'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of Vanguard Value Index Fund is 27.7%, which is lower, thus worse compared to the benchmark SPY (46.1%) in the same period.
- Compared with SPY (23.5%) in the period of the last 3 years, the total return, or performance of 7.3% is lower, 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:- Compared with the benchmark SPY (7.9%) in the period of the last 5 years, the annual return (CAGR) of 5% of Vanguard Value Index Fund is lower, thus worse.
- Looking at compounded annual growth rate (CAGR) in of 2.4% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (7.3%).

'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:- The 30 days standard deviation over 5 years of Vanguard Value Index Fund is 18.3%, which is larger, thus worse compared to the benchmark SPY (18.3%) in the same period.
- Looking at 30 days standard deviation in of 20.9% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (20.8%).

'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 volatility over 5 years of Vanguard Value Index Fund is 13.4%, which is larger, thus worse compared to the benchmark SPY (13.4%) in the same period.
- Compared with SPY (15.4%) in the period of the last 3 years, the downside deviation of 15.5% is higher, thus worse.

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.14 in the last 5 years of Vanguard Value Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.29)
- Looking at risk / return profile (Sharpe) in of -0.01 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.23).

'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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Vanguard Value Index Fund is 0.19, which is lower, thus worse compared to the benchmark SPY (0.4) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is -0.01, which is lower, thus worse than the value of 0.31 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.'

Using this definition on our asset we see for example:- Looking at the Ulcer Ratio of 5.66 in the last 5 years of Vanguard Value Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.27 )
- During the last 3 years, the Ulcer Index is 6.41 , which is larger, thus worse than the value of 6.08 from the benchmark.

'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:- The maximum DrawDown over 5 years of Vanguard Value Index Fund is -36.8 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 -36.8 days in the period of the last 3 years, we see it is relatively smaller, thus worse 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:- The maximum days under water over 5 years of Vanguard Value Index Fund is 228 days, which is larger, thus worse compared to the benchmark SPY (187 days) in the same period.
- During the last 3 years, the maximum days below previous high is 162 days, which is greater, 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:- Compared with the benchmark SPY (42 days) in the period of the last 5 years, the average days below previous high of 55 days of Vanguard Value Index Fund is larger, thus worse.
- Compared with SPY (36 days) in the period of the last 3 years, the average days under water of 46 days is larger, 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 Value 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.