'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 (100.7%) in the period of the last 5 years, the total return of 29% of Vanguard Emerging Markets Stock Index Fund is lower, thus worse.
- Compared with SPY (33.2%) in the period of the last 3 years, the total return of -4.8% is smaller, thus worse.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of Vanguard Emerging Markets Stock Index Fund is 5.2%, which is lower, thus worse compared to the benchmark SPY (15%) in the same period.
- During the last 3 years, the annual performance (CAGR) is -1.6%, which is lower, thus worse than the value of 10% 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 (20.9%) in the period of the last 5 years, the volatility of 18.4% of Vanguard Emerging Markets Stock Index Fund is lower, thus better.
- Compared with SPY (17.3%) in the period of the last 3 years, the historical 30 days volatility of 15.5% 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.'

Applying this definition to our asset in some examples:- Looking at the downside risk of 13.5% in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (15%)
- Looking at downside risk in of 10.9% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (12%).

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of Vanguard Emerging Markets Stock Index Fund is 0.15, which is smaller, thus worse compared to the benchmark SPY (0.6) in the same period.
- Compared with SPY (0.44) in the period of the last 3 years, the Sharpe Ratio of -0.27 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.83) in the period of the last 5 years, the excess return divided by the downside deviation of 0.2 of Vanguard Emerging Markets Stock Index Fund is lower, thus worse.
- Looking at downside risk / excess return profile in of -0.38 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.62).

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of Vanguard Emerging Markets Stock Index Fund is 17 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 19 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

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 reduction from previous high of -34.3 days of Vanguard Emerging Markets Stock Index Fund is smaller, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -32.7 days is lower, 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). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- The maximum days below previous high over 5 years of Vanguard Emerging Markets Stock Index Fund is 818 days, which is larger, thus worse compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum days under water is 745 days, which is higher, thus worse than the value of 488 days from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 297 days of Vanguard Emerging Markets Stock Index Fund is greater, thus worse.
- Looking at average time in days below previous high water mark in of 372 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (180 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 Emerging Markets Stock Index Fund are hypothetical and do not account for slippage, fees or taxes.