Mathematics And Markets - A Helicopter View Of Major Stock Market Indices - Mar. 4, 2018

Summary

• Chaos theory mathematics allows for objective comparison between stock market indices, thus providing a helicopter view of the risks and potential associated to major financial markets.
• All indices point to potential medium and long term weakness.
• Russell2000 index shows elevated and significant risk.
• S&P 500 index and Nasdaq100 show unfavorable risk/reward.
• Dow30 index shows short term favorable risk/reward.

References

Applying Mathematics to Analyse Financial Markets – Part 1, Innovation

Applying Dynamic Chaos Theory to Analyse Financial Markets – Part 2, Good Investment Practice

A Helicopter View of major stock market indices – Feb 18th, 2018

Chaos theory mathematics - Abstract

When Chaos Theory mathematics starts to work on multiple distinct layers, it yields two time dependent price values for each distinct layer. The time dependency of these price values is a direct consequence of the irregular shape of Julia-sets. One of these price values represents the price-target for an underlying asset. This price-target equals the value an underlying asset will assume in future. The other price value is the price-edge and represents the lowest or highest value the underlying asset may assume without jeopardizing the price-target. In other words, the value of the underlying asset should stay within the boundaries of both time dependent price values generated by the method. This applies to all distinct layers. (See Part 1, Innovation).

A Helicopter View of major stock market indices

This publication elaborates on the idea to objectively compare major stock market indices with the help of chaos theory mathematics, thus providing a helicopter view of financial markets. First we will review the individual status of the S&P 500 index, the Dow 30, Nasdaq 100 and Russell 2000 indices. Then we will compare the actual status of these indices with the help of our decision criteria and try to draw a few objective helicopter level conclusions.

Readers should be aware of two important characteristics of dynamic chaos theory mathematics, which has been described in previous publications (see references):

1. All calculations use time dependent price-target and time dependent price-edge information
2. All research is relative to the actual price of an asset at the moment of publication

Although the information remains valid for medium and longer term, it is obvious that this research loses its relevance over time when observing shorter time windows.

S&P 500 index

Early Feb 2018, the S&P 500 index retraced considerably, creating a bottom near 2530 points. Our Feb 18^th, 2018 publication indicated unfavorable conditions due to conflicting directional price movements and unfavorable, wildly varying risk/reward ratios for most distinct layers.

In the meantime, the S&P 500 index declined 1.6% from Feb 18^th levels. Below table shows the actual situation per March 4^th.

Medium term conflicting directional price movements indicate caution when trading the S&P 500 index. The dominant long term directional price movement is UP (layers 1 and 2), but layers 3 and 4 show conflicts in directional price movement. This has been visualized in below graph where both lines representing price-edge and price-target cross each other.

Conclusions for S&P 500 index

Basically, the above table and graph indcate caution to trade the S&P 500 index due to:

1. Wildly varying risk/reward ratios for short term indicate high risk
2. Medium term risk due to conflicting dominant directional price movements

Dow 30 index

Since our Feb 18^th article, the Dow 30 index retraced 2.8%, in line with our expectations regarding multiple conflicting directional price movements and likely short/medium term price pressure.

So, what does the current situation look like? Below table shows a single conflict for dominant directional price movement in layer 6. This may allow for short term upward potential (due to favorable risk/reward), while the outlook for medium/long term remains negative.

Risk/reward for medium/long term is favorable as well, in other words chances for a longer term negative outlook remain high. This is also reflected in below graph, representing price target and price edge for the Dow 30 index with short term upward potential (layers 8 and 7) and medium/long term price pressure resulting from a widening trading range.

Conclusions for Dow 30 index

The Dow 30 index may allow for short term upward potential, but continued medium/long term price pressure is highly likely.

Nasdaq 100 index

The Nasdaq 100 index increased by 0.3% since Feb 18^th. We indicated potential short term weakness. Associated risk/reward ratios were unfavorable indicating it was not worth trading the Nasdaq 100 index. The situation on March 4^th shows multiple conflicts in dominant directional price movement and overall unfavorable risk/reward ratios.

Below graph tells the same story, indicating lack of short/medium term potential and medium/long term conflicts in dominant direction. Most distinct layers show an unfavorable risk/reward ratio, indicating it is not a good moment to trade the Nasdaq 100 index.

Conclusions Nasdaq 100 index

The majority of layers (polynomials) show an unfavorable risk/reward ratio for the Nasdaq 100 index. As of March 4th it is not the right moment to enter this market.

Russell 2000 index

On Feb 18^th, the Russell 2000 index showed no conflicting internal directional price movements, but the situation changed considerably. Since Feb 18^th, the Russell 2000 index lost 0.9% and medium/long term layers now indicate conflicting directional price movements. Overall, risk/reward ratios are unfavorable, indicating it is not worth trading the Russell 2000 index per March 4th.

The graphical representation for the trading range indicates a similar situation. Short and medium term upward potential is very limited while longer term layers indicate increasing and significant weakness for the Russell 2000 index.

Conclusions Russell 2000 index

Short and medium term upward potential is limited while longer term we expect increasing downward risk.

A Helicopter View of major stock market indices

From a helicopter perspective it is important to understand three key decision criteria:

1. Internal conflicts in dominant directional price movement (table 1)
2. Relative potential gain versus relative potential loss per distinct layer per index (Graph 1).
3. Risk and reward per distinct layer for each of the indices under investigation (Graph 2).

Another note of importance is the fact that I am using a risk/reward threshold equal to 0.5. Readers could opt for a higher value, which would increase opportunities to enter the market but this would also increase risk exposure. Obviously, choosing a threshold for risk/reward is arbitrary but also directly related to the preservation of assets under management.

Conflicting directional price movements per March 4^th

Conflicting directional price movements can be identified when distinct layers are compared with each other. For that purpose we have created below table in which red cells indicate a conflicting dominant directional price movement compared to adjacent layers. The basic rule is that any conflict increases risk.

Calculations are based on the actual relative position within a price range per distinct layer (see Good Investment Practice).

_{Table 1 – Conflicting directional price movement (red cells) per March 4th. Values indicate the relative position within the trading range of each distinct layer.}

Conclusions per March 4th

• The S&P5 00 index declined 1.6% from Feb 18^th levels and shows reduced medium term weakness due to downward risk in layer 3.
• The Dow 30 index retraced 2.8% and still shows multiple medium and long term conflicts with respect to dominant directional price movement. Again, the Dow 30 shows elevated medium and long term risk compared to the other indices.
• The Nasdaq 100 index increased by 0.3% since Feb 18^th, while the risk shifted from shorter term to medium/long term. Previously mentioned short term downward risk indeed played out, but the recovery was equally strong.
• The Russell 2000 index lost 0.9% compared to Feb 18^th and the Russell2000 index shows potential medium term weakness.

Overall, knowing the risks associated to conflicting internal dominant directional price movements provides insight into the relative strength of these stock market indices. Clearly, from a price directional perspective, all indices currently show potential medium/long term weakness due to conflicting directional price movements in layers 5 to 1.

Potential gain and potential loss per March 4th

So, on March 4^th we signal conflicting directional price movements in medium and long term layers and this applies to all indices. It would be interesting to review how this translates into potential gain and potential loss, based on actual values of these indices on March 4th. Potential gain per distinct layer is calculated by taking the difference between price-target and actual price. Potential loss is calculated as the difference between actual price and price-edge. Below graphs have comparable vertical scales and represent potential gain and potential loss per distinct layer for each of the four indices discussed per March 4th.

_{Graph 1 – Potential gain and potential loss for S&P 500, Dow 30, Nasdaq 100 and Russell 2000 indices}

Conclusions per March 4th

1. All indices currently show a lack of short term directional conflicts which translates in reduced short term downward risk. Please keep in mind this conclusion is based on actual March 4th index levels compared to Feb 18^th index levels.
2. Potential loss may be significant for the Russell 2000 index (layers 2 and 1) because potential gain in the same layers is limited.
3. The Nasdaq 100 index may experience increased volatility due to large differences in potential gain for medium/long term layers 3 and 2 and potential loss in layer 1.
4. Potential loss for Dow 30 seems limited due to significant potential gain in medium/long term layers.

Risk/Reward per March 4th

In our Feb 18^th publication we cautioned for drawing conclusions based on potential gain only. The impact of potential loss is on risk and risk should be carefully managed. For that reason we will also look into the risk/reward ratios prior to drawing conclusions with respect to which index currently shows relative strength. Graph 2 provides an overview of risk and reward per layer for each index per March 4^th.

The vertical axis of this graph has been capped with a maximum value of 1.4 to ensure that the most interesting zone between zero and our threshold of 0.5 remains clearly visible.

_{Graph 2 – Risk/Reward ratios for S&P 500, Dow 30, Nasdaq 100 and Russell 2000 indices}

Conclusions with respect to Risk/Reward on March 4th

Comparing risk and reward amongst indices provides the following insight:

1. The S&P 500 index still shows wildly varying R/R ratios. Only layers 5 and 4 show a favorable risk/reward, but we should also keep in mind there is a price directional conflict in layer 3. Overall, we don’t think this is a good moment to trade the S&P 500.
2. The Dow 30 index only shows favorable short term R/R ratios (layers 8, 7 and 6). Layers 5 to 1 show conflicting dominant price movements.
3. The Nasdaq 100 index shows R/R ratios less than our threshold of 0.5 in layers 3 and 2. These layers however also show a conflict in directional price movement, so this is not a good moment to generate profits in this market.
4. The Russell 2000 index shows unfavorable risk/reward ratios for all layers. This is not a good moment to generate profit in this market.

Major stock market indices - Overall conclusions per March 4th

S&P 500 index

• Wildly varying and unfavorable risk/reward ratios indicate elevated overall risk
• Comparable overall potential gain and potential loss indicating elevated risk
• Potential medium term weakness due to directional price conflicts.

Dow 30 index

• Short term upward potential seems likely due to favorable risk/reward
• Limited potential loss in all layers, which translates into limited overall downward risk
• Medium and long term weakness seems highly likely due multiple conflicting dominant price movements

Nasdaq 100 index

• Overall unfavorable risk/reward ratios, currently above our threshold for trading
• Medium/long term weakness seems highly likely due to conflicting directional price movements

Russell 2000 index

• Elevated long term potential weakness
• The Russell2000 index currently shows unfavorable risk/reward ratios for all layers.

Although all indices currently point to medium term and long term potential weakness, the Russell 2000 index shows elevated and significant risk.

Best option seems trading the Dow 30 index, which shows short term upward potential with favorable risk/reward ratios.

Both the S&P 500 index and the Nasdaq 100 index currently show wildly varying and unfavorable risk/reward ratios. We stay away from these markets because the potential gain is not worth the potential risk.

Obviously, if the reader decides to apply a higher threshold for risk/reward the picture may look different, but keep in mind you also increase your risk exposure by doing so.

Thank you for reading.

Analyst’s Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Comments

[Laomedeia Ltd]

thank you xpan. It may actually be a bit of all, Art, Math, Physics, Psychology...
But, when you see this all playing out it certainly is mind boggling and continues to amaze me every day.

[xpan]

In my early years of trading/investing, I was told that it's not math, it's art. After all these years, now I finally know what went wrong: it's not art either, it's actually physics!