Vanguard European Stock Index Fund Investor Shares

'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:- The total return, or performance over 5 years of Vanguard European Stock Index Fund is 9.4%, which is lower, thus worse compared to the benchmark SPY (66.2%) in the same period.
- During the last 3 years, the total return, or performance is 1.8%, which is lower, thus worse than the value of 36.8% from the benchmark.

'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 Vanguard European Stock Index Fund is 1.8%, which is lower, thus worse compared to the benchmark SPY (10.7%) in the same period.
- Compared with SPY (11%) in the period of the last 3 years, the annual return (CAGR) of 0.6% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (19%) in the period of the last 5 years, the historical 30 days volatility of 19.3% of Vanguard European Stock Index Fund is larger, thus worse.
- During the last 3 years, the volatility is 20.5%, which is lower, thus better than the value of 22% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.9%) in the period of the last 5 years, the downside risk of 14.9% of Vanguard European Stock Index Fund is higher, thus worse.
- Compared with SPY (16.1%) in the period of the last 3 years, the downside deviation of 15.9% is lower, thus better.

'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.'

Which means for our asset as example:- Looking at the ratio of return and volatility (Sharpe) of -0.04 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 (0.43)
- Looking at Sharpe Ratio in of -0.09 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.39).

'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.'

Applying this definition to our asset in some examples:- Looking at the ratio of annual return and downside deviation of -0.05 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 (0.59)
- During the last 3 years, the ratio of annual return and downside deviation is -0.12, which is smaller, thus worse than the value of 0.53 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 11 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 (5.9 )
- During the last 3 years, the Downside risk index is 12 , which is larger, thus worse than the value of 6.98 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- 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 lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum drop from peak to valley in of -37 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). 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:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days below previous high of 612 days of Vanguard European Stock Index Fund is larger, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days below previous high of 612 days is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the average days under water of 240 days 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 (44 days)
- Compared with SPY (41 days) in the period of the last 3 years, the average time in days below previous high water mark of 265 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.