From Percentages to Paychecks: The Math Behind the Calculator

Most investors describe their portfolio in percentages: “I’m 70% in stocks and 30% in bonds.” That’s useful for planning, but percentages don’t pay the bills. The key question: How do you turn a portfolio into a steady paycheck?

The Paycheck Calculator answers this by turning percentages into dollars using basic algebra.

The Paycheck Equation

To maintain your target allocation after taking a withdrawal, you need to adjust your cash and investment positions. This formula calculates the change in cash ( $\Delta c$ ) required to keep the portfolio balanced.

p = \frac{c + \Delta c}{c + i - w}

Where:

$p$ : Target cash percentage
$c$ : Starting cash position
$i$ : Starting investments position
$w$ : Withdrawal (paycheck amount)
$\Delta c$ : Cash position change (positive increases cash, negative decreases cash)

The equation shows how much to withdraw from cash vs. investments to maintain your target allocation. At its core, it’s just a percentage equation ( $\frac{\text{part}}{\text{whole}}$ ).

$c + \Delta c$ is the cash part after withdrawal ( $\Delta c$ and the investment draw together make up the total withdrawal).
$c + i - w$ is the portfolio value after withdrawal

Example: A Paycheck from a Balanced Portfolio

Given a $1,000,000 portfolio with a 70% investments and 30% cash target allocation, a starting cash position of $300,000, starting investments of $700,000, and a withdrawal (paycheck) of $3,500, calculate the change in cash required ( $\Delta c$ ) to maintain the target allocation.

0.3 = \frac{300,000 + \Delta c}{300,000 + 700,000 - 3,500}

Rearranged to solve for $\Delta c$ the equation becomes:

\Delta c = 0.3 \times (300,000 + 700,000 - 3,500) - 300,000

To maintain a 30% cash allocation, withdraw $1,050 from cash ( $\Delta c$ = -$1050). The remaining $2,450 comes from selling investments.

Handling an Unbalanced Portfolio

Markets shift, so your portfolio may become unbalanced. The same equation can be used with an unbalanced portfolio.

Example: Cash Tilt (Market -1%)

\Delta c = 0.3 \times (300,000 + 693,000 - 3,500) - 300,000

To achieve a 30% cash allocation, withdraw $3,150 from cash ( $\Delta c$ = -$3,150). The remaining $350 comes from selling investments.

Example: Investment Tilt (Market +1%)

\Delta c = 0.3 \times (300,000 + 707,000 - 3,500) - 300,000

To achieve a 30% cash allocation, add $1,050 to your cash position ( $\Delta c$ = $1,050). The paycheck (withdrawal) and increase in cash position comes from selling $4,550 of investments ($3,500 + $1,050).

NOTE: If you expect another paycheck next month, you might choose to skip rebalancing $1,050 from investments to cash.

What the Calculator Doesn’t Cover

The equation represents your portfolio as two buckets: cash and investments.

It tells you how much cash and how much investments to sell to rebalance and draw a paycheck. It doesn’t specify which asset to sell or tax implications.

Within each bucket, you’ll need to decide on the details and how to optimize for taxes:

Cash (and Fixed Income): HYSAs, CDs, money markets, bonds, Treasuries
Investments: S&P 500, small-cap stocks, international stocks, REITs

Benefits of the Formula

Simplifies withdrawals with a clear, rules-based formula.
Prevents emotional decisions about what to sell.
Aligns with your existing asset strategy.
Offers clarity for further customization (e.g., tax planning).

Conclusion

Percentages are theoretical; paychecks are practical. The Paycheck Calculator automates the calculations to turn your portfolio into a predictable paycheck, keeping your allocation on track.