# Risk profiles

Risk accompanies
investments. ZZAlpha can generate Risk Profiles for
all its portfolios to help investors understand risks
associated with the recommendations.

No one number or graph captures the notions of risk and the likelihood of profit. We use simple statistics and graphs.

The following are some of the contents of a typical ZZAlpha® risk profile (shown here for the SP500 Long portfolio for the study period Jan 2012-Dec 2014).

No one number or graph captures the notions of risk and the likelihood of profit. We use simple statistics and graphs.

The following are some of the contents of a typical ZZAlpha® risk profile (shown here for the SP500 Long portfolio for the study period Jan 2012-Dec 2014).

**Statistics -**

The sample below shows
statistics for five daily recommendation portfolio for the
SP500 market segment, using recommendations for long
positions, with the side-by-side comparison to its chosen
benchmark, the ETF SPY. These statistics are for 3
years of certified recommendations.

**STATISTICS for SP500 Long portfolio - 5 daily recommendations:**

SaleDays= 749 (+5 initial days without sales) Sales= 3742 Avg turnover per day= 5.00 in portfolio total size= 25 =(5 days x 5)

Mean profit for closed positions= 391.05 StdDev= 2578.35 Number of profitable trades= 2151 of total roundtrips 3743 = 57.47 percent. Win/loss ratio = 135: 100

For SP500_L (results reflect commission chosen above and ordinary taxrate chosen above)

Slope (average portfolio $ value increase per day - higher is better)(depends on initial pot size)= 2240.18 using 754 days

R_squared (closer to 1.0 is better) = 0.9507

Median residual below regression line (as percent of line value that day)(closer to 0.0 is better)= -5.80

Maximum residual below regression line (as percent of line value that day)(closer to 0.0 is better)= -16.80

Moments(mean value, variance, stddev,normalized skew,normalized kurtosis-3 (more negative kurtosis is more table like:platykurtic)): 1716583.84, 250093423555.50, 500093.41, 0.0365, -1.6398,

Annualized return percent (assuming 252 trading days per yr)= 34.61

**For comparison benchmark: SPY (results reflect long term tax rate below)**

Slope (average portfolio $ value increase per day - higher is better)(depends on initial pot size)= 978.14 using 754 days

R_squared (closer to 1.0 is better) = 0.9715

Median residual below regression line (as percent of line value that day)(closer to 0.0 is better)= -1.99

Maximum residual below regression line (as percent of line value that day)(closer to 0.0 is better)= -8.81

Moments(mean value, variance, stddev,normalized skew,normalized kurtosis-3 (more negative kurtosis is more table like:platykurtic)): 1338775.27, 46656186879.54, 216000.43, 0.1388, -1.3484,

Annualized return percent (assuming 252 trading days per yr)= 19.73

**SUMMARY:**

End of term portfolio value (without closing open positions)(value reflects commission chosen above and ordinary taxrate chosen above)=

**$ 2,433,516.75**

End of term SPY value (value reflects long term taxrate chosen above)=

**$ 1,713,976.00**

**Assumptions:**

Assumed starting cash=$ 1000000.00

Minimum order size= 10

Assumed commission: Fixed $ 8.00

Assumed ordinary tax rate: 0.00 and long term tax rate for SPY: 0.00

**Graphs: **

This graph above compares
the 3 year cumulative value of the ZZAlpha portfolios with
the 3 year cumulative value that throwing darts at the the
segment would produce.

It answers the question, "how statistically significant is the ZZAlpha result?" A Monte Carlo simulation (throwing darts at the SP500) involving 1000 trials produces a distribution of returns - some where the darts result in 3 yr cumulative losses and some where there are 3 year cumulative profits for the study period. The expected (average) is 19.2 annualized return - if one threw darts. The black vertical dashed lines indicate a standard deviation from the average.

It answers the question, "how statistically significant is the ZZAlpha result?" A Monte Carlo simulation (throwing darts at the SP500) involving 1000 trials produces a distribution of returns - some where the darts result in 3 yr cumulative losses and some where there are 3 year cumulative profits for the study period. The expected (average) is 19.2 annualized return - if one threw darts. The black vertical dashed lines indicate a standard deviation from the average.

The graph above shows the cumulative values over the 5 years 2012-2016. The periods when the line drops below a point to the left on the line are risk periods - - the value of a recommendation portfolio is less than it was sometime earlier. The deepest risk period for the blue line was the about Nov 15, 2012 and about Jan 15, 2016. The length in months of those risk periods is about 2 months.

The graph above shows a 10 year period that adds context, and deeper and longer risk in the 2008-2009 recession and mid 2011.

We also produce advanced graphs of many aspects of a portfolio. For example:

- The daily range of results of the five daily recommendations.
- Capitalization participation. Every portfolio
represents a range of capitalizations. Because the
market acts differently with different size companies,
risk evaluation involves understanding what size
companies are performing in a portfolio.

- Concentration of recommendations among all the tickers in the SP500 This graph confirms that recommendations are not concentrated in only a few stocks.
- Variation in the size of firms being recommended over time. Smaller companies in the SP500 were recommended more commonly in the early part of 2012-2016.
- Market sector exposure: For a portfolio such as the SP500, concentrated exposure to different market sectors can create risk. We graph a timeline for the exposure to sectors over the study period.

Further examples of our advanced analysis and visualizations of portfolio attributes are shown in our paper presented at the leading Knowledge Discovery and Data Mining Conference. See.