'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:- The total return over 5 years of Vanguard Real Estate Index Fund is 15.4%, which is lower, thus worse compared to the benchmark SPY (100.7%) in the same period.
- Looking at total return, or performance in of -2.8% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (33.2%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- The compounded annual growth rate (CAGR) over 5 years of Vanguard Real Estate Index Fund is 2.9%, which is smaller, thus worse compared to the benchmark SPY (15%) in the same period.
- Compared with SPY (10%) in the period of the last 3 years, the annual return (CAGR) of -0.9% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The volatility over 5 years of Vanguard Real Estate Index Fund is 25.6%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at historical 30 days volatility in of 20.6% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.3%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the downside deviation of 18.8% of Vanguard Real Estate Index Fund is greater, thus worse.
- Compared with SPY (12%) in the period of the last 3 years, the downside risk of 14.5% is larger, thus worse.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the Sharpe Ratio of 0.02 of Vanguard Real Estate Index Fund is lower, thus worse.
- Looking at Sharpe Ratio in of -0.17 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.44).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.83) in the period of the last 5 years, the excess return divided by the downside deviation of 0.02 of Vanguard Real Estate Index Fund is lower, thus worse.
- Compared with SPY (0.62) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.24 is smaller, 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.'

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 Ratio of 18 of Vanguard Real Estate Index Fund is greater, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 20 is higher, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -42.3 days of Vanguard Real Estate Index Fund is lower, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -34.6 days is smaller, thus worse.

'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 under water of 597 days in the last 5 years of Vanguard Real Estate Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum time in days below previous high water mark in of 597 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (488 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 time in days below previous high water mark of 189 days in the last 5 years of Vanguard Real Estate Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (123 days)
- During the last 3 years, the average days below previous high is 249 days, which is larger, thus worse than the value of 180 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 Real Estate Index Fund are hypothetical and do not account for slippage, fees or taxes.