'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.'

Using this definition on our asset we see for example:- Looking at the total return, or performance of 59% in the last 5 years of SPDR Gold Trust, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (97.7%)
- Compared with SPY (26%) in the period of the last 3 years, the total return, or performance of 38.9% is greater, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the compounded annual growth rate (CAGR) of 9.7% in the last 5 years of SPDR Gold Trust, we see it is relatively lower, thus worse in comparison to the benchmark SPY (14.6%)
- Compared with SPY (8%) in the period of the last 3 years, the annual performance (CAGR) of 11.6% is greater, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 15.3% of SPDR Gold Trust is lower, thus better.
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 14.2% is lower, thus better.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- The downside deviation over 5 years of SPDR Gold Trust is 10.8%, which is lower, thus better compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 9.6% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (12.3%).

'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 (0.58) in the period of the last 5 years, the Sharpe Ratio of 0.47 of SPDR Gold Trust is smaller, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is 0.64, which is larger, thus better than the value of 0.32 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.81) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.67 of SPDR Gold Trust is lower, thus worse.
- Looking at ratio of annual return and downside deviation in of 0.95 in the period of the last 3 years, we see it is relatively greater, thus better 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 (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 9.8 of SPDR Gold Trust is higher, thus worse.
- During the last 3 years, the Ulcer Ratio is 8.26 , which is smaller, thus better than the value of 10 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.'

Applying this definition to our asset in some examples:- Looking at the maximum drop from peak to valley of -22 days in the last 5 years of SPDR Gold Trust, we see it is relatively higher, thus better in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum reduction from previous high of -21 days is larger, 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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days under water of 897 days of SPDR Gold Trust is larger, thus worse.
- During the last 3 years, the maximum days below previous high is 436 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 344 days of SPDR Gold Trust is higher, thus worse.
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 142 days is smaller, thus better.

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 SPDR Gold Trust are hypothetical and do not account for slippage, fees or taxes.