'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:- The total return over 5 years of Paychex is 71.2%, which is larger, thus better compared to the benchmark SPY (59.9%) in the same period.
- During the last 3 years, the total return, or performance is 33.8%, which is lower, thus worse than the value of 34.2% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Looking at the compounded annual growth rate (CAGR) of 11.4% in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (9.8%)
- Looking at annual performance (CAGR) in of 10.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10.3%).

'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 volatility of 25.7% in the last 5 years of Paychex, we see it is relatively higher, thus worse in comparison to the benchmark SPY (18.7%)
- Looking at volatility in of 30.1% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (21.5%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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:- Looking at the downside deviation of 18.4% in the last 5 years of Paychex, we see it is relatively higher, thus worse in comparison to the benchmark SPY (13.6%)
- During the last 3 years, the downside volatility is 21.7%, which is greater, thus worse than the value of 15.7% from the benchmark.

'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 0.34 in the last 5 years of Paychex, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.39)
- Looking at Sharpe Ratio in of 0.26 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.36).

'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 0.48, which is lower, thus worse compared to the benchmark SPY (0.54) in the same period.
- Looking at downside risk / excess return profile in of 0.36 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.5).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Applying this definition to our asset in some examples:- Looking at the Downside risk index of 8.11 in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (5.81 )
- Looking at Downside risk index in of 9.46 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (6.86 ).

'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 -44.2 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -44.2 days is smaller, thus worse.

'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 days under water of 150 days in the last 5 years of Paychex, we see it is relatively smaller, thus better in comparison to the benchmark SPY (187 days)
- Looking at maximum days below previous high in of 150 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (139 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.'

Which means for our asset as example:- The average time in days below previous high water mark over 5 years of Paychex is 43 days, which is higher, thus worse compared to the benchmark SPY (43 days) in the same period.
- Compared with SPY (39 days) in the period of the last 3 years, the average days below previous high of 44 days is larger, 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, 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.