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.'

Which means for our asset as example:- Compared with the benchmark SPY (91.2%) in the period of the last 5 years, the total return of 23.6% of Vanguard European Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return, or performance is -0.7%, which is lower, thus worse than the value of 41.5% 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:- Compared with the benchmark SPY (13.8%) in the period of the last 5 years, the annual return (CAGR) of 4.3% of Vanguard European Stock Index Fund is smaller, thus worse.
- During the last 3 years, the annual performance (CAGR) is -0.2%, which is smaller, thus worse than the value of 12.3% 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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 19.2% 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 (18.8%)
- During the last 3 years, the historical 30 days volatility is 21%, which is lower, thus better than the value of 22.4% from the benchmark.

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

Which means for our asset as example:- The downside volatility over 5 years of Vanguard European Stock Index Fund is 14.7%, which is larger, thus worse compared to the benchmark SPY (13.7%) in the same period.
- Compared with SPY (16.5%) in the period of the last 3 years, the downside volatility of 16.2% is smaller, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.1 of Vanguard European Stock Index Fund is lower, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.13 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.44).

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

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 0.12, which is smaller, thus worse compared to the benchmark SPY (0.83) in the same period.
- Looking at excess return divided by the downside deviation in of -0.17 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.59).

'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 Index over 5 years of Vanguard European Stock Index Fund is 9.94 , which is greater, thus worse compared to the benchmark SPY (5.79 ) in the same period.
- Looking at Downside risk index in of 12 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (7.09 ).

'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.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley 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)
- 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'

Which means for our asset as example:- The maximum days under water over 5 years of Vanguard European Stock Index Fund is 672 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Looking at maximum days under water in of 672 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (139 days).

'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 time in days below previous high water mark of 242 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 (37 days)
- Looking at average days under water in of 311 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (45 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.