'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 investment’s overall performance.'

Applying this definition to our asset in some examples:- The total return, or increase in value over 5 years of Vanguard Value Index Fund is 72.1%, which is lower, thus worse compared to the benchmark SPY (98.3%) in the same period.
- Compared with SPY (27.2%) in the period of the last 3 years, the total return of 30.2% is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- The compounded annual growth rate (CAGR) over 5 years of Vanguard Value Index Fund is 11.5%, which is lower, thus worse compared to the benchmark SPY (14.7%) in the same period.
- Compared with SPY (8.4%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 9.2% is larger, thus better.

'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:- Looking at the historical 30 days volatility of 20.1% in the last 5 years of Vanguard Value Index Fund, we see it is relatively smaller, thus better in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.7%) in the period of the last 3 years, the volatility of 14.4% 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:- The downside deviation over 5 years of Vanguard Value Index Fund is 14.3%, which is lower, thus better compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside deviation in of 10.1% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (12.4%).

'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.'

Applying this definition to our asset in some examples:- Looking at the Sharpe Ratio of 0.45 in the last 5 years of Vanguard Value Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.58)
- Compared with SPY (0.33) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.47 is higher, thus better.

'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:- Looking at the ratio of annual return and downside deviation of 0.63 in the last 5 years of Vanguard Value Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.82)
- During the last 3 years, the downside risk / excess return profile is 0.67, which is higher, thus better than the value of 0.47 from the benchmark.

'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:- The Ulcer Index over 5 years of Vanguard Value Index Fund is 7.59 , which is smaller, thus better compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 5.45 , which is lower, thus better than the value of 10 from the benchmark.

'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.'

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 drop from peak to valley of -36.8 days of Vanguard Value 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 -17.2 days is greater, thus better.

'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 under water over 5 years of Vanguard Value Index Fund is 313 days, which is lower, thus better compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum days below previous high is 313 days, which is smaller, thus better than the value of 488 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 76 days of Vanguard Value Index Fund is smaller, thus better.
- During the last 3 years, the average time in days below previous high water mark is 85 days, which is lower, thus better than the value of 177 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 Value Index Fund are hypothetical and do not account for slippage, fees or taxes.