A good explanation does three things: it shows the worked steps to the answer, says what concept is being tested, and explains why each wrong choice looks tempting. That last part is what makes a missed question worth something. If your practice bank only tells you "the correct answer is B," you won't learn much from your misses.
When I was studying for the CFA, whether I kept using a question bank came down to one thing: did getting a question wrong teach me anything, or did it just mark me down?
Why the right letter isn't enough
When you miss a question, one of two things happened. You didn't know the concept, or you knew it and fell for a trap. An answer key can't tell those apart. It can't tell you whether you picked C because you flipped a sign, misread the question or don't understand the method.
If you flipped a sign, you need a quick habit fix. If you don't understand the method, you need to go back to the curriculum. A bare answer key tells both candidates the same thing, and both will probably miss the next version of the question.
A complete explanation has three parts:
- The worked steps. Not just the final number, but how to get there: which formula, which inputs, in what order. You should be able to reproduce it on the next question.
- The concept being tested, in a sentence or two, so you can connect it to the rest of the curriculum instead of memorizing one question.
- Why each wrong choice is wrong. This is the part that matters most. On a well-built question, each wrong choice is written around a specific misunderstanding. The note on the one you picked gives you a likely reason for your miss. Check it against your working, then try a fresh problem on the same idea to see whether it's fixed.
A worked example
Here's a Level I style question with the kind of explanation that teaches.
Question: A portfolio returns +50% in year 1 and -50% in year 2. What is its geometric mean (compound) annual return?
- A. -25.00%
- B. -13.40%
- C. 0.00%
Correct answer: B.
An answer key stops there. A good explanation goes through each choice.
Scroll horizontally to view all columns.
| Choice | Value | Why it's tempting, and why it's right or wrong |
|---|---|---|
| A | -25.00% | This is the total return over the two years (0.75 minus 1), not the annual rate. The question asks for the annual geometric mean, so this stops one step short. |
| B | -13.40% | Correct. The geometric mean is the square root of (1.50 times 0.50), minus 1, which is -13.40%. That's the constant annual rate that gets you the real two-year result. |
| C | 0.00% | This is the arithmetic mean of +50% and -50%, and it's the trap. The arithmetic mean overstates compound performance whenever returns vary. It answers "what's the average of the annual returns," not "what did you earn per year." |
There's one more wrong route the choices don't show: dividing the two-year return of -25% by 2 to get -12.50%, a simple average that ignores compounding.
The geometric mean is the actual compound rate of return. It only equals the arithmetic mean when every period's return is the same. When returns vary, the arithmetic mean is higher, which is why C is the trap and why "a portfolio that gains 50% and then loses 50% is back to even" is wrong.
If you picked C, the likely reason is that you averaged the two returns instead of compounding them. Check that against your scratch work, since a guess lands on C too. If it was the averaging, try another uneven pair, say +20% then -10%, and see whether you now get the compound rate of about 3.92% rather than the 5% average. That's a specific misunderstanding you can fix, not a general weakness in portfolio math, and the answer key alone would have left you guessing.
What to look for in any question bank
You can use these to check any CFA question bank, free or paid:
- Does it show the full worked solution, or just the final number?
- Does it say what concept is being tested?
- Does it explain the wrong choices, or only the right one?
- After a miss, can you tell what likely went wrong, or only which letter you should have picked?
If the answer to the last one is "only the letter," the bank isn't teaching you much.
FreeFellow is a CFA Institute Prep Provider, independent of CFA Institute, and does not promise a passing score. Every FreeFellow CFA Level I question has a step-by-step solution, and most also have notes on why each wrong choice is wrong, free. You can see for yourself on the free CFA Level I practice page.