'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (57.1%) in the period of the last 5 years, the total return of 16.7% of Vanguard European Stock Index Fund is lower, thus worse.
- Compared with SPY (32%) in the period of the last 3 years, the total return, or performance of 17.1% is smaller, thus worse.

'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:- Compared with the benchmark SPY (9.5%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 3.1% of Vanguard European Stock Index Fund is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is 5.4%, which is smaller, thus worse than the value of 9.7% from the benchmark.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the 30 days standard deviation of 21.2% of Vanguard European Stock Index Fund is smaller, thus better.
- Compared with SPY (17.9%) in the period of the last 3 years, the 30 days standard deviation of 18.8% is greater, thus worse.

'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 (15.5%) in the period of the last 5 years, the downside deviation of 15.6% of Vanguard European Stock Index Fund is larger, thus worse.
- During the last 3 years, the downside risk is 13%, which is greater, thus worse than the value of 12.5% from the benchmark.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Applying this definition to our asset in some examples:- Looking at the risk / return profile (Sharpe) of 0.03 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 (0.32)
- Looking at Sharpe Ratio in of 0.16 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.41).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.45) in the period of the last 5 years, the downside risk / excess return profile of 0.04 of Vanguard European Stock Index Fund is lower, thus worse.
- Compared with SPY (0.58) in the period of the last 3 years, the downside risk / excess return profile of 0.23 is lower, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (9.57 ) in the period of the last 5 years, the Downside risk index of 12 of Vanguard European Stock Index Fund is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 12 is higher, 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.'

Applying this definition to our asset in some examples:- The maximum reduction from previous high 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 DrawDown in of -32.8 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 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). 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:- The maximum days below previous high over 5 years of Vanguard European Stock Index Fund is 523 days, which is larger, thus worse compared to the benchmark SPY (439 days) in the same period.
- During the last 3 years, the maximum days below previous high is 523 days, which is larger, thus worse than the value of 439 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:- Compared with the benchmark SPY (106 days) in the period of the last 5 years, the average days under water of 148 days of Vanguard European Stock Index Fund is larger, thus worse.
- Compared with SPY (149 days) in the period of the last 3 years, the average time in days below previous high water mark of 201 days is larger, thus worse.

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.