'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- Looking at the total return of 78.7% in the last 5 years of Merck & Company, we see it is relatively higher, thus better in comparison to the benchmark SPY (66.2%)
- Compared with SPY (45.7%) in the period of the last 3 years, the total return, or performance of 69.9% is greater, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (10.7%) in the period of the last 5 years, the annual return (CAGR) of 12.3% of Merck & Company is higher, thus better.
- Compared with SPY (13.4%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 19.4% is higher, thus better.

'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.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of Merck & Company is 19.5%, which is greater, thus worse compared to the benchmark SPY (13.3%) in the same period.
- Looking at historical 30 days volatility in of 18.8% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.5%).

'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 19.4% of Merck & Company is greater, thus worse.
- During the last 3 years, the downside deviation is 18.2%, which is greater, thus worse than the value of 14.1% 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 ratio of return and volatility (Sharpe) of 0.5 in the last 5 years of Merck & Company, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.62)
- Compared with SPY (0.87) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.9 is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of 0.51 in the last 5 years of Merck & Company, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.56)
- Looking at excess return divided by the downside deviation in of 0.93 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.77).

'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.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of Merck & Company is 8.15 , 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 6.9 is higher, 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.'

Applying this definition to our asset in some examples:- Looking at the maximum drop from peak to valley of -21.3 days in the last 5 years of Merck & Company, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-19.3 days)
- During the last 3 years, the maximum reduction from previous high is -18.2 days, which is larger, 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'

Which means for our asset as example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days below previous high of 390 days of Merck & Company is larger, thus worse.
- Looking at maximum days under water in of 217 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (131 days).

'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.'

Which means for our asset as example:- Looking at the average days below previous high of 95 days in the last 5 years of Merck & Company, we see it is relatively larger, thus worse in comparison to the benchmark SPY (39 days)
- Compared with SPY (34 days) in the period of the last 3 years, the average days below previous high of 49 days is larger, thus worse.

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 Merck & Company 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.