'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.'

Using this definition on our asset we see for example:- Looking at the total return, or increase in value of 12.7% 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 (68.1%)
- Looking at total return, or increase in value in of 28.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (47%).

'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:- Compared with the benchmark SPY (11%) in the period of the last 5 years, the annual return (CAGR) of 2.4% of Vanguard Total International Stock Index Fund is smaller, thus worse.
- Looking at annual return (CAGR) in of 8.7% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (13.7%).

'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.'

Using this definition on our asset we see for example:- The 30 days standard deviation over 5 years of Vanguard Total International Stock Index Fund is 18.4%, which is smaller, thus better compared to the benchmark SPY (21.4%) in the same period.
- Compared with SPY (18.7%) in the period of the last 3 years, the historical 30 days volatility of 16.2% is lower, 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 (15.4%) in the period of the last 5 years, the downside volatility of 13.6% of Vanguard Total International Stock Index Fund is lower, thus better.
- Looking at downside volatility in of 11.3% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (13.3%).

'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 ratio of return and volatility (Sharpe) over 5 years of Vanguard Total International Stock Index Fund is 0, which is smaller, thus worse compared to the benchmark SPY (0.4) in the same period.
- During the last 3 years, the risk / return profile (Sharpe) is 0.38, which is lower, thus worse than the value of 0.6 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:- Compared with the benchmark SPY (0.55) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.01 of Vanguard Total International Stock Index Fund is lower, thus worse.
- Compared with SPY (0.84) in the period of the last 3 years, the excess return divided by the downside deviation of 0.55 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.45 ) in the period of the last 5 years, the Downside risk index of 11 of Vanguard Total International Stock Index Fund is higher, thus worse.
- Looking at Downside risk index in of 12 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (10 ).

'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:- The maximum drop from peak to valley over 5 years of Vanguard Total International Stock Index Fund is -34.8 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 DrawDown of -29.6 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 time in days below previous high water mark of 492 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 (351 days)
- During the last 3 years, the maximum time in days below previous high water mark is 492 days, which is larger, thus worse than the value of 351 days from the benchmark.

'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:- Compared with the benchmark SPY (78 days) in the period of the last 5 years, the average days below previous high of 174 days of Vanguard Total International Stock Index Fund is higher, thus worse.
- Looking at average days below previous high in of 180 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (101 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 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.