'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:- Looking at the total return, or performance of 44.6% 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 (103.3%)
- Compared with SPY (37.7%) in the period of the last 3 years, the total return of 11.1% 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:- The compounded annual growth rate (CAGR) over 5 years of Vanguard European Stock Index Fund is 7.7%, which is smaller, thus worse compared to the benchmark SPY (15.3%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 3.6%, which is smaller, thus worse than the value of 11.3% from the benchmark.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of Vanguard European Stock Index Fund is 21%, which is greater, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the 30 days standard deviation is 18.3%, which is higher, thus worse than the value of 17.3% 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 volatility of 15.4% 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 (14.9%)
- Looking at downside deviation in of 12.6% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the Sharpe Ratio of 0.25 of Vanguard European Stock Index Fund is lower, thus worse.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.06, which is smaller, thus worse than the value of 0.51 from the benchmark.

'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:- Looking at the ratio of annual return and downside deviation of 0.34 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 (0.85)
- Looking at excess return divided by the downside deviation in of 0.09 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.73).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Downside risk index of 11 of Vanguard European Stock Index Fund is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 12 is greater, thus worse.

'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 DrawDown 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.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -32.8 days is smaller, 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) in days.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 619 days of Vanguard European Stock Index Fund is higher, thus worse.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 619 days is greater, 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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of Vanguard European Stock Index Fund is 190 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (181 days) in the period of the last 3 years, the average days under water of 266 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 and do not account for slippage, fees or taxes.