'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:- Compared with the benchmark SPY (78.4%) in the period of the last 5 years, the total return, or increase in value of 56% of Goldman Sachs Group is lower, thus worse.
- Looking at total return in of 65.7% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (44.1%).

'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:- Compared with the benchmark SPY (12.3%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 9.3% of Goldman Sachs Group is lower, thus worse.
- During the last 3 years, the compounded annual growth rate (CAGR) is 18.3%, which is larger, thus better than the value of 12.9% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 32.1% in the last 5 years of Goldman Sachs Group, we see it is relatively larger, thus worse in comparison to the benchmark SPY (19.9%)
- Looking at 30 days standard deviation in of 36.6% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (23.1%).

'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:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside volatility of 22.1% of Goldman Sachs Group is larger, thus worse.
- Looking at downside volatility in of 25% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.9%).

'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 (0.49) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.21 of Goldman Sachs Group is smaller, thus worse.
- Compared with SPY (0.45) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.43 is smaller, thus worse.

'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.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of 0.31 in the last 5 years of Goldman Sachs Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.67)
- Compared with SPY (0.62) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.63 is higher, thus better.

'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.'

Which means for our asset as example:- Looking at the Downside risk index of 18 in the last 5 years of Goldman Sachs Group, we see it is relatively higher, thus worse in comparison to the benchmark SPY (6.16 )
- Compared with SPY (6.87 ) in the period of the last 3 years, the Downside risk index of 14 is greater, thus worse.

'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 reduction from previous high of -48.7 days in the last 5 years of Goldman Sachs Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum DrawDown in of -45.6 days in the period of the last 3 years, we see it is relatively lower, 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.'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of Goldman Sachs Group is 704 days, which is larger, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (119 days) in the period of the last 3 years, the maximum days below previous high of 227 days is greater, thus worse.

'The Average 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. 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:- The average days under water over 5 years of Goldman Sachs Group is 220 days, which is larger, thus worse compared to the benchmark SPY (35 days) in the same period.
- Compared with SPY (27 days) in the period of the last 3 years, the average days under water of 60 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 Goldman Sachs Group 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.