk and can be used to evaluate past performance. The higher the Sharpe ratio, the better the performance is relative to the risk required to generate the returns.

Increasing the diversification of a portfolio often results in a higher Sharpe ratio.

### How do you calculate the Sharpe ratio?

The Sharpe ratio is calculated by subtracting the risk-free rate of return from the portfolio’s return and dividing the value by the portfolio’s standard deviation of returns. The numerator is known as the portfolio's excess return. Excess return refers to any gains earned beyond the risk-free rate of return.

Treasury bills typically represent the risk-free rate.

### What is the difference between the Sharpe ratio and the Treynor ratio?

The Treynor and Sharpe ratios are used to evaluate performance and are often used to compare a portfolio’s performance relative to a benchmark. The Sharpe ratio measures the return of an investment relative to its risk. The Sharpe ratio helps to determine if returns are the result of sound investing or a product of taking on too much risk and can be used to evaluate past performance.

The Treynor ratio is a risk to reward measurement that investors can use to calculate and adjust a portfolio’s exposure to the unavoidable, systematic risk involved with investing. The Treynor ratio uses a portfolio’s beta to determine its risk exposure.

The Treynor ratio is similar to the Sharpe ratio, but the Treynor ratio assesses systematic risk only.

### How do you calculate the Treynor ratio?

The Treynor ratio is calculated by subtracting the risk-free rate from the portfolio’s return and dividing it by the portfolio’s beta. The risk-free rate is typically represented by Treasury bills.

### What does Jensen's alpha measure?

Jensen’s alpha measures the excess returns earned by a portfolio compared to the projected returns of the capital asset pricing model (CAPM). When evaluating a portfolio, Jensen’s alpha helps to determine if the returns generated were consistent with the risk taken to achieve the results.

The “alpha” in Jensen’s alpha is the amount by which the portfolio outperformed the benchmark.

### How is the information ratio calculated?

To calculate the information ratio, subtract the benchmark’s return from the portfolio return, and divide by the difference in the standard deviation between the two. The difference between a portfolio’s volatility and the benchmark’s volatility is known as tracking error. The information ratio is the portfolio’s alpha divided by its tracking error.

### How is the Calmar ratio calculated?

The Calmar ratio is calculated by dividing the average annual return by the maximum drawdown. The maxim drawdown is calculated by subtracting the portfolio’s lowest value from its highest value and dividing by the highest value.

For example, if the portfolio’s highest value was $120,000 and the lowest value was $100,000, then the maximum drawdown for the portfolio was 16.67%.

The Calmar ratio uses a portfolio’s maximum drawdown as a measure of its risk and compares it to the compounded annual rate of return. The Calmar ratio uses a three year lookback period and is updated monthly.

A high Calmar ratio equates to a low risk of large drawdowns while a low Calmar ratio indicates a higher risk of a large drawdown.

### What is the difference between the Sharpe ratio and the Sortino ratio?

The Sharpe measures the return of an investment relative to its risk. The Sharpe ratio helps to determine if returns are the result of sound investing or a product of taking on too much risk, and can be used to evaluate past performance.

The Sortino ratio is similar to the Sharpe ratio, but focuses primarily on negative volatility in a portfolio. In calculating the standard deviation for the Sortino ratio, only the returns that lie below the mean are used. Therefore, the Sortino ratio gives investors a way to evaluate an investment’s return based on its downside risk only.

### How do you calculate the Sortino ratio?

The Sortino ratio is calculated by subtracting the risk-free rate from the actual or expected return of a portfolio and dividing it by the standard deviation of the downside returns. The Sortino ratio gives investors a way to evaluate an investment’s return based on its downside risk only.