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**Calculating integral indices - freight, TCE and
shipping profitability indices.**

Subregional indices are calculated according to the data from the list of the main routes in a given region. Time-charter equivalent index as well as profitability index are the arithmetic mean of the values on the most popular transportation routes in a certain subregion:

Where - time-charter equivalent, - profitability level.

One can not use the unweighted average during freight index calculation. So,

1. It is assumed that the freight rate is linearly dependent on the distance:

where F – freight rate, D - route extension, k and b - parameters depending on market conditions.

2. The entered parameters are estimated by using the least square method according to the available data on the freight rate and known distance value. Thus, linear regression parameters are determined.

3. Freight index for a given set of routes is calculated as:

where - average value of route extensions included in the analyzed set. All elements of the set are summed up. The top number indicates that the index refers to the first subregional level. The lower one indicates the freight index.

The integral index of the regional level is the weighted average of the index values of the corresponding subregions. The weighting factors are proportional to the number of ships of a certain type in a given region:

Where - weighting factor of a certain subregion.

Global index is calculated in much the same way by using weighting factors for each region:

It should be noted that regional and global TCE and profitability indices are calculated similarly by using the same weighting factors.

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