You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Quantitative Methods guide.
Gross, net, after-tax, real and leveraged returns
Start from the gross return (before fees), subtract fees to get net, taxes to get after-tax, and strip out inflation to get real. Borrowing to invest magnifies the return in both directions: leveraged return = R + (debt ÷ equity) × (R − cost of debt).
Before this: Holding period return, Annualized and continuously compounded returns
On the exam
- Calculate and interpret major return measures and describe their appropriate uses
Calculate and interpret gross, net, after-tax, real and leveraged returns, and describe when to use each. Expect an exact real return, a leveraged return where the interest cost matters, and a "which return compares managers" question.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What is the return ladder?
Each step takes something away from the one before. The question is always which step the question wants, and the answer depends on who is asking.
- The gross return is the return before management and administrative fees. Trading costs are already inside it. It is best for comparing managers’ investment skill.
- The net return is the gross return minus fees and expenses. This is what the investor earned.
- The after-tax nominal return is the net return minus tax on income and realized gains.
- The real return is the return after removing inflation. Use it to compare across countries and periods with different inflation.
Inflation is 3.00%. To earn a real return of 2.00%, a portfolio's nominal return must be closest to:
(1 + 0.02) × (1 + 0.03) − 1 = 5.06%
Nominal return, r_i5.06%
- 1.02×1.03−1=0.0506, so 5.06%
- 1.02ENTER1.03×1−0.0506
ENTER enter (on the HP, puts the number on the stack)
Try this 0 of 2
- Make the real return negative while the gross return is still positive
- Find where the subtraction shortcut for real return is off by 0.3% or more
- Gross9.00%
- Net of fees7.80%
- After tax5.85%
- Real (net, after inflation)4.66%
Show working
Net = 9.0% − 1.20% = 7.80%
After tax = 7.80% × (1 − 0.25) = 5.85%
Real = (1 + 0.0780) ÷ (1 + 0.030) − 1 = 4.66% (shortcut 4.80%)
Exam tip Use the division form for real return unless the question says to approximate.
What is a leveraged return?
It is the return on your own equity when part of the portfolio is bought with borrowed money. The portfolio’s return applies to the whole position, but the interest is paid on the debt alone.
Here V_B is the amount borrowed, V_E is your own equity and r_D is the cost of borrowing. The leveraged return is above the portfolio return only when R exceeds r_D.
A question can also fix the return you want on your equity and ask what the portfolio must earn, or how much to borrow.
An investor puts in 600,000.00 of their own money and borrows 400,000.00 at 5.00%. The portfolio returns 9.00%. The return on the investor's equity is closest to:
9.00% + (400,000.00 ÷ 600,000.00) × (9.00% − 5.00%) = 11.67%
Leveraged return, r_LP11.67%
- 9−5=the spread over the borrowing cost
- ×400000÷600000times debt to equity
- +9=in percent
- 9ENTER5−the spread
- 400000×600000÷times debt to equity
- 9+
ENTER enter (on the HP, puts the number on the stack)
Which return fits which purpose?
| Purpose | Use |
|---|---|
| Comparing the investment skill of managers | Gross |
| What the investor actually received | Net |
| What the investor kept after tax | After-tax |
| Comparing across countries or periods with different inflation | Real |
| Return on equity when borrowing | Leveraged |
Go deeper Why gross returns compare managers
A manager’s fee is a business decision. A firm can charge more because it offers extra services, or less because it wants to win clients, and neither choice says anything about how good its investment decisions are. Comparing gross returns removes that noise. Two managers with the same gross return but different fees have the same skill and different prices. Performance standards used in the industry reflect this by asking firms to show gross and net figures side by side, so an investor can see both the skill and the cost.
Go deeper Why after-tax return depends on turnover
Tax is paid on income as it arrives and on gains when they are realized. A gain that has not been realized is deferred, and the deferral is worth something because the money keeps compounding. Two portfolios with the same pre-tax return can therefore have different after-tax returns: the one that trades often realizes gains each year and pays tax sooner, while a buy-and-hold portfolio postpones the bill. For an exam question, apply the tax rate to the stated taxable amount, and read whether the question tells you to assume everything is taxed this year.
Go deeper Leverage through derivatives
Borrowing is not the only way to gain leverage. A futures contract controls a large exposure for a small margin deposit. If a USD 100,000 exposure requires USD 10,000 of margin, a 5% rise in the underlying earns USD 5,000, which is a 50% return on the margin. A 5% fall loses the same amount. The mechanics are the same as with borrowed money: exposure divided by your own capital sets the multiplier, and the result moves in both directions. The formula in this lesson handles the case of a plain loan.
Memorize this
MemorizeThe return ladder
| Step | Take away | Use for |
|---|---|---|
| Gross | Nothing (trading costs already in) | Comparing managers |
| Net | Fees and expenses | What the investor got |
| After-tax | Taxes | What the investor kept |
| Real | Inflation (divide) | Comparing across inflation |
Memory hook Gross for skill, net for the client, real for comparing countries or decades.
Know it cold and real .
Quick example
Nominal 6.5%, inflation 2.5%. 1.065 ÷ 1.025 − 1 = 3.90%, against 4.00% from subtraction.
- 1.065÷1.025−1= 0.0390
- 1.065ENTER1.025÷1− 0.0390
ENTER enter (on the HP, puts the number on the stack)
Quick example
Equity 600,000, borrowed 400,000 at 5%, portfolio return 9%. 9% + (400 ÷ 600)(9% − 5%) = 11.67%.
- 9−5=×400÷600+9= in percent: 11.67
- 9ENTER5−400×600÷9+ 11.67
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Leveraged return
Equity 500k, borrow 250k at 4%, portfolio +10%.
10% + 0.5 × (10% − 4%) = 13%. Ignoring the interest (15%) is the trap.
-
Real return
Nominal 6.5%, inflation 2.5%.
1.065 ÷ 1.025 − 1 = 3.90%. Subtraction (4.00%) is the trap.
-
Which return compares managers
Two managers with different fee schedules.
Gross returns. Net mixes skill with pricing.
Exam traps
- Computing a leveraged return without subtracting the interest cost. The first example would give 15%.
- Real return by subtraction when the answer options are close.
- Calling a return net when only trading costs are deducted. That is still a gross return.
Checkpoint
3 exam-style questions. About 90 seconds each.
1An investor puts in EUR 500,000 of their own money and borrows EUR 250,000 at 4% to buy a EUR 750,000 portfolio that returns 10%. The leveraged return is closest to:
2A fund's nominal return is 6.5% and inflation is 2.5%. The real return is closest to:
3To compare the investment skill of two managers with different fee schedules, an analyst should most appropriately use:
Key takeaways
- Gross (before fees), then net (after fees), then after-tax, then real (after inflation).
- Compare managers on gross returns. Investors care about net, after-tax and real.
- Leveraged return = R + (V_B ÷ V_E)(R − r_D). It magnifies losses as well as gains.
Quick example
Nominal 6.5%, inflation 2.5%. 1.065 ÷ 1.025 − 1 = 3.90%, against 4.00% from subtraction.
- 1.065÷1.025−1= 0.0390
- 1.065ENTER1.025÷1− 0.0390
ENTER enter (on the HP, puts the number on the stack)
Quick example
Equity 600,000, borrowed 400,000 at 5%, portfolio return 9%. 9% + (400 ÷ 600)(9% − 5%) = 11.67%.
- 9−5=×400÷600+9= in percent: 11.67
- 9ENTER5−400×600÷9+ 11.67
ENTER enter (on the HP, puts the number on the stack)
Questions about this lesson?
Where this comes back
- Alternative Investment Performance and Returns Alternative Investments
- Time Value of Money in Finance Quantitative Methods
Questions candidates ask
What is the difference between gross and net return?
Gross return is before management and administrative fees. Trading costs are already inside it. Net return is gross minus those fees and expenses, so it is what the investor earned. A 9.0% gross return with 1.2% of fees is a 7.8% net return.
How do you calculate real return exactly?
Divide the growth factors: (1 + nominal) ÷ (1 + inflation) − 1. With a 7.8% nominal return and 3% inflation, that is 1.078 ÷ 1.03 − 1 = 4.66%. Subtracting gives 4.8%, which is only an approximation.
How does leverage affect portfolio return?
Borrowing adds (debt ÷ equity) × (portfolio return − borrowing cost) to the portfolio return. It helps only when the portfolio earns more than the cost of debt. When it earns less, the loss on the equity is larger than the loss on the portfolio itself.
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