Portfolio Decomposition Calculator

Decomposes the P90−P10 total wealth-return gap into asset-level contributions, and each asset's contribution into composition, within, and interaction components. Companion to Appendix F of Housing Capital Gains across the Income Distribution by Claes Bäckman, Walter D'Lima, and Natalia Khorunzhina.

R_i = ∑_a s_i,a · r_i,a

Asset contribution = s_P90,a·r_P90,a − s_P10,a·r_P10,a
= (s_P90−s_P10)·r_P10 [composition] + s_P10·(r_P90−r_P10) [within] + (s_P90−s_P10)·(r_P90−r_P10) [interaction]

Data sources

Each preset combines a source for portfolio shares (P10, P90 of the income distribution) with a source for asset returns by income rank.

Portfolio shares. Danish 2014–2019: administrative registers from Statistics Denmark, averaged over 2014–2019 for households at the 10th and 90th percentiles of the income distribution. SCF 2013: Survey of Consumer Finances, same percentile cuts.
Housing returns. Estimated in this paper from ~250,000 Danish repeat-sale transactions (1996–2022), using the linear fit r(i) = 0.036 + 0.0017·(i−5.5) over income deciles i = 1,…,10, evaluated at i=1 (P10) and i=10 (P90).
Financial returns. Fagereng et al.: Norwegian administrative data on returns to financial wealth across the financial wealth distribution (Fagereng, Guiso, Malacrino, and Pistaferri, 2020). Bach et al.: Swedish administrative data (Bach, Calvet, and Sodini, 2020). Passive: country-internal mix r_fin,i=α_ir_stock+(1−α_i)r_safe, using OMXC20+10y bond for Denmark (α_P10=0.07, α_P90=0.27 from Danish registers) and S&P 500+10y T for the SCF (α from SCF risky-asset shares). Captures only the composition channel; gives a lower bound on the financial-wealth gap.
Pension returns. Held flat at 4.47% for both percentiles.

Inputs are editable: click a preset to load it, then adjust any cell to explore alternative scenarios.

Presets

*Passive = r_fin,i = α_i·r_stock + (1−α_i)·r_safe, with country-specific real stock and bond means over 2014–2022. The Danish risky shares (α_P10=0.07, α_P90=0.27) are constructed from Danish administrative registers (2014–2019 average). Default values are illustrative; replace with Stata-computed means after re-running 15_PortfolioDecomposition.do.

Portfolio shares

Asset	P10	P90
Housing
Financial
Pension
Sum	1.00	1.00

Shares should sum to 1 within each decile (turns red otherwise).

Returns (% annual)

Asset	P10	P90
Housing
Financial
Pension

Housing default from r=0.036+0.0017(i−5.5) at i=1, 10. Pension flat at 4.47%.

Asset contributions to the P90−P10 gap

Total contribution of each asset class to the income gap in wealth returns. Bars in absolute percentage points; share of gap shown in parentheses.

Decomposition (P90−P10 gap, in percentage points)

Asset	Composition	Within	Interaction	Total	Share of gap
Housing	—	—	—	—	—
Financial	—	—	—	—	—
Pension	—	—	—	—	—
Total	—	—	—	—	100%

Three-way decomposition by asset

Composition Within Interaction ◆ Net total