'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:- Compared with the benchmark SPY (60.6%) in the period of the last 5 years, the total return of 9.2% of Vanguard Pacific Stock Index Fund is smaller, thus worse.
- During the last 3 years, the total return, or performance is 8.2%, which is lower, thus worse than the value of 38% 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 (10%) in the period of the last 5 years, the annual return (CAGR) of 1.8% of Vanguard Pacific Stock Index Fund is lower, thus worse.
- Compared with SPY (11.3%) in the period of the last 3 years, the annual return (CAGR) of 2.7% 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.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 17.8% in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (21.5%)
- Looking at historical 30 days volatility in of 15.4% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (17.9%).

'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 Pacific Stock Index Fund is 13%, which is smaller, thus better compared to the benchmark SPY (15.5%) in the same period.
- During the last 3 years, the downside deviation is 10.8%, which is lower, thus better than the value of 12.5% 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:- Compared with the benchmark SPY (0.35) in the period of the last 5 years, the Sharpe Ratio of -0.04 of Vanguard Pacific Stock Index Fund is lower, thus worse.
- Compared with SPY (0.49) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.01 is smaller, thus worse.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of -0.06 in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.48)
- During the last 3 years, the downside risk / excess return profile is 0.02, which is smaller, thus worse than the value of 0.71 from the benchmark.

'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 (9.55 ) in the period of the last 5 years, the Ulcer Ratio of 13 of Vanguard Pacific Stock Index Fund is greater, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 14 is greater, thus worse.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

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 DrawDown of -31.3 days of Vanguard Pacific Stock Index Fund is greater, thus better.
- Looking at maximum DrawDown in of -31.3 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (431 days) in the period of the last 5 years, the maximum days under water of 507 days of Vanguard Pacific Stock Index Fund is higher, thus worse.
- During the last 3 years, the maximum days below previous high is 507 days, which is larger, thus worse than the value of 431 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.'

Which means for our asset as example:- Looking at the average days below previous high of 160 days in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (105 days)
- Looking at average days under water in of 189 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (144 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 Pacific 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.