'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, or increase in value over 5 years of ASML Holding is 717.8%, which is higher, thus better compared to the benchmark SPY (129.1%) in the same period.
- Compared with SPY (71.3%) in the period of the last 3 years, the total return of 368.2% 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.'

Using this definition on our asset we see for example:- The annual performance (CAGR) over 5 years of ASML Holding is 52.3%, which is greater, thus better compared to the benchmark SPY (18.1%) in the same period.
- During the last 3 years, the annual return (CAGR) is 67.3%, which is higher, thus better than the value of 19.7% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 34.8% of ASML Holding is larger, thus worse.
- During the last 3 years, the historical 30 days volatility is 39.5%, which is higher, thus worse than the value of 22.5% 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:- Looking at the downside deviation of 23.9% in the last 5 years of ASML Holding, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.6%)
- During the last 3 years, the downside volatility is 27%, which is greater, thus worse than the value of 16.3% 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 ratio of return and volatility (Sharpe) of 1.43 in the last 5 years of ASML Holding, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.83)
- During the last 3 years, the risk / return profile (Sharpe) is 1.64, which is higher, thus better than the value of 0.76 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.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of ASML Holding is 2.09, which is higher, thus better compared to the benchmark SPY (1.15) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is 2.4, which is larger, thus better than the value of 1.05 from the benchmark.

'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.'

Which means for our asset as example:- Looking at the Ulcer Index of 9.23 in the last 5 years of ASML Holding, we see it is relatively greater, thus worse in comparison to the benchmark SPY (5.59 )
- Looking at Ulcer Index in of 7.11 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (6.38 ).

'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.'

Using this definition on our asset we see for example:- The maximum drop from peak to valley over 5 years of ASML Holding is -37.9 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -37.9 days, which is lower, thus worse than the value of -33.7 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) in days.'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 247 days in the last 5 years of ASML Holding, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- Looking at maximum time in days below previous high water mark in of 74 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (119 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:- Compared with the benchmark SPY (32 days) in the period of the last 5 years, the average days below previous high of 39 days of ASML Holding is greater, thus worse.
- During the last 3 years, the average days below previous high is 16 days, which is lower, thus better than the value of 25 days from the benchmark.

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 ASML Holding 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.