'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, or increase in value of 67.7% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (133.2%)
- Looking at total return, or performance in of 46.3% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (80.4%).

'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.'

Which means for our asset as example:- The compounded annual growth rate (CAGR) over 5 years of Vanguard European Stock Index Fund is 10.9%, which is lower, thus worse compared to the benchmark SPY (18.5%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 13.5% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (21.8%).

'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 30 days standard deviation of 18.1% of Vanguard European Stock Index Fund is smaller, thus better.
- Compared with SPY (22.4%) in the period of the last 3 years, the historical 30 days volatility of 21.5% is smaller, thus better.

'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.'

Using this definition on our asset we see for example:- Looking at the downside risk of 13.6% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.6%)
- Looking at downside deviation in of 16.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.2%).

'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:- The risk / return profile (Sharpe) over 5 years of Vanguard European Stock Index Fund is 0.47, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Looking at Sharpe Ratio in of 0.51 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.86).

'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:- Compared with the benchmark SPY (1.18) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.62 of Vanguard European Stock Index Fund is smaller, thus worse.
- During the last 3 years, the ratio of annual return and downside deviation is 0.68, which is lower, thus worse than the value of 1.19 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The Ulcer Ratio over 5 years of Vanguard European Stock Index Fund is 9.4 , which is greater, thus worse compared to the benchmark SPY (5.59 ) in the same period.
- Compared with SPY (6.36 ) in the period of the last 3 years, the Ulcer Index of 8.38 is larger, thus worse.

'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:- Looking at the maximum reduction from previous high of -37 days 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 (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -36.6 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Using this definition on our asset we see for example:- The maximum days under water over 5 years of Vanguard European Stock Index Fund is 712 days, which is greater, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (119 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 215 days is higher, 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.'

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 229 days of Vanguard European Stock Index Fund is larger, thus worse.
- Looking at average time in days below previous high water mark in of 49 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (25 days).

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.