'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:- Compared with the benchmark SPY (93.6%) in the period of the last 5 years, the total return, or increase in value of 90.7% of Paychex is lower, thus worse.
- Looking at total return, or performance in of 49.5% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (33.2%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- Looking at the annual performance (CAGR) of 13.8% in the last 5 years of Paychex, we see it is relatively lower, thus worse in comparison to the benchmark SPY (14.2%)
- Looking at compounded annual growth rate (CAGR) in of 14.4% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (10%).

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 29.1% of Paychex is greater, thus worse.
- Looking at historical 30 days volatility in of 23.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.5%).

'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.'

Applying this definition to our asset in some examples:- The downside volatility over 5 years of Paychex is 20.6%, which is higher, thus worse compared to the benchmark SPY (15%) in the same period.
- During the last 3 years, the downside volatility is 16.3%, which is larger, thus worse than the value of 12.2% from the benchmark.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Which means for our asset as example:- Looking at the ratio of return and volatility (Sharpe) of 0.39 in the last 5 years of Paychex, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.56)
- Compared with SPY (0.43) in the period of the last 3 years, the Sharpe Ratio of 0.51 is higher, thus better.

'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:- Compared with the benchmark SPY (0.78) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.55 of Paychex is lower, thus worse.
- Looking at ratio of annual return and downside deviation in of 0.73 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.62).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Paychex is 12 , which is greater, thus worse compared to the benchmark SPY (9.33 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 12 is greater, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Using this definition on our asset we see for example:- Looking at the maximum DrawDown of -44.2 days in the last 5 years of Paychex, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum DrawDown is -23.4 days, which is greater, thus better than the value of -24.5 days from the benchmark.

'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) in days.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 469 days of Paychex is lower, thus better.
- During the last 3 years, the maximum days under water is 469 days, which is lower, thus better than the value of 488 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.'

Which means for our asset as example:- The average days below previous high over 5 years of Paychex is 125 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average time in days below previous high water mark is 165 days, which is lower, thus better than the value of 180 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal 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.