# Rating Method Sovereign Wikirating Index (SWI)

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 Last update: 2020-12-31 - Credit rating table

## Criteria and Base-Data

The Sovereign Wikirating Index (SWI) is a framework which evaluates the credit rating of sovereign countries/territories based on economic indicators. The following five mid-term and three long-term criteria are used:

The resulting value is calibrated by multiplying it with a scaling factor, which is composed by three long-term indicators, the Human Development Index (HDI)[1], the Corruption Perceptions Index (CPI)[2] and the Economic Freedom Index (EFI). Originally, the third index Political Instability Index[3] was used for the first version of the SWI[4]. Each criterium is calibrated with respect to the relative minimum and maximum value of all countries. For some criterion a threshold value is defined in order to avoid distorted values.

Short Title Long Title Value Weight Real Min Real Max SWI Min SWI Max
HDI Human Development Index Weighted index of development indicators 50% 0 1[scale 1] 0 1
CPI Corruption Perceptions Index Index of perceived corruption 30% 0 10[scale 1] 0 1
EFI Economic Freedom Index Index of economic freedom 20% 0 10[scale 1] 0 1
PII Political Instability Index Index of political instability (not used any more)[4] [4] 0 10[scale 1] 0 1
PD Public Debt Debt/GDP as %, reflects the economies ability to honour loans. 40% 0 0.2 2.0
AB Current Account Balance Current account balance as % of GDP, reflects foreign inflows and outflows. 15% -∞ -0.2 0.2
PG GDP Growth Domestic growth an an annual % 15% -1 -0.03 0.06
IR Consumer Price Index Consumer Price index as % 15% -1 0.02 0.2
UR Unemployment Rate Rate of unemployment as % 15% 0 1 0.02 0.3
R Rating Result of SWI calculation as % 0 1 0 1
1. Raw Data of social scaling factors is divided by the Real Max value to normalize the input.

## Formula

Definition Explanation
Let c be an element in the set of countries C:
${\displaystyle c\in \left\{\mathbf {C} \right\}}$
That means that every c is a country.
Let R be the vector of ratings, so that
${\displaystyle \forall c:\ R_{c}\in \left[0,1\right]\subset \mathbb {R} }$
That means that Rc is the rating for the country c and every rating is ranging from 0 to 100%.
Let ${\displaystyle \operatorname {dim} \left(v\right)}$ be the dimension of v. The function ${\displaystyle \operatorname {dim} }$ basically counts the number of elements in the vector. In example, ${\displaystyle \operatorname {dim} \left(R\right)}$ is the total number of ratings and thus the number of rated countries.
Let ${\displaystyle \operatorname {min} \left(v\right)}$ the minimal, and ${\displaystyle \operatorname {max} \left(v\right)}$the maximal value of v. These functions find the smallest and the biggest number in a set of numbers, such as a vector. This is needed for normalization.
${\displaystyle \operatorname {norm} (v)={\frac {v-\min(v)}{\max(v)-\min(v)}}}$. We are defining a scale-normalizating function on an vector ${\displaystyle v}$.
Let ${\displaystyle \operatorname {B} (x)={\mathbf {C} }\times \left\{\mathrm {HDI,CPI,EFI,PD,AB,PG,IR,UR} \right\}}$. x is a matrix. We define the base B of this matrix, so that it contains vectors with factors for individual countries in the direction ${\displaystyle x_{c}}$, while the economic and social factors are in direction ${\displaystyle x^{i}}$.
Let ${\displaystyle s\in \left\{\mathrm {HDI,CPI,EFI} \right\}}$ and ${\displaystyle e\in \left\{\mathrm {PD,AB,PG,IR,UR} \right\}}$ s is an indexer for the social factors and e is the indexer for economic factors.
${\displaystyle w^{\mathrm {HDI} }=50\%}$, ${\displaystyle w^{\mathrm {CPI} }=30\%}$, ${\displaystyle w^{\mathrm {EFI} }=20\%}$, ${\displaystyle w^{\mathrm {PD} }=40\%}$, ${\displaystyle w^{\mathrm {AB} }=15\%}$, ${\displaystyle w^{\mathrm {PG} }=15\%}$, ${\displaystyle w^{\mathrm {IR} }=10\%}$, ${\displaystyle w^{\mathrm {UR} }=15\%}$ Applying the weights. The vector ${\displaystyle w^{i}}$ contains the (scalar) weights for the individual economic and social factors.
${\displaystyle r=\left(x^{s}\,w^{s}\right)\cdot \left(x^{e}\,w^{e}\right)}$ By using the Einstein notation, we weight and sum the social factors to get the scaling factor. We also weight and sum the economic factors. Then we multiply the two results.
${\displaystyle R=\operatorname {norm} \left(r\right)+\left(1-n\right)\cdot \left(1-\operatorname {norm} \left(r\right)\right)}$ We finally do some normalisation on the rating r, so that the resulting values are ranging from 0 to 100% and the values represent the performance relative to the other rated countries. The result of this formula is the SWI rating R. n is a vector that contains the number of given ratings for a specific country and thus the trust in the values.

## Calculation

The calculations of the values are done with a spreadsheet framework:

Old version:

General Variable Modifiers
For example, the variable AB.

• AB = Number used in calculations for SWI.
• rAB = Raw or real value, actual data from source in whichever format it is acquired.
• wAB = Weighting value for the data.
• minAB = Floor value of variable, will cause ABC to equal 0 or 100 if ABC is below this value.
• maxAB = Ceiling value of variable, will cause ABC to equal 0 or 100 if ABC is above this variable.
• nAB = Number of ratings (for rating)

So for instance, if the real value (rAB) was 4 on a 10 point scale, this would be divided by 10 to create the value for calculations (AB) which, in calculations, is multiplied by the weighting (e.g. 0.5 for 50% weight.)