'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:- Compared with the benchmark SPY (98.3%) in the period of the last 5 years, the total return, or increase in value of 86.7% of Paychex is lower, thus worse.
- Compared with SPY (27.2%) in the period of the last 3 years, the total return of 29.2% is higher, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.7%) in the period of the last 5 years, the annual performance (CAGR) of 13.3% of Paychex is lower, thus worse.
- During the last 3 years, the annual return (CAGR) is 9%, which is larger, thus better than the value of 8.4% from the benchmark.

'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:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 29.2% of Paychex is higher, thus worse.
- Looking at volatility in of 23.5% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.7%).

'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 (14.9%) in the period of the last 5 years, the downside volatility of 20.6% of Paychex is higher, thus worse.
- Looking at downside deviation in of 16.6% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.4%).

'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:- Compared with the benchmark SPY (0.58) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.37 of Paychex is smaller, thus worse.
- Looking at Sharpe Ratio in of 0.28 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.33).

'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:- Looking at the excess return divided by the downside deviation of 0.52 in the last 5 years of Paychex, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.82)
- Compared with SPY (0.47) in the period of the last 3 years, the excess return divided by the downside deviation of 0.39 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of Paychex is 12 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Index is 13 , which is greater, thus worse than the value of 10 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Which means for our asset as example:- The maximum drop from peak to valley over 5 years of Paychex is -44.2 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -23.4 days is greater, 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'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 603 days in the last 5 years of Paychex, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum days below previous high in of 603 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (488 days).

'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:- The average days under water over 5 years of Paychex is 176 days, which is larger, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (177 days) in the period of the last 3 years, the average time in days below previous high water mark of 256 days is greater, thus worse.

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 and do not account for slippage, fees or taxes.