'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.'

Which means for our asset as example:- Looking at the total return, or increase in value of 113.6% in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (62.7%)
- Looking at total return, or performance in of 48.8% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (34.7%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of 16.4% in the last 5 years of Paychex, we see it is relatively larger, thus better in comparison to the benchmark SPY (10.2%)
- Looking at compounded annual growth rate (CAGR) in of 14.2% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (10.5%).

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of Paychex is 28.4%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at historical 30 days volatility in of 33.4% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (24.1%).

'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.'

Which means for our asset as example:- The downside volatility over 5 years of Paychex is 20.2%, which is larger, thus worse compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (17.6%) in the period of the last 3 years, the downside volatility of 23.7% is higher, 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.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.49 in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.37)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.35, which is greater, thus better than the value of 0.33 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- The downside risk / excess return profile over 5 years of Paychex is 0.69, which is higher, thus better compared to the benchmark SPY (0.51) in the same period.
- Compared with SPY (0.45) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.49 is greater, thus better.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (7.71 ) in the period of the last 5 years, the Ulcer Ratio of 9.71 of Paychex is greater, thus worse.
- Compared with SPY (9.08 ) in the period of the last 3 years, the Ulcer Index of 12 is higher, 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.'

Which means for our asset as example:- The maximum reduction from previous high over 5 years of Paychex is -44.2 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -44.2 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 days).

'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.'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of Paychex is 181 days, which is smaller, thus better compared to the benchmark SPY (189 days) in the same period.
- Compared with SPY (189 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 181 days is smaller, thus better.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. 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:- The average time in days below previous high water mark over 5 years of Paychex is 48 days, which is greater, thus worse compared to the benchmark SPY (46 days) in the same period.
- During the last 3 years, the average days under water is 45 days, which is greater, thus worse than the value of 45 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.