'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:- The total return, or increase in value over 5 years of Vanguard Total International Stock Index Fund is 32%, which is lower, thus worse compared to the benchmark SPY (109.2%) in the same period.
- Looking at total return in of 3.3% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (33.3%).

'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.'

Which means for our asset as example:- Looking at the compounded annual growth rate (CAGR) of 5.7% in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (15.9%)
- Compared with SPY (10.1%) in the period of the last 3 years, the annual performance (CAGR) of 1.1% 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.'

Applying this definition to our asset in some examples:- Looking at the historical 30 days volatility of 18.4% in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (20.9%)
- Looking at 30 days standard deviation in of 15.4% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (17.6%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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 (14.9%) in the period of the last 5 years, the downside risk of 13.5% of Vanguard Total International Stock Index Fund is lower, thus better.
- During the last 3 years, the downside volatility is 10.6%, which is lower, thus better than the value of 12.3% from the benchmark.

'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:- Looking at the risk / return profile (Sharpe) of 0.17 in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.64)
- Compared with SPY (0.43) in the period of the last 3 years, the Sharpe Ratio of -0.09 is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of Vanguard Total International Stock Index Fund is 0.24, which is smaller, thus worse compared to the benchmark SPY (0.9) in the same period.
- Compared with SPY (0.62) in the period of the last 3 years, the downside risk / excess return profile of -0.13 is smaller, thus worse.

'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 Ulcer Ratio of 12 of Vanguard Total International Stock Index Fund is greater, thus worse.
- During the last 3 years, the Downside risk index is 12 , which is higher, thus worse than the value of 10 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -34.8 days of Vanguard Total International Stock Index Fund is lower, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -28.9 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:- Looking at the maximum days under water of 734 days in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 628 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.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 248 days of Vanguard Total International Stock Index Fund is larger, thus worse.
- Compared with SPY (176 days) in the period of the last 3 years, the average days below previous high of 269 days is greater, thus worse.

Historical returns have been extended using synthetic data.
[Show Details]

- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of Vanguard Total International Stock Index Fund are hypothetical and do not account for slippage, fees or taxes.