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The general idea of this model is to incorporate previous knowledge of market, sector, and asset movement to predict whether the asset will move from its current “state” to

1. an increasing state,
2. a decreasing state, or
   
3. the same state

Where the state is represented by a model-weighted combination of factors that influence an asset’s price in the market.

Much of this approach relies on models that are based on Bayes theorem (Bayesian models).

\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \\ \]

\[ \begin{align*} \text{where...}\\ &A, B &&= \text{events} \\ &P(A|B) &&= \text{the probability of A, given B} \\ &P(B|A) &&= \text{the probability of B, given A} \\ &P(A), P(B) &&= \text{the independent probabilities of A and B} \end{align*} \]

Basically, we use our knowledge of event \(B\) to predict event \(A\).

In the context of market modeling, this theorem can be utilized to predict a market’s “state” based on knowledge of past states.

Partitioning market levels

Overall market

Within each state (time period), there are factors that influence market movements. On the highest level, there is the overall market. Some examples of factors that we could use to measure the state of the overall market are

• import/export tariffs
• federal interest rates
• inflation

Within sector

We can also look at factors that influence the sector a specific asset is in

• asset price movement relative to competing stocks

These variables can be used in statistical models to answer questions such as

• how did the state of the asset’s market sector differ when the value of an asset increased vs. time periods when it decreased?
• relative to all other sectors in the market, how much more/less price variance do these factors tend to result in?
• is there another stock that closely follows patterns of the asset of interest?

Specific asset

Then there are, of course, factors that influence the specific asset above the aforementioned types of variation

• popularity on social or televised media
• release of a new product
• success/failure of a new or upcoming product

Example

As a simple example, let’s say we have factors

• A1, A2, A3 - which mainly influence the overall market
• B1, B2, B3 - which mainly influence an asset’s sector
• C1, C2, C3 - which mainly influence a specific asset

Each of these levels will influence each other in accord with the diagram. Additionally, some variables at one level may influence a variable at another level. These arrows are not added to the diagram, but would be accounted for in the analyses.

This diagram represents a lone state. The idea is to then compare each variables’ impact during different market states.

For this example, we will define three states:

1. The current state of the market
2. A range of time where an asset’s value significantly decreases for d days
3. A range of time where an asset’s value significantly increases for d days

We then make all pairwise comparisons:

• State 1 vs. State 2
• State 1 vs. State 3
• State 2 vs. State 3

The algorithm will then use the information on variables within and between states to provide us with probabilities that the market will enter a state where an asset’s value will increase or decrease from the current state.

• the model also measures the probability that an asset will stay in a current state

Uses

• An investor wants to put money into a stock for 14 days. The investor does not know what stock they want, but they do know that they want to invest in the energy sector.