Excerpt from Regulation (2002:780) on the Calculation of the Balance Ratio1
In accordance with Ch. 58 § 14 of the Social Insurance Code (SFB, 2010:110), a balance ratio is to be calculated annually. The regulations (2002:780) require the Swedish Pensions Agency to prepare a calculation of the balance ratio, to be confirmed subsequently by the Government.
The balance ratio is calculated as follows:
\(\text{(B.1.1)}\quad\) \(\displaystyle BT_{t} = \frac{ AT_{t-2} + BF_{t-2} }{ S_{t-2} }\)
\(\text{(B.1.2)}\quad\) \(\displaystyle AT_t = {A}_t \cdot OT_{t-1}\)
- \(t\)
- calender year if the variable refers to flows, end of calender year if the variable refers to stocks
- \(AT_t\)
- contribution asset, year \(t\)
- \(BF_t\)
- buffer fund, the aggregate market value of the assets of the First–Fourth and Sixth National Pension Funds in year \(t\). By market value is meant the value which according to Ch. 6 § 3 of the National Pension Funds Act (2000:192) and Ch. 4 § 2 Sixth National Pension Fund Act (2000:193), is to be shown in the annual reports of these funds
- \(S_t\)
- pension liability, year \(t\)
- \(A_t\)
- contribution revenue of the pay-as-you-go system, year \(t\)
- \(OT_t\)
- turnover duration, year \(t\)
The damped balance ratio for a year is equal to 1 plus one-third of the difference between the balance ratio fixed for that year and the number 1. The damped balance ratio is rounded to four decimal places.
\(\text{(B.2.1)}\quad\) \(BT^* = \frac{BT-1}{3}+1\)
\(\text{(B.3.1)}\quad\) \(\displaystyle OT_{t} = \textit{U\AA}_t - \textit{I\AA}_t\)
\(\text{(B.4.1)}\quad\) \(\displaystyle \textit{I\AA}_t = \frac{\sum\limits_{i=16}^{R_{intj,t}}{\overline{PR}_{i,t} \cdot L_{i,t} \cdot (i+0.5)}}{\sum\limits_{i=16}^{R_{intj,t}}{\overline{PR}_{i,t} \cdot L_{i,t}}}\)
\(\text{(B.4.2)}\quad\) \(\displaystyle \overline{PR}_{i,t} = \frac{\frac{PR_{i,t}}{N_{i,t}}+\frac{PR_{i+1,t}}{N_{i+1,t}}}{2}, \quad i = 16, 17, ..., R_{intj,t}-1\)
\(\text{(B.4.3)}\quad\) \(\displaystyle \overline{PR}_{ R_{intj,t} } = \frac{ PR_{ R_{intj,t} } }{ N_{ R_{intj,t} } }\)
\(\text{(B.4.4)}\quad\) \(\displaystyle L_{i,t} = L_{i-1,t} \cdot h_{i,t}, \quad i = 17,18,...,R_{intj,t} \text{ där } L_{16,t} = 1\)
\(\text{(B.4.5)}\quad\) \(\displaystyle h_{i,t} = \frac{N_{i,t}}{N_{i-1,t-1}}, \quad i = 17,18,..., R_{intj,t}\)
- \(i\)
- age at year-end
- \(R_{intj,t}\)
- the highest age group to have earned pension credit for year \(t\)
- \(PR_{i,t}\)
- the sum of 16 percent of pension qualifying-income calculated according to Ch. 59 of the Social Insurance Code and 16 percent of the pension-qualifying amounts calculated according to Ch. 60 of said code, income year \(t\), age group \(i\)
- \(N_{i,t}\)
- number of individuals in age group \(i\) who at any time through income year \(t\) have been credited with pension-qualifying income or pension-qualifying amounts and have not been registered as deceased
- \(L_{i,t}\)
- proportion of persons in age group \(i\) year \(t\)
- \(h_{i,t}\)
- change in proportion of persons in age group \(i\) year \(t\)
The proportion of pension liability relating to pensioners \(R^*_i\) indicates how large a share of pension liability in age group \(i\) concerns pensioners and is included in the calculation of the payment age \(\textit{U\AA}\).
\(\text{(B.5.1)}\quad\) \(\displaystyle R^*_i = \frac{ SP_{i,t} }{SP_{i,t} + PB^*_{i,t} }\)
- \(SP_{i,t}\)
- pension liability in year \(t\) for age group \(i\) concerning pensioners in the distribution system in respect to pensions paid
- \(PB^{*}_{i,t}\)
- the sum of pension balances without regard to change in the income index between year \(t\) and \(t + 1\)
\(\text{(B.6.1)}\quad\) \(\displaystyle \textit{U\AA}_t = \frac{\sum\limits_{i=61}^{R_{utb,t}} 1.016^{-(i- 61 + 0.5)} \cdot L_{i,t}^* \cdot (i + 0.5) \cdot R_{i}^{*}}{\sum\limits_{i=61}^{R_{utb,t}} 1.016^{-(i-61 + 0.5)} \cdot L_{i,t}^* \cdot R_{i}^{*}}\)
\(\text{(B.6.2)}\quad\) \(\displaystyle L_{i,t}^* = L_{i-1,t}^* \cdot he_{i,t} \quad \text{ where } L_{60, t}^* = 1\)
\(\text{(B.6.3)}\quad\) \(\displaystyle he_{i,t} = \frac{U_{i,t}}{U_{i,t}+Ud_{i,t}+ 2 \cdot Ud_{i,t}^*}, \quad i=61,62,...,R_{utb,t}\)
- \(R_{utb,t}\)
- oldest age group receiving a pension, year \(t\)
- \(L_{i,t}^*\)
- proportion of remaining disbursements to age group \(i\) year \(t\)
- \(R^{*}_{i}\)
- the proportion of pension liability in age group \(i\) concerning pensioners
- \(he_{i,t}\)
- change in pension disbursements due to deaths, year \(t\), age group \(i\)2
- \(U_{i,t}\)
- total pension disbursements in December of year \(t\) to age group \(i\)
- \(Ud_{i,t}\)
- total of last monthly pension disbursements to persons in age group \(i\) who received pensions in December of year \(t-1\), but not in December of year \(t\)3
- \(Ud_{i,t}^*\)
- total of last monthly pension disbursements to persons in age group \(i\) who were granted pensions in year \(t\) but did not receive a pension payment in December of year \(t\) 4
\(\text{(B.7.1)}\quad\) \(\displaystyle S_t = SA_t + SP_t\)
\(\text{(B.7.2)}\quad\) \(\displaystyle SA_t = PB^{*}_t + IPR_t + TP_t\)
\(\text{(B.7.3)}\quad\) \(\displaystyle PB^{*} = \frac{ PB_t }{ \frac{ I_{t+1} }{ I_t } }\)
\(\text{(B.7.4)}\quad\) \(\displaystyle SP_t = BT^*_{t+1} \cdot \sum\limits_{i=61}^{ R_{utb,t} } U_{i,t} \cdot 12 \cdot \left( \frac{De_{i,t} + De_{i, t-1} + De_{i, t-2}}{3} \right)\)
\(\text{(B.7.5)}\quad\) \(\displaystyle \begin{aligned} De_{i,t} &= \frac{\sum\limits_{j=i}^{ R_{utb,t} } \frac{1}{2} \cdot (L_{j,t}^* + L_{j+1, t}^*) \cdot 1.016^{i-j-1}}{L_{i,t}^*}, \quad \\ i&=61,62,...,R_{utb,t} \quad \text{ where } L_{R_{utb,t}+1}^* = 0\end{aligned}\)
- \(SA_t\)
- pension liability in year \(t\) in regard to pension commitment for which disbursement has not commenced (pension liability to the economically active)
- \(SP_t\)
- pension liability in year \(t\) in regard to pensions being disbursed to retired persons in the pay-as-you-go system
- \(PB^{*}_t\)
- the sum of pension balances without regard to change in the income index between year \(t\) and \(t + 1\)
- \(IPR_t\)
- estimated value of pension credit earned in year \(t\) for inkomstpension according to Ch. 61 §§ 5-10 of the Swedish Social Insurance Code, calculated according to Ch. 62 § 5, second paragraph of same code
- \(TP_t\)
- estimated value of ATP, year \(t\) for persons who have not begun to draw this pension
- \(PB_t\)
- the sum of pension balances for year \(t\) according to Ch. 62 §§ 2, 5 and 7 of the Swedish Social Insurance Code
- \(I_t\)
- income index for year \(t\) according to Ch. 58 § 11 of the Swedish Social Insurance Code
- \(BT^{*}_{t}\)
- damped balance ratio, calculated according to Ch. 58 § 20a of the Swedish Social Insurance Code, when the balance index has been fixed for the same year5
- \(De_{i,t}\)
- economic annuity divisor for age group \(i\) year \(t\)
- Some editing has been done to simplify the presentation. ↩
- The minimum age for drawing a pension has been raised in 2020 from 61 to 62. In the end of 2020 there are therefore missing pension payments, \(U_{61,2020}\), for age 61 and the Pensions Agency therefore considers that \(he\) is set at 1, i.e. \({he_{61,2020}=1}\). ↩
- As of 2016, only payments terminated due to death are included. In previous years payments terminated as a result of pension deferral were also included. The risk period has been changed to cover an entire year. Previously the only payments included were those made to individuals who had received at least one payment in year \(t\) (in practice, to be included in the variable, previous payments in December of year \(t-1\) and January of year \(t\) was required). ↩
- As of 2016, only payments terminated due to death are included. In previous years payments terminated as a result of pension deferral were also included. ↩
- When the balance index has not been fixed, \(BT^{*}_{t}\) is set to \(1\). ↩
