Buy Amazon or Walmart on this Cyber Monday?

What woud you say is a better Investment this Cyber Monday, Amazon or Walmart? Here are some statistical calculations using stock prices and returns. First the definitions of the screen output.

β

Beta (Β) is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns.

BMrk α

Benchmark Alpha (α), often considered the active return on an investment, gauges the performance of an investment against a market index used as a benchmark, since they are often considered to represent the market’s movement as a whole. The excess returns of a fund relative to the return of a benchmark index is the fund's alpha.

CAPM α

CAPM Alpha (α) is determined by the difference between how much a security, or portfolio, should be returning according to the Capital Asset Pricing Model (CAPM) vs the actual security or portfolio. This is sometimes referred to as Jensen's Alpha.

CAPM Price

The expected price of the underlying stock using the Capital Asset Pricing Model. It uses the S&P 500 benchmark from the start of the year to the current day, and the CAPM calculated expected return (CAPM RoR).

CAPM RoR

The expected return of the stock using the CAPM, or Capital Asset Pricing Model, for the calculation. The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The risk-free rate is customarily the yield on government bonds like U.S. Treasuries.

CVaR

Conditional Value At Risk (CVaR) is also known as mean excess loss, mean shortfall, tail Var, average value at risk or expected shortfall. CVaR was created to serve as an extension of value at risk (VaR). The VaR model allows managers to limit the likelihood of incurring losses caused by certain types of risk, but not all risks. The problem with relying solely on the VaR model is that the scope of risk assessed is limited, since the tail end of the distribution of loss is not typically assessed. Therefore, if losses are incurred, the amount of the losses will be substantial in value. Zoonova calculates CVAR for both 95% and 99% confidence levels.

Drawdown

Take the minimum stock price over the 2 year period and look at the most recent price. If Max is the maximum and Min is the minimum price over the past umpteen years, and P is the current price, we look at: LOSS = 1 – P / Max and GAIN = P / Min – 1 The more positive the ratio the better. A maximum drawdown (MDD) is the maximum loss from a peak to a trough of a portfolio before a new peak is attained. (Trough Value – Peak Value) ÷ Peak Value.

ExpReturn

Expected Return is the annual expected return of a stock using 2 years of closing prices.

Info Ratio

The information ratio (IR) is a ratio of portfolio returns above the returns of a benchmark – usually an index – to the volatility of those returns. The information ratio (IR) measures a portfolio manager's ability to generate excess returns relative to a benchmark but also attempts to identify the consistency of the investor. The higher Info Ratio the better.

M2

(a.k.a. M2, M-Squared) In simple words, it measures the returns of an investment portfolio for the amount of risk taken relative to some benchmark portfolio. Popularly known as Modigliani Risk Adjustment Performance Measure or M2, it was developed by Nobel prize winner Franco Modigliani and his grandaughter, Leah Modigliani, in 1997.

Skewness

Skewness measures the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values; negative skewness indicates a distribution with an asymmetric tail extending toward more negative values; zero skewness means the tails are symmetric. Interpreted as downside risk, positive skewness suggests fewer/smaller negative outcomes whereas negative skewness suggest more/greater.

Kurtosis

Kurtosis measures the "tail-heaviness" (as opposed to "peakedness" or "flatness") of a distribution compared against a normal distribution (k = 3). A "low" kurtosis (k < 3) indicates fewer/smaller outliers whereas a "high" kurtosis (k > 3) indicates more/greater. With high kurtosis, one will have "fat" tails, higher frequency of outcomes at the extreme negative and positive ends of the distribution curve.

Pds Down

How many periods the stock was down.

Pds Up

How many periods the stock was up.

R2

(a.k.a. R2, R-Squared) R-squared is a statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For example, an R-squared for a fixed-income security versus the Barclays Aggregate Index identifies the security's proportion of variance that is predictable from the variance of the Barclays Aggregate Index. The same can be applied to an equity security versus the Standard and Poor's 500 or any other relevant index. R squared is measured from 0–1 or 0–100%. A level of 1, or 100%, means a perfect correlation to the benchmark.

Sharpe

The Sharpe Ratio is a measure that indicates the average return minus the risk-free return divided by the standard deviation of return on an investment. The Sharpe Ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations. The higher the Sharpe Ratio the better.

C‑Sharpe

The Conditional Sharpe Ratio is defined as the ratio of expected excess return to the expected shortfall. CVaR is used as the denominator in the C-Sharpe calcuation whereas the standard Sharpe ratio uses Standard Deviation as the denominator.

Sortino

The Sortino ratio is the excess return over the risk-free rate divided by the downside semi-variance, and so it measures the return to "bad" volatility. (Volatility caused by negative returns is considered bad or undesirable by an investor, while volatility caused by positive returns is good or acceptable.) A higher Sortino Ratio is better.

Treynor

The Treynor ratio, also known as the reward-to-volatility ratio, is a metric for returns that exceed those that might have been gained on a risk-less investment, per each unit of market risk. The Treynor ratio, developed by Jack Treynor, is calculated as follows: (Average Return of a Portfolio – Average Return of the Risk-Free Rate)/Beta of the Portfolio. The higher the Treynor Ratio the better. P&L. This is the return of the stock from the beginning of the year to the present.

VaR

Value At Risk (VaR) is a statistical technique used to measure and quantify the level of financial risk within a firm or investment portfolio over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios. VaR calculations can be applied to specific positions or portfolios as a whole or to measure firm-wide risk exposure. Zoonova calculates historical VAR using 2 years of daily prices and returns both VAR at 95% and 99% level of confidence.

Variance

Variance is used in statistics for probability distribution. Since variance measures the variability (volatility) from an average or mean and volatility is a measure of risk, the variance statistic can help determine the risk an investor might take on when purchasing a specific security. A variance value of zero indicates that all values within a set of numbers are identical; all variances that are non-zero will be positive numbers. A large variance indicates that numbers in the set are far from the mean and each other, while a small variance indicates the opposite.

Variance Neg

The calculated negative variance of the stock over the specified period, 2 years.

Volatility

Standard deviation is a statistical term that measures the amount of variability or dispersion around an average. Standard deviation is also a measure of volatility. Generally speaking, dispersion is the difference between the actual value and the average value. The square root of the variance equals the standard deviation.

Volatility Neg

The negative volatility, or standard deviation, of the sock over the specified period of time.

YTD%

Profit or loss of the stock during the current year.

Cheers.

All definitions and calculations are from Zoonova.com.