'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Applying this definition to our asset in some examples:- Looking at the total return, or performance of 109.3% in the last 5 years of Paychex, we see it is relatively larger, thus better in comparison to the benchmark SPY (74.2%)
- Compared with SPY (50.1%) in the period of the last 3 years, the total return, or performance of 64.3% is greater, thus better.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (11.8%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 15.9% of Paychex is higher, thus better.
- Looking at compounded annual growth rate (CAGR) in of 18% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (14.5%).

'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 17.3% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.3%)
- Looking at historical 30 days volatility in of 17.1% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (13%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- The downside risk over 5 years of Paychex is 12.1%, which is greater, thus worse compared to the benchmark SPY (9.6%) in the same period.
- During the last 3 years, the downside deviation is 12.2%, which is greater, thus worse than the value of 9.4% 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.'

Applying this definition to our asset in some examples:- Looking at the risk / return profile (Sharpe) of 0.78 in the last 5 years of Paychex, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.69)
- Compared with SPY (0.93) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.91 is smaller, thus worse.

'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.'

Which means for our asset as example:- The downside risk / excess return profile over 5 years of Paychex is 1.11, which is higher, thus better compared to the benchmark SPY (0.96) in the same period.
- Compared with SPY (1.27) in the period of the last 3 years, the excess return divided by the downside deviation of 1.27 is higher, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (3.97 ) in the period of the last 5 years, the Ulcer Ratio of 5.71 of Paychex is larger, thus worse.
- Compared with SPY (4.1 ) in the period of the last 3 years, the Ulcer Index of 5.77 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:- Looking at the maximum DrawDown of -17.4 days in the last 5 years of Paychex, we see it is relatively greater, thus better in comparison to the benchmark SPY (-19.3 days)
- During the last 3 years, the maximum drop from peak to valley is -17.4 days, which is higher, thus better than the value of -19.3 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). 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:- The maximum days under water over 5 years of Paychex is 150 days, which is lower, thus better compared to the benchmark SPY (187 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 150 days is larger, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 47 days in the last 5 years of Paychex, we see it is relatively larger, thus worse in comparison to the benchmark SPY (42 days)
- Looking at average time in days below previous high water mark in of 51 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (37 days).

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.