'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Which means for our asset as example:- Compared with the benchmark SPY (78.4%) in the period of the last 5 years, the total return, or performance of 20.9% of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return is 16.9%, which is lower, thus worse than the value of 44.1% 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:- The annual return (CAGR) over 5 years of Vanguard Total International Stock Index Fund is 3.9%, which is lower, thus worse compared to the benchmark SPY (12.3%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 5.3%, which is smaller, thus worse than the value of 12.9% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (19.9%) in the period of the last 5 years, the volatility of 17.2% of Vanguard Total International Stock Index Fund is lower, thus better.
- During the last 3 years, the 30 days standard deviation is 20.1%, which is lower, thus better than the value of 23.1% from the benchmark.

'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:- The downside volatility over 5 years of Vanguard Total International Stock Index Fund is 13%, which is lower, thus better compared to the benchmark SPY (14.6%) in the same period.
- Compared with SPY (16.9%) in the period of the last 3 years, the downside volatility of 15.2% is lower, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.49) in the period of the last 5 years, the Sharpe Ratio of 0.08 of Vanguard Total International Stock Index Fund is lower, thus worse.
- Compared with SPY (0.45) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.14 is lower, 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.'

Which means for our asset as example:- The downside risk / excess return profile over 5 years of Vanguard Total International Stock Index Fund is 0.11, which is lower, thus worse compared to the benchmark SPY (0.67) in the same period.
- Compared with SPY (0.62) in the period of the last 3 years, the excess return divided by the downside deviation of 0.19 is smaller, thus worse.

'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:- Looking at the Downside risk index of 10 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 (6.16 )
- During the last 3 years, the Ulcer Index is 8.48 , which is larger, thus worse than the value of 6.87 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -35.9 days of Vanguard Total International Stock Index Fund is smaller, thus worse.
- Looking at maximum reduction from previous high in of -34.8 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 Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

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 days below previous high in of 237 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (119 days).

'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.'

Applying this definition to our asset in some examples:- Looking at the average days below previous high of 242 days in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (35 days)
- During the last 3 years, the average days below previous high is 79 days, which is larger, thus worse than the value of 27 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.