'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.'

Which means for our asset as example:- Compared with the benchmark SPY (58.9%) in the period of the last 5 years, the total return, or performance of 14% of Vanguard European Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return, or performance is 17.4%, which is lower, thus worse than the value of 33.9% 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.'

Applying this definition to our asset in some examples:- The annual return (CAGR) over 5 years of Vanguard European Stock Index Fund is 2.7%, which is smaller, thus worse compared to the benchmark SPY (9.7%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 5.5%, which is lower, thus worse than the value of 10.2% 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:- Looking at the historical 30 days volatility of 21% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (21.6%)
- Looking at 30 days standard deviation in of 25% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (25%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of Vanguard European Stock Index Fund is 15.6%, which is lower, thus better compared to the benchmark SPY (15.7%) in the same period.
- Compared with SPY (18.1%) in the period of the last 3 years, the downside volatility of 18.4% is larger, thus worse.

'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:- The ratio of return and volatility (Sharpe) over 5 years of Vanguard European Stock Index Fund is 0.01, which is smaller, thus worse compared to the benchmark SPY (0.33) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.12, which is smaller, thus worse than the value of 0.31 from the benchmark.

'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 ratio of annual return and downside deviation over 5 years of Vanguard European Stock Index Fund is 0.01, which is lower, thus worse compared to the benchmark SPY (0.46) in the same period.
- Compared with SPY (0.43) in the period of the last 3 years, the downside risk / excess return profile of 0.16 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the Downside risk index of 12 in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (8.91 )
- Looking at Ulcer Index in of 14 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (11 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of Vanguard European Stock Index Fund is -36.6 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -36.3 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 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) in days.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (271 days) in the period of the last 5 years, the maximum days below previous high of 478 days of Vanguard European Stock Index Fund is greater, thus worse.
- Compared with SPY (271 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 355 days is greater, thus worse.

'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:- Looking at the average days under water of 168 days in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (60 days)
- Looking at average days under water in of 121 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (72 days).

Historical returns have been extended using synthetic data.
[Show Details]

- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of Vanguard European Stock Index Fund 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.