'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 investmentâ€™s overall performance.'

Applying this definition to our asset in some examples:- Looking at the total return of 22% in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (102%)
- During the last 3 years, the total return, or increase in value is -7.1%, which is lower, thus worse than the value of 31.5% from the benchmark.

'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.'

Which means for our asset as example:- The annual performance (CAGR) over 5 years of Vanguard Emerging Markets Stock Index Fund is 4.1%, which is smaller, thus worse compared to the benchmark SPY (15.1%) in the same period.
- Looking at annual performance (CAGR) in of -2.4% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (9.6%).

'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:- The historical 30 days volatility over 5 years of Vanguard Emerging Markets Stock Index Fund is 18.4%, which is lower, thus better compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the historical 30 days volatility is 15.4%, which is lower, thus better than the value of 17.6% from the benchmark.

'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.'

Which means for our asset as example:- The downside risk over 5 years of Vanguard Emerging Markets Stock Index Fund is 13.5%, which is lower, thus better compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.4%) in the period of the last 3 years, the downside risk of 10.9% is lower, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.09 of Vanguard Emerging Markets Stock Index Fund is smaller, thus worse.
- Looking at Sharpe Ratio in of -0.32 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.4).

'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:- Looking at the downside risk / excess return profile of 0.12 in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.84)
- Compared with SPY (0.57) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.45 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:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 17 of Vanguard Emerging Markets Stock Index Fund is larger, thus worse.
- Looking at Ulcer Index in of 16 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'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 -34.3 days of Vanguard Emerging Markets Stock Index Fund is smaller, thus worse.
- Looking at maximum drop from peak to valley in of -30.1 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 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.'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 899 days in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (488 days)
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 728 days is higher, thus worse.

'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.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of Vanguard Emerging Markets Stock Index Fund is 352 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average time in days below previous high water mark in of 353 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (177 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.