'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:- Compared with the benchmark SPY (68.1%) in the period of the last 5 years, the total return, or performance of 1.4% of Vanguard Emerging Markets Stock Index Fund is smaller, thus worse.
- Looking at total return, or increase in value in of 17.1% in the period of the last 3 years, we see it is relatively lower, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (11%) in the period of the last 5 years, the annual performance (CAGR) of 0.3% of Vanguard Emerging Markets Stock Index Fund is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is 5.4%, which is lower, thus worse than the value of 13.7% 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.'

Which means for our asset as example:- Compared with the benchmark SPY (21.4%) in the period of the last 5 years, the 30 days standard deviation of 19.1% of Vanguard Emerging Markets Stock Index Fund is lower, thus better.
- Compared with SPY (18.7%) in the period of the last 3 years, the 30 days standard deviation of 17.3% is lower, thus better.

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

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 14.1% of Vanguard Emerging Markets Stock Index Fund is smaller, thus better.
- Compared with SPY (13.3%) in the period of the last 3 years, the downside deviation of 12% is smaller, 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.'

Applying this definition to our asset in some examples:- The risk / return profile (Sharpe) over 5 years of Vanguard Emerging Markets Stock Index Fund is -0.12, which is lower, thus worse compared to the benchmark SPY (0.4) in the same period.
- Compared with SPY (0.6) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.17 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.'

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 -0.16 of Vanguard Emerging Markets Stock Index Fund is smaller, thus worse.
- Looking at downside risk / excess return profile in of 0.24 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.84).

'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.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Vanguard Emerging Markets Stock Index Fund is 15 , which is higher, thus worse compared to the benchmark SPY (9.45 ) in the same period.
- During the last 3 years, the Ulcer Index is 16 , which is larger, thus worse than the value of 10 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:- The maximum DrawDown over 5 years of Vanguard Emerging Markets Stock Index Fund is -34.3 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 reduction from previous high of -34.3 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.'

Applying this definition to our asset in some examples:- The maximum days below previous high over 5 years of Vanguard Emerging Markets Stock Index Fund is 573 days, which is greater, thus worse compared to the benchmark SPY (351 days) in the same period.
- Looking at maximum days under water in of 573 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (351 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 under water of 211 days in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (78 days)
- During the last 3 years, the average days below previous high is 236 days, which is greater, thus worse than the value of 101 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 Emerging Markets 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.