'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.'

Which means for our asset as example:- The total return, or performance over 5 years of Vanguard European Stock Index Fund is 57%, which is smaller, thus worse compared to the benchmark SPY (120.8%) in the same period.
- Looking at total return, or increase in value in of 21.9% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (66.3%).

'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.'

Applying this definition to our asset in some examples:- Looking at the annual performance (CAGR) of 9.5% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (17.2%)
- Looking at annual return (CAGR) in of 6.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (18.5%).

'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 volatility of 19% 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 (18.7%)
- During the last 3 years, the volatility is 21.4%, which is lower, thus better than the value of 22.4% 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.'

Which means for our asset as example:- Looking at the downside risk of 14.6% 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 (13.6%)
- Looking at downside risk in of 16.4% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.3%).

'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.'

Which means for our asset as example:- Looking at the ratio of return and volatility (Sharpe) of 0.37 in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.78)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.2, which is smaller, thus worse than the value of 0.71 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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Vanguard European Stock Index Fund is 0.48, which is lower, thus worse compared to the benchmark SPY (1.08) in the same period.
- Looking at downside risk / excess return profile in of 0.26 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.98).

'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 Ratio of 9.54 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 (5.59 )
- During the last 3 years, the Ulcer Index is 9.92 , which is larger, thus worse than the value of 6.83 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The maximum drop from peak to valley over 5 years of Vanguard European Stock Index Fund is -37 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 -36.6 days is lower, 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 time in days below previous high water mark of 712 days in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum days under water is 416 days, which is greater, thus worse than the value of 139 days from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the average days below previous high of 231 days in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (33 days)
- During the last 3 years, the average time in days below previous high water mark is 154 days, which is larger, thus worse than the value of 35 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 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.