'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Which means for our asset as example:- The total return, or increase in value over 5 years of Travelers is 82%, which is lower, thus worse compared to the benchmark SPY (102%) in the same period.
- Looking at total return, or increase in value in of 59.5% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (31.5%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15.1%) in the period of the last 5 years, the annual return (CAGR) of 12.7% of Travelers is lower, thus worse.
- Compared with SPY (9.6%) in the period of the last 3 years, the annual performance (CAGR) of 16.9% is greater, thus better.

'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.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 29% in the last 5 years of Travelers, we see it is relatively higher, thus worse in comparison to the benchmark SPY (20.9%)
- Looking at volatility in of 21.9% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.6%).

'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.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of Travelers is 21.5%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside risk in of 15.3% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12.4%).

'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.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.35 in the last 5 years of Travelers, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.6)
- Compared with SPY (0.4) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.65 is higher, thus better.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Travelers is 0.48, which is smaller, thus worse compared to the benchmark SPY (0.84) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is 0.94, which is higher, thus better than the value of 0.57 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:- Looking at the Ulcer Index of 12 in the last 5 years of Travelers, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- During the last 3 years, the Downside risk index is 8.16 , which is smaller, thus better than the value of 10 from the benchmark.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- The maximum reduction from previous high over 5 years of Travelers is -44.4 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum drop from peak to valley in of -18.9 days in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (-24.5 days).

'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). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- The maximum time in days below previous high water mark over 5 years of Travelers is 328 days, which is smaller, thus better compared to the benchmark SPY (488 days) in the same period.
- Looking at maximum days under water in of 240 days in the period of the last 3 years, we see it is relatively lower, thus better 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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of Travelers is 91 days, which is smaller, thus better compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average days under water is 71 days, which is lower, thus better than the value of 177 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 Travelers are hypothetical and do not account for slippage, fees or taxes.