'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- Compared with the benchmark SPY (62.7%) in the period of the last 5 years, the total return, or performance of -2.3% of Vanguard Emerging Markets Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return, or performance is 1.4%, which is lower, thus worse than the value of 34.7% 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:- Looking at the compounded annual growth rate (CAGR) of -0.5% 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 (10.2%)
- Compared with SPY (10.5%) in the period of the last 3 years, the annual return (CAGR) of 0.5% is lower, thus worse.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 18.9% in the last 5 years of Vanguard Emerging Markets Stock Index Fund, we see it is relatively smaller, thus better in comparison to the benchmark SPY (20.9%)
- Looking at volatility in of 21.2% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (24.1%).

'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 risk over 5 years of Vanguard Emerging Markets Stock Index Fund is 14%, which is lower, thus better compared to the benchmark SPY (15.3%) in the same period.
- During the last 3 years, the downside risk is 15.8%, which is smaller, thus better than the value of 17.6% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the risk / return profile (Sharpe) of -0.16 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 (0.37)
- Compared with SPY (0.33) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.1 is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of -0.21 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 (0.51)
- Looking at excess return divided by the downside deviation in of -0.13 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.45).

'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 (7.71 ) in the period of the last 5 years, the Ulcer Ratio of 15 of Vanguard Emerging Markets Stock Index Fund is higher, thus worse.
- Looking at Ulcer Index in of 13 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (9.08 ).

'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.'

Which means for our asset as example:- The maximum reduction from previous high over 5 years of Vanguard Emerging Markets Stock Index Fund is -36.3 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -33.2 days in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (-33.7 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.'

Which means for our asset as example:- Looking at the maximum days under water of 706 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 (189 days)
- Looking at maximum days below previous high in of 411 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (189 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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 278 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 (46 days)
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 148 days is higher, thus worse.

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.