'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- The total return over 5 years of Paychex is 135.7%, which is larger, thus better compared to the benchmark SPY (66.7%) in the same period.
- During the last 3 years, the total return, or increase in value is 53.4%, which is larger, thus better than the value of 46% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Applying this definition to our asset in some examples:- Looking at the annual performance (CAGR) of 18.7% in the last 5 years of Paychex, we see it is relatively larger, thus better in comparison to the benchmark SPY (10.8%)
- Compared with SPY (13.5%) in the period of the last 3 years, the annual performance (CAGR) of 15.4% is larger, thus better.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 17.1% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.4%)
- Looking at historical 30 days volatility in of 16.8% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.3%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside risk of 18.4% of Paychex is greater, thus worse.
- Compared with SPY (13.9%) in the period of the last 3 years, the downside volatility of 18.9% is greater, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Which means for our asset as example:- The Sharpe Ratio over 5 years of Paychex is 0.95, which is higher, thus better compared to the benchmark SPY (0.62) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of 0.77 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.89).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- Looking at the downside risk / excess return profile of 0.88 in the last 5 years of Paychex, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.57)
- Looking at downside risk / excess return profile in of 0.68 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.79).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- Looking at the Ulcer Ratio of 5.58 in the last 5 years of Paychex, we see it is relatively higher, thus worse in comparison to the benchmark SPY (3.99 )
- Compared with SPY (4.04 ) in the period of the last 3 years, the Downside risk index of 5.97 is greater, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- The maximum reduction from previous high over 5 years of Paychex is -17.4 days, which is larger, thus better compared to the benchmark SPY (-19.3 days) in the same period.
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum drop from peak to valley of -17.4 days is higher, thus better.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- Looking at the maximum days under water of 149 days in the last 5 years of Paychex, we see it is relatively smaller, thus better in comparison to the benchmark SPY (187 days)
- During the last 3 years, the maximum days below previous high is 139 days, which is higher, thus worse than the value of 139 days from the benchmark.

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Using this definition on our asset we see for example:- Looking at the average days below previous high of 40 days in the last 5 years of Paychex, we see it is relatively lower, thus better in comparison to the benchmark SPY (41 days)
- Compared with SPY (36 days) in the period of the last 3 years, the average days under water of 40 days is larger, thus worse.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to the sum of monthly returns due to compounding.
- Performance results of Paychex are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.