CFA Level I · CFA Level I Exam

Returns of Financial Assets and Instruments for CFA Level I

Returns measure how much an investment gained or lost as a percentage of the money put in. You solve questions by picking the right measure: holding period return for one period, arithmetic or geometric mean for several periods, money-weighted or time-weighted return when cash flows occur, then annualize and adjust for fees, inflation or leverage.

What this chapter covers

This chapter teaches you how to measure investment performance. It starts with the simplest idea, the holding period return (HPR), and builds to averages across periods, returns that account for deposits and withdrawals, annualizing, and adjustments for costs, inflation and borrowing.

The chapter sits in Quantitative Methods, but its ideas reach well beyond it. Geometric and arithmetic means appear again in statistics and in portfolio math. The Global Investment Performance Standards (GIPS) require time-weighted returns for performance presentation, so this idea links to portfolio management and ethics-related standards on performance presentation. Real returns link to Economics, and leveraged returns link to Derivatives and Portfolio Construction.

Questions here are mostly short calculations. You are given a few prices, dividends or cash flows and must choose among three numerical options. The skill is choosing the correct measure and applying it cleanly, not doing hard algebra.

Quantitative Methods carries 11-14% of the Level I exam, and return calculations are among its most reliable scoring areas because the formulas are short and the questions are predictable. A solid grip on this chapter also makes later chapters faster, since you will use returns in portfolio, equity, fixed income and derivatives questions. With 180 questions and about 90 seconds each, quick, accurate return calculations buy you time for harder items elsewhere, and there is no penalty for a wrong answer, so you should always answer.

Returns of Financial Assets and Instruments: topics in the order to study them

1Return Measures: HPR, Arithmetic and Geometric MeanEverything else builds on single-period return and on how to average returns across periods, so start here.
2Money-Weighted vs Time-Weighted ReturnIt extends the averaging idea to portfolios with cash flows and relies on HPR and geometric linking from the first topic.
3Annualizing Returns and Compounding ConventionsOnce you can compute returns over any period, you learn to put them on a common yearly basis and handle compounding frequency.
4Other Return Measures: Gross, Net, Real and LeveragedThese are adjustments applied to a return you already know how to compute, so they come last.

How to prepare Returns of Financial Assets and Instruments

Treat this chapter as a set of formulas you can apply without hesitation. Short daily sessions on your phone and calculator work well.

Write each core formula from memory: HPR = (P1 − P0 + income) ÷ P0, arithmetic mean = Σr ÷ n, geometric mean = [Π(1 + r)]^(1/n) − 1.
Practise the geometric mean on your approved calculator (TI BA II Plus or HP 12C) using the power key, until the keystrokes are automatic.
For money-weighted return, learn to set up the cash flow list and solve for IRR with the calculator's cash flow function. Then compute time-weighted return by chaining sub-period HPRs.
Drill annualizing with both directions: from a short period up to a year, and from a multi-year total return down to a yearly rate. Check the compounding frequency in every question.
Do a mixed set of questions covering gross, net, real and leveraged returns, and practise stating which measure the question asks for before computing.
Finish with timed three-option sets at about 90 seconds each. Use rough estimates to eliminate options, since the answer choices are listed from smallest to largest.

Common mistakes in Returns of Financial Assets and Instruments

Using the arithmetic mean to describe multi-period growth.
Fix: Use the geometric mean when the question asks for compound or average annual growth over several periods.
Confusing money-weighted and time-weighted return.
Fix: Ask whether cash flow timing should count. If yes, it is money-weighted (IRR). If you must remove its effect, chain sub-period HPRs for time-weighted.
Forgetting to include income such as dividends or interest in HPR.
Fix: Always check the stem for dividends, coupons or other distributions and add them to the numerator.
Ignoring the compounding frequency when annualizing.
Fix: Read whether the rate is stated or effective and note the compounding frequency. If you have a stated annual rate r compounded m times a year, convert with (1 + r/m)^m − 1. If you have a periodic return, use (1 + periodic return)^m − 1.
Subtracting inflation directly when the question asks for an exact real return.
Fix: Use (1 + nominal) ÷ (1 + inflation) − 1 when the options are close together or the stem asks for the exact figure.
Dividing leveraged gains by total assets instead of your own equity.
Fix: Subtract interest paid from the total gain, then divide by the equity you invested.

Last-day revision: Returns of Financial Assets and Instruments

HPR = (ending value − beginning value + income) ÷ beginning value.
Arithmetic mean = sum of returns ÷ number of periods; it is never lower than the geometric mean.
Geometric mean = [(1 + r1)(1 + r2)...(1 + rn)]^(1/n) − 1, and it measures compound growth.
The two means are equal only when all returns are identical.
Money-weighted return is the IRR of the cash flows and is affected by the timing and size of contributions.
Time-weighted return chains sub-period returns and removes the effect of cash flow timing.
GIPS require time-weighted returns for performance presentation.
Time-weighted return is the better measure of a manager's skill when the manager does not control the flows.
Annualize a return over a period shorter than a year by compounding: (1 + r)^(periods per year) − 1, where r is the periodic return for that shorter period.
Effective annual rate = (1 + periodic rate)^m − 1, where m is compounding periods per year. If you are given a stated annual rate r, the periodic rate is r ÷ m, so EAR = (1 + r/m)^m − 1.
Gross return is before fees; net return is after fees and expenses.
Real return ≈ nominal return − inflation; the exact form is (1 + nominal) ÷ (1 + inflation) − 1.
Leveraged return = [gain on total position − borrowing cost] ÷ your own equity.

Returns of Financial Assets and Instruments practice questions

Returns of Financial Assets and Instruments in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Returns of Financial Assets and Instruments: frequently asked questions

What is the difference between arithmetic and geometric mean return?

The arithmetic mean is the simple average of period returns. The geometric mean is the compound average growth rate. For returns that vary, the geometric mean is lower than the arithmetic mean, and it better reflects what an investor actually earned over time.

When should I use time-weighted return instead of money-weighted return?

Use time-weighted return to judge a manager who does not control when clients add or withdraw money, because it removes the effect of those flows. GIPS also require time-weighted returns for performance presentation. Use money-weighted return to see what the investor actually earned given the timing of their own contributions.

Which calculator functions do I need for this chapter?

You mainly need the power function, the percentage and compounding keys, and the cash flow and IRR functions on the TI BA II Plus or HP 12C. Practise them until you can finish a return question well within 90 seconds.

Is this chapter easy to score on?

It is usually considered approachable because the calculations are short and the formulas are few. The marks are lost on choosing the wrong measure or missing a detail such as income or compounding frequency, so careful reading matters more than difficult math.