Math Analysis for Wealth Simulation

Current Implementation Analysis

1. Return Calculation (Lines 184-209)

Base for Return Calculation:

baseForReturn = Math.max(0, wealth - 0.5 * totalOutflowsPreTax + 0.5 * totalInflowsPreTax)

• Uses mid-year approximation (reasonable)
• Assumes outflows/inflows happen evenly throughout year

Return Components: - publicReturn = params.assetReturn.public (total return, e.g., 6%) - publicDivYield = params.publicDivYield (dividend yield, e.g., 2%) - publicPriceReturn = Math.max(0, publicReturn - publicDivYield) (price appreciation, e.g., 4%) - publicRealized = params.publicRealizationRate * publicPriceReturn (realized gains) - cashReturn = params.assetReturn.cash (interest rate, e.g., 3%) - privateReturn = params.assetReturn.private (private equity return, e.g., 11%) - privateRealized = params.privateRealizationRate * Math.max(0, privateReturn)

Gross Return:

grossReturn = allocation.public * publicReturn + 
              allocation.private * privateReturn + 
              allocation.cash * cashReturn

This is correct - weighted average return.

Net Return:

netReturn = baseForReturn * grossReturn - taxes

This applies the gross return to the base, then subtracts taxes. This is correct IF taxes are calculated correctly.

2. Tax Calculation (Lines 120-147)

Tax on Dividends:

taxOnDiv = publicBase * publicDivYield * params.taxDividends

✅ Correct - taxes dividend income

Tax on Public Realized Gains:

taxOnPublicRealized = publicBase * publicRealized * params.taxRealizedGains

✅ Correct - taxes realized capital gains

Tax on Cash Interest:

taxOnCash = cashBase * cashReturn * params.taxInterest

✅ Correct - taxes interest income

Tax on Private Realized:

taxOnPrivate = privateBase * privateRealized * params.taxRealizedGains

✅ Correct - taxes private realized gains

Total Taxes:

taxes = taxOnDiv + taxOnPublicRealized + taxOnCash + taxOnPrivate

✅ Correct - sums all tax components

3. Wealth Update (Line 211)

wealth = wealth + totalInflowsPreTax + netReturn - totalOutflowsPreTax

✅ Correct - adds inflows and net return, subtracts outflows

4. Liquid Wealth Calculation (Lines 213-228)

ISSUE IDENTIFIED:

liquidReturn = baseForReturn * (allocation.public * publicReturn + allocation.cash * cashReturn)
liquidAfter = liquidBefore + totalInflowsPreTax - privateCall - expense - philanthropy - oneOffs.outflows + liquidReturn - taxes

Problem: The taxes variable includes taxes on ALL assets (public, private, cash), but liquid wealth should only pay taxes on liquid assets (public + cash). Currently, liquid wealth is being reduced by taxes on private assets too, which is incorrect.

Fix Needed: Calculate taxes separately for liquid vs. illiquid assets, or calculate liquid taxes as a proportion.

5. Returns Breakdown - MISSING

Currently, the simulation only tracks netReturn as a single value. The user wants to see: - Dividend income (publicDivYield * publicBase) - Interest income (cashReturn * cashBase) - Capital gains (realized and unrealized) - Private returns breakdown

These components are calculated internally but not exposed in the results.

Issues Found

1. Liquid Wealth Tax Issue: Liquid wealth was being reduced by taxes on private assets, which is incorrect. ✅ FIXED

2. Missing Returns Breakdown: No visibility into dividend income, interest income, or capital gains separately. ✅ FIXED

3. Returns Not Explicitly Shown: While returns were calculated and reinvested, they weren’t broken down in the display. ✅ FIXED

Fixes Implemented

1. ✅ Fixed Liquid Wealth Tax Calculation: - Created computeLiquidTaxes() function that only calculates taxes on liquid assets (public + cash) - Updated liquid wealth calculation to use liquidTaxes instead of full taxes - This ensures liquid wealth is only reduced by taxes on liquid assets

2. ✅ Added Return Breakdown Fields: - Extended SimulationRow type with:

   • dividendIncome: Dividend income from public equities
   • interestIncome: Interest income from cash
   • publicRealizedGains: Realized capital gains on public equities
   • publicUnrealizedGains: Unrealized capital gains on public equities
   • privateRealizedGains: Realized gains on private investments
   • privateUnrealizedGains: Unrealized gains on private investments
   • grossReturnPct: Gross return percentage (before taxes)
   • netReturnPct: Net return percentage (after taxes)

3. ✅ Updated Results Table: - Added all return breakdown columns to the results table - Properly formatted percentages and currency values - Users can now see exactly how returns are composed

4. ✅ Return Calculation Verification: - All returns are properly calculated and reinvested - Dividends and interest are included in the gross return calculation - Returns are correctly applied to the base wealth and reinvested - Tax calculations are accurate and applied correctly

Math Verification Summary

✅ Return Calculation: Correct - Gross return is weighted average of asset class returns - Dividends and interest are included in total returns - Returns are applied to mid-year base and reinvested

✅ Tax Calculation: Correct - Taxes calculated on actual income (dividends, interest, realized gains) - Different tax rates applied correctly to different income types - Liquid wealth taxes calculated separately (only on liquid assets)

✅ Wealth Update: Correct - Wealth = previous wealth + inflows + net return - outflows - All returns are reinvested (included in netReturn) - Mid-year approximation for base calculation is reasonable

✅ Liquid Wealth: Fixed - Now correctly calculates taxes only on liquid assets - Liquid wealth properly tracks public + cash assets only