'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 over 5 years of Vanguard Pacific Stock Index Fund is 23.7%, which is smaller, thus worse compared to the benchmark SPY (77.4%) in the same period.
- Compared with SPY (43.3%) in the period of the last 3 years, the total return of 5% is smaller, thus worse.

'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 Pacific Stock Index Fund is 4.3%, which is lower, thus worse compared to the benchmark SPY (12.1%) in the same period.
- Looking at annual return (CAGR) in of 1.6% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (12.7%).

'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:- Compared with the benchmark SPY (19%) in the period of the last 5 years, the historical 30 days volatility of 17% of Vanguard Pacific Stock Index Fund is lower, thus better.
- Looking at historical 30 days volatility in of 18.1% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (22%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- The downside volatility over 5 years of Vanguard Pacific Stock Index Fund is 12.5%, which is lower, thus better compared to the benchmark SPY (13.9%) in the same period.
- Looking at downside volatility in of 13.7% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (16.2%).

'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:- Compared with the benchmark SPY (0.51) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.11 of Vanguard Pacific Stock Index Fund is lower, thus worse.
- During the last 3 years, the Sharpe Ratio is -0.05, which is smaller, thus worse than the value of 0.46 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Using this definition on our asset we see for example:- Looking at the ratio of annual return and downside deviation of 0.15 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 (0.7)
- During the last 3 years, the ratio of annual return and downside deviation is -0.06, which is smaller, thus worse than the value of 0.63 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.'

Which means for our asset as example:- Looking at the Downside risk index of 10 in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.87 )
- During the last 3 years, the Ulcer Index is 12 , which is greater, thus worse than the value of 7.01 from the benchmark.

'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:- Looking at the maximum DrawDown of -33.9 days 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 (-33.7 days)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum reduction from previous high of -33.9 days is smaller, thus worse.

'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 below previous high over 5 years of Vanguard Pacific Stock Index Fund is 637 days, which is larger, thus worse compared to the benchmark SPY (139 days) in the same period.
- Looking at maximum days below previous high in of 637 days in the period of the last 3 years, we see it is relatively larger, 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.'

Which means for our asset as example:- Looking at the average days below previous high of 205 days in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (37 days)
- During the last 3 years, the average days below previous high is 284 days, which is higher, 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 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.