Lesson 8 of 25 · 7 min

Mental accounting: the line and the portfolio as separate objects

A 9.2 percent return and a 7.85 percent rate look like a comfortable margin, and they are not comparable numbers at all.

Mental accounting is the practice of sorting money into separate notional accounts and evaluating each on its own terms, even though money is fungible and the accounts interact. A portfolio and a line secured on it are an unusually clean case, because they are administered separately, reported separately, and reviewed at different times.

The portfolio is judged on its return. The line is judged on its rate. When the return is 9.2 percent and the rate is 7.85 percent the comparison appears to leave 1.35 points of margin, and it appears to be a comparison. It is not. The two percentages are computed on different bases, and until the bases are restored the numbers cannot be subtracted.

Restore them. A portfolio of $1,760,000 returning 9.2 percent produces $1,760,000 × 0.092 = $161,920. A balance of $430,000 at 7.85 percent costs $430,000 × 0.0785 = $33,755. The net is $128,165 against equity of $1,760,000 − $430,000 = $1,330,000, which is $128,165 ÷ $1,330,000 = 9.64 percent. The leverage added 0.44 points, not 1.35.

Then run the other year. The portfolio falls 14 percent, a loss of $246,400, and the interest still costs $33,755, for a total of $280,155 against the same $1,330,000 of equity — a decline of 21.1 percent. The unlevered outcome was a 14 percent decline. The line added 0.44 points in the good year and 7.1 points in the bad one, which is the entire asymmetry of the arrangement in two figures.

The rate is charged on the balance and the return is earned on the portfolio. Comparing the two percentages compares a small base with a large one and reports the result as a margin.

Key terms

Mental accounting: Treating money in different notional pots as though it followed different rules, when in fact every pot draws on the same net position.
Fungibility: The property that a dollar is a dollar wherever it sits. It is what makes the separate-pots treatment an error rather than a convention.
Return on equity: Net gain divided by the value of the position after the balance is deducted. The only figure that combines both sides.

Worked example

The good year and the bad year, both on equity

Portfolio $1,760,000, balance $430,000 at an illustrative 7.85%. Equity is $1,330,000.

Portfolio return in a 9.2% year: $161,920
Interest cost: $33,755
Return on equity, good year: 9.64%
Portfolio loss in a 14% year: $246,400
Return on equity, bad year: −21.1%
Effect of the line: +0.44 points / −7.1 points

One arrangement, two years, and the help it gave in the first is worth a sixteenth of the harm it did in the second.

Check yourself

A $1,760,000 portfolio carries a $430,000 balance at 7.85 percent. In a year the portfolio falls 14 percent. What is the return on equity, and how does it compare with the unlevered outcome?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.