'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, or performance over 5 years of Vanguard Developed Markets Index Fund is 62.3%, which is lower, thus worse compared to the benchmark SPY (120.8%) in the same period.
- Looking at total return, or performance in of 24.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (66.3%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 10.2% in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (17.2%)
- Looking at compounded annual growth rate (CAGR) in of 7.7% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (18.5%).

'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:- The historical 30 days volatility over 5 years of Vanguard Developed Markets Index Fund is 17.1%, which is smaller, thus better compared to the benchmark SPY (18.7%) in the same period.
- Compared with SPY (22.4%) in the period of the last 3 years, the volatility of 19.8% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside deviation of 13% of Vanguard Developed Markets Index Fund is lower, thus better.
- Compared with SPY (16.3%) in the period of the last 3 years, the downside risk of 15% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.78) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.45 of Vanguard Developed Markets Index Fund is lower, thus worse.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.26, which is lower, thus worse than the value of 0.71 from the benchmark.

'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 (1.08) in the period of the last 5 years, the downside risk / excess return profile of 0.59 of Vanguard Developed Markets Index Fund is lower, thus worse.
- Compared with SPY (0.98) in the period of the last 3 years, the downside risk / excess return profile of 0.34 is lower, thus worse.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Which means for our asset as example:- Compared with the benchmark SPY (5.59 ) in the period of the last 5 years, the Ulcer Index of 8.97 of Vanguard Developed Markets Index Fund is larger, thus worse.
- During the last 3 years, the Ulcer Ratio is 9.2 , which is larger, thus worse than the value of 6.83 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:- The maximum DrawDown over 5 years of Vanguard Developed Markets Index Fund is -35.7 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum drop from peak to valley is -35.1 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'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'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 706 days in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum days below previous high is 398 days, which is higher, thus worse than the value of 139 days from the benchmark.

'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 time in days below previous high water mark of 226 days in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (33 days)
- Looking at average time in days below previous high water mark in of 143 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (35 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 Developed Markets 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.