'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.'

Using this definition on our asset we see for example:- The total return, or performance over 5 years of Paychex is 148.7%, which is higher, thus better compared to the benchmark SPY (67.9%) in the same period.
- Looking at total return, or increase in value in of 82.4% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (46.6%).

'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:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual performance (CAGR) of 20% of Paychex is larger, thus better.
- Looking at compounded annual growth rate (CAGR) in of 22.2% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.6%).

'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.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 17% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.3%)
- During the last 3 years, the 30 days standard deviation is 17.2%, which is higher, thus worse than the value of 12.5% from the benchmark.

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

Which means for our asset as example:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside volatility of 18.2% of Paychex is greater, thus worse.
- Looking at downside deviation in of 18.9% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (14.2%).

'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:- Compared with the benchmark SPY (0.64) in the period of the last 5 years, the Sharpe Ratio of 1.03 of Paychex is higher, thus better.
- Compared with SPY (0.89) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 1.15 is larger, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.58) in the period of the last 5 years, the excess return divided by the downside deviation of 0.96 of Paychex is higher, thus better.
- Looking at ratio of annual return and downside deviation in of 1.04 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.78).

'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:- The Ulcer Index over 5 years of Paychex is 5.56 , which is greater, thus better compared to the benchmark SPY (3.96 ) in the same period.
- Compared with SPY (4.01 ) in the period of the last 3 years, the Downside risk index of 5.93 is larger, thus better.

'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.'

Which means for our asset as example:- Looking at the maximum reduction from previous high 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 reduction from previous high 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 time in days below previous high water mark over 5 years of Paychex is 149 days, which is smaller, 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 below previous high of 139 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.'

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

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.