'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:- Looking at the total return, or increase in value of 90.8% in the last 5 years of Boeing, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (122.1%)
- During the last 3 years, the total return, or performance is -33.3%, which is smaller, thus worse than the value of 64.6% from the benchmark.

'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:- Compared with the benchmark SPY (17.3%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 13.8% of Boeing is lower, thus worse.
- Compared with SPY (18.1%) in the period of the last 3 years, the annual return (CAGR) of -12.6% is lower, thus worse.

'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:- Looking at the historical 30 days volatility of 46.3% in the last 5 years of Boeing, we see it is relatively larger, thus worse in comparison to the benchmark SPY (18.7%)
- During the last 3 years, the 30 days standard deviation is 57%, which is higher, thus worse than the value of 22.5% from the benchmark.

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

Using this definition on our asset we see for example:- The downside volatility over 5 years of Boeing is 31.1%, which is greater, thus worse compared to the benchmark SPY (13.6%) in the same period.
- During the last 3 years, the downside deviation is 38.7%, which is larger, thus worse than the value of 16.4% from the benchmark.

'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:- Compared with the benchmark SPY (0.79) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.24 of Boeing is smaller, thus worse.
- Compared with SPY (0.69) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.27 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.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of Boeing is 0.36, which is smaller, thus worse compared to the benchmark SPY (1.09) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is -0.39, which is lower, thus worse than the value of 0.95 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of Boeing is 31 , which is greater, thus worse compared to the benchmark SPY (5.58 ) in the same period.
- During the last 3 years, the Ulcer Index is 40 , which is greater, thus worse than the value of 6.83 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.'

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 drop from peak to valley of -77.9 days of Boeing is smaller, thus worse.
- Looking at maximum DrawDown in of -77.9 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days below previous high of 607 days of Boeing is higher, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 607 days is larger, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days below previous high of 173 days of Boeing is higher, thus worse.
- Compared with SPY (35 days) in the period of the last 3 years, the average days below previous high of 256 days is greater, 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 Boeing 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.