'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (120.7%) in the period of the last 5 years, the total return, or performance of 72.7% of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return, or performance is 15%, which is lower, thus worse than the value of 44% from the benchmark.

'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 (17.2%) in the period of the last 5 years, the annual return (CAGR) of 11.5% of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is 4.8%, which is lower, thus worse than the value of 12.9% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (18.8%) in the period of the last 5 years, the historical 30 days volatility of 17% of Vanguard Total International Stock Index Fund is lower, thus better.
- Compared with SPY (22.8%) in the period of the last 3 years, the volatility of 19.4% is smaller, thus better.

'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:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside deviation of 12.8% of Vanguard Total International Stock Index Fund is smaller, thus better.
- Looking at downside deviation in of 14.9% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (16.7%).

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- The Sharpe Ratio over 5 years of Vanguard Total International Stock Index Fund is 0.53, which is lower, thus worse compared to the benchmark SPY (0.78) in the same period.
- Looking at Sharpe Ratio in of 0.12 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.46).

'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.'

Using this definition on our asset we see for example:- The downside risk / excess return profile over 5 years of Vanguard Total International Stock Index Fund is 0.7, which is lower, thus worse compared to the benchmark SPY (1.08) in the same period.
- Compared with SPY (0.62) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.15 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.'

Which means for our asset as example:- Compared with the benchmark SPY (5.59 ) in the period of the last 5 years, the Ulcer Index of 9.61 of Vanguard Total International Stock Index Fund is greater, thus worse.
- Looking at Ulcer Ratio in of 12 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (7.15 ).

'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.'

Which means for our asset as example:- Looking at the maximum drop from peak to valley of -35.9 days 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 (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -35.9 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'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.'

Which means for our asset as example:- The maximum days under water over 5 years of Vanguard Total International Stock Index Fund is 706 days, which is greater, thus worse compared to the benchmark SPY (139 days) in the same period.
- Looking at maximum time in days below previous high water mark in of 706 days in the period of the last 3 years, we see it is relatively higher, 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.'

Using this definition on our asset we see for example:- Looking at the average days below previous high of 226 days in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (33 days)
- During the last 3 years, the average time in days below previous high water mark is 343 days, which is larger, thus worse than the value of 45 days from the benchmark.

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 Total International 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.