'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 increase in value over 5 years of Paychex is 121.4%, which is larger, thus better compared to the benchmark SPY (68.1%) in the same period.
- During the last 3 years, the total return, or increase in value is 61.2%, which is larger, thus better than the value of 47.1% from the benchmark.

'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:- The annual performance (CAGR) over 5 years of Paychex is 17.2%, which is larger, thus better compared to the benchmark SPY (11%) in the same period.
- Looking at annual return (CAGR) in of 17.3% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.8%).

'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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 17% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.2%)
- During the last 3 years, the volatility is 17.1%, which is higher, thus worse than the value of 12.4% from the benchmark.

'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:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside risk of 18.1% of Paychex is greater, thus worse.
- Looking at downside volatility in of 18.5% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (14%).

'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 Sharpe Ratio of 0.87 in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.64)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.87, which is smaller, thus worse than the value of 0.91 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of Paychex is 0.81, which is higher, thus better compared to the benchmark SPY (0.58) in the same period.
- During the last 3 years, the downside risk / excess return profile is 0.8, which is larger, thus better than the value of 0.8 from the benchmark.

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of Paychex is 5.63 , which is higher, thus better compared to the benchmark SPY (3.95 ) in the same period.
- During the last 3 years, the Ulcer Index is 5.99 , which is greater, thus better than the value of 4 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 reduction from previous high over 5 years of Paychex is -17.4 days, which is higher, thus better compared to the benchmark SPY (-19.3 days) in the same period.
- Looking at maximum reduction from previous high in of -17.4 days in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (-19.3 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). 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:- The maximum days below previous high over 5 years of Paychex is 149 days, which is smaller, thus better compared to the benchmark SPY (187 days) in the same period.
- During the last 3 years, the maximum days below previous high is 139 days, which is greater, thus worse than the value of 131 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (39 days) in the period of the last 5 years, the average time in days below previous high water mark of 42 days of Paychex is higher, thus worse.
- Looking at average days below previous high in of 40 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (33 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.