'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of Viacom is -67.3%, which is lower, thus worse compared to the benchmark SPY (100.7%) in the same period.
- Compared with SPY (33.2%) in the period of the last 3 years, the total return, or increase in value of -33.7% is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of -20.1% of Viacom is smaller, thus worse.
- Compared with SPY (10%) in the period of the last 3 years, the annual return (CAGR) of -12.8% 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.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 34.9% in the last 5 years of Viacom, we see it is relatively larger, thus worse in comparison to the benchmark SPY (20.9%)
- During the last 3 years, the 30 days standard deviation is 32.4%, which is higher, thus worse than the value of 17.3% from the benchmark.

'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:- The downside deviation over 5 years of Viacom is 26.6%, which is higher, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 23.8% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12%).

'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:- The ratio of return and volatility (Sharpe) over 5 years of Viacom is -0.65, which is smaller, thus worse compared to the benchmark SPY (0.6) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is -0.47, which is lower, thus worse than the value of 0.44 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.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of Viacom is -0.85, which is lower, thus worse compared to the benchmark SPY (0.83) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is -0.64, which is lower, thus worse than the value of 0.62 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.'

Which means for our asset as example:- The Ulcer Ratio over 5 years of Viacom is 52 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 35 , which is greater, thus worse than the value of 10 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.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley of -72.4 days in the last 5 years of Viacom, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -54.5 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 1245 days of Viacom is higher, thus worse.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 674 days is greater, 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:- Looking at the average days under water of 618 days in the last 5 years of Viacom, we see it is relatively larger, thus worse in comparison to the benchmark SPY (123 days)
- During the last 3 years, the average time in days below previous high water mark is 310 days, which is higher, 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 Viacom are hypothetical and do not account for slippage, fees or taxes.