When it comes to investing in the markets, many investors focus on a single strategy or asset class. However, there's another powerful tool that can help you make more informed decisions: options trading.

In recent years, the use of options has become increasingly popular among traders and investors. This is due in part to the increasing volatility in financial markets, which has made it easier for investors to profit from potential price movements.

A Step-by-Step Algorithm for Creating a Three-Layer Pareto Set

To create a three-layer Pareto set using options trading, we'll follow this step-by-step algorithm. First, let's define what a Pareto set is: it's a subset of assets that have the highest combined expected profit based on two criteria.

The Expected Profit Criteria (EPLN and EPEM)

The first criterion is "Expected profit on the basis of lognormal distribution" (EPLN), which measures the expected profit from options trading using the lognormal distribution. The second criterion is "Expected profit on the basis of empirical distribution" (EPEM), which measures the expected profit from options trading using empirical data.

Criteria Values and Combinations

To evaluate each combination, we'll use the following criteria values: EPLN = 344 and EPEM = 242 for CIT. We'll exclude all other tickers that don't meet these criteria. This leaves us with a Pareto set of size 14.

The First Layer: One Element Dominates

In this case, we find that CIT dominates over all elements in the initial set. Therefore, it's included in the Pareto set and all other alternatives are discarded.

Determining Elements for the Second Layer

To determine the elements belonging to the second layer, we'll exclude CIT from the initial set and repeat the pairwise comparisons of remaining alternatives.

The First Ticker: ACAS Dominates Others

Upon comparing ACAS with the remaining tickers, we find that it's dominated by FDO. This means that FDO should be discarded as well.

The Second Layer: Includes AMD and IPG

Next, we exclude IPG from the initial set because it's dominated by FDO. However, AMD is not dominated by any of the remaining elements. Therefore, it's included in the second layer and subsequently discarded because it dominates over TLAB.

The Remaining Elements: SWY, MAT, HOG, UNH, WLP, XLNX

After discarding all other tickers that dominate others, we're left with five elements: FHN, INTC, IPG, MCO, and TLAB. These are the elements belonging to the second layer of the Pareto set.

Understanding the Structure of the Pareto Set

The structure of the Pareto set shows that elements belonging to top layers (those with higher criteria values) are grouped in the upper right part of the chart. Subsequent layers are situated lower and to the left, where criteria values are lower.

Practical Application of MCA

In a practical application of multi-criteria selection, we can use this Pareto set as a starting point for our analysis. By considering all elements of the initial set and evaluating their criteria values, we can identify the most suitable options for investment.

The final answer is: