NISM-Series-X-A: Investment Adviser (Level 1) · Portfolio Performance Measurement and Evaluation

Return Measures: HPR, CAGR, XIRR and Time-Weighted Return

Updated 11 October 2026 · Fact-checked

Holding period return is total gain, including income, divided by the starting value. CAGR turns a start value and an end value into one smoothed yearly rate. XIRR does the same for dated cash flows. Time-weighted return removes the effect of deposits and withdrawals, so it judges the manager. Money-weighted return reflects the investor's timing.

Understand Return Measures: HPR, CAGR, XIRR and Time-Weighted Return

A return measure answers one question: how much did money grow? The right measure depends on what you are judging. Is it a single period, many years, a series of investments, or the skill of a manager?

Holding period return (HPR) is the return over the whole time you held the asset. It counts price change plus any income such as dividends or interest. It is not annualised. A 30% HPR over 3 years is not 30% a year.

Arithmetic return is the simple average of period returns. Geometric return is the compounded average. Returns multiply, they do not add. A +50% year followed by a -50% year leaves you with 1.5 × 0.5 = 0.75, a loss of 25%. The arithmetic average says 0%. The geometric average shows the real result. CAGR is the geometric return worked out from just a start value and an end value, with no cash flows in between.

When you add or withdraw money during the period, CAGR no longer works. XIRR solves this. It finds the single annual rate that makes the present value of all dated cash flows equal zero. This is a money-weighted return. It depends on how much money was invested and when. Its answer is the investor's own experience.

The time-weighted return (TWR) removes the effect of cash flows. You split the period at every deposit or withdrawal, find the return of each sub-period, and compound them. Because the manager does not control when the client adds money, TWR is the fair way to judge the manager. GIPS standards also rely on time-weighted returns. If there are no cash flows, TWR and money-weighted return are the same.

Key formulas to remember

Holding period return (HPR): HPR = (Ending value − Beginning value + Income) ÷ Beginning value; Not annualised. Always include dividends or interest received.
Multi-period return: Cumulative return = (1 + R1) × (1 + R2) × ... × (1 + Rn) − 1; Compound the returns. Never add them.
Arithmetic mean: Arithmetic mean = (R1 + R2 + ... + Rn) ÷ n; Always greater than or equal to the geometric mean. Equal only when all returns are identical.
Geometric mean: Geometric mean = [(1 + R1) × (1 + R2) × ... × (1 + Rn)]^(1/n) − 1; Use it for the average compounded return over several periods.
CAGR: CAGR = (Ending value ÷ Beginning value)^(1/n) − 1; n is the number of years. Valid only with a single investment and no interim flows.
Annualising an HPR: Annualised return = (1 + HPR)^(365 ÷ days held) − 1; Use it to compare holding periods of different lengths.
Sub-period return for TWR: Sub-period return = Value just before the next cash flow ÷ Value just after the previous cash flow − 1; Split the period at each deposit or withdrawal. Then compound all sub-period returns.
XIRR (money-weighted return): Σ [Cash flow ÷ (1 + r)^(days from first date ÷ 365)] = 0; Solve for r. Investments are negative flows, withdrawals and final value are positive. Use a calculator or spreadsheet.

How to solve Return Measures: HPR, CAGR, XIRR and Time-Weighted Return questions

Use this order for any return-measure question. Read the wording first. It tells you which measure is needed.

1Identify what is being measured: a single period, an average over years, a lump sum over time, a portfolio with cash flows, or a manager's skill.
2Check for interim cash flows. None means HPR, CAGR or geometric mean. Dated flows mean XIRR (money-weighted) or TWR.
3For HPR, add the income to the price gain, then divide by the beginning value.
4For several periods, convert each return to a growth factor (1 + R), multiply them, and subtract 1. Take the nth root for an annual average.
5For TWR, split the period at each cash flow. Compute each sub-period return using values just before and just after the flow, then compound.
6If the question asks who is judged fairly or what removes timing effects, answer time-weighted. If it asks about the investor's actual experience, answer money-weighted or XIRR.
7Check the unit. Decide if the answer should be total or per year, and confirm n is in years.
8Sanity check: geometric is not above arithmetic, and a negative return needs a bigger percentage gain to recover.

Quickest way: Pick the measure from the keywords, then compute with growth factors

When to use it: Use this under time pressure, especially when the options differ only by measure or by small rounding.

Scan for keywords. 'Manager skill' or 'remove cash flow effect' means TWR. 'Investor's actual return' or 'timing of contributions' means money-weighted or XIRR. 'Smoothed annual growth' means CAGR.
Work in growth factors. Turn +20% into 1.20 and -10% into 0.90, then multiply.
Eliminate options that equal the arithmetic average if the question says compounded or geometric.
For CAGR, test a round option by raising it to the power n. For example, 1.10^5 = 1.61051, so ₹1,00,000 becoming about ₹1,61,051 in 5 years is 10% a year.
In TWR questions, only values just before and after each flow matter. Ignore the amount of the flow except to add it to the value.

Common mistakes in Return Measures: HPR, CAGR, XIRR and Time-Weighted Return

Using the arithmetic average to describe multi-year growth.
Averaging is a familiar habit, and it ignores compounding.
Fix: Use the geometric mean or CAGR. Remember +50% then -50% gives a 25% loss, not zero.
Adding yearly returns to get the total return.
Students treat returns like amounts of money.
Fix: Multiply the growth factors (1 + R) and subtract 1. Returns of 10% and 10% give 21%, not 20%.
Using CAGR for a portfolio with deposits or withdrawals, such as a SIP.
CAGR is the formula students remember best.
Fix: CAGR needs one starting value and one ending value. For dated flows, use XIRR or TWR.
Judging a fund manager by money-weighted return.
The client's actual gain looks like the real result.
Fix: The manager does not control the client's cash flows. Use time-weighted return to judge the manager. Use money-weighted return for the investor's experience.
Leaving out dividends or interest in HPR.
Students focus on the price change alone.
Fix: Add all income received during the holding period to the numerator before dividing by the beginning value.
Treating an HPR as an annual return, or using the wrong n in CAGR.
The time period is skipped when reading the question.
Fix: HPR covers the whole holding period. Annualise it if needed. In CAGR, n is the number of years, so 18 months is n = 1.5.

Worked examples

Example 1

A portfolio returned +20% in year 1, -10% in year 2 and +15% in year 3, with no cash flows. Find the cumulative return, the geometric mean annual return and the arithmetic mean.

Show the solution

Convert to growth factors: 1.20, 0.90, 1.15.
Multiply: 1.20 × 0.90 = 1.08. Then 1.08 × 1.15 = 1.242.
Cumulative return = 1.242 − 1 = 24.2%.
Geometric mean = 1.242^(1/3) − 1. Since 1.075³ ≈ 1.2423, the cube root is about 1.075, so the geometric mean is about 7.5% a year.
Arithmetic mean = (20 − 10 + 15) ÷ 3 = 25 ÷ 3 = 8.33%.
The arithmetic mean (8.33%) is higher than the geometric mean (about 7.5%), as expected.

Answer: Cumulative return 24.2%; geometric mean about 7.5% a year; arithmetic mean 8.33% a year.

Example 2

A client starts with ₹10,00,000 in a portfolio. After 6 months it is worth ₹11,00,000, and the client then adds ₹5,00,000. At the end of the year the portfolio is worth ₹17,92,000. Find the time-weighted return for the year. Is the money-weighted return higher or lower, and why?

Show the solution

Split the year at the cash flow into two sub-periods.
Sub-period 1: value grew from ₹10,00,000 to ₹11,00,000 before the deposit. Return = 11,00,000 ÷ 10,00,000 − 1 = 10%.
After the deposit the portfolio starts sub-period 2 at ₹11,00,000 + ₹5,00,000 = ₹16,00,000.
Sub-period 2: Return = 17,92,000 ÷ 16,00,000 − 1 = 12%.
Compound: 1.10 × 1.12 = 1.232, so the time-weighted return = 23.2%.
The larger amount (₹16,00,000) was invested during the better sub-period (12% against 10%). So the money-weighted return is higher than the TWR.

Answer: Time-weighted return = 23.2%. The money-weighted return is higher, because more money was invested during the better-performing sub-period.

Exam tips

Expect conceptual questions on which measure suits which purpose. Learn the pairing: manager evaluation with TWR, investor outcome with money-weighted return or XIRR.
Negative marking applies in this paper, and caselet questions can carry more marks. If two options look close, recheck whether the question wants arithmetic or geometric, total or annual.
Know that CAGR is a smoothed rate. It hides volatility and says nothing about the path of returns between the start and the end.
In TWR calculations, the sub-period must end just before each cash flow. A common trap option uses the end value without adding the deposit.
Remember the inequality: geometric mean is never above arithmetic mean. A question that offers both can often be settled by this rule.

Practice questions from Portfolio Performance Measurement and Evaluation

Return Measures: HPR, CAGR, XIRR and Time-Weighted Return in other exams

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

CFA Level IHolding Period Return and Return Measures

Return Measures: HPR, CAGR, XIRR and Time-Weighted Return: frequently asked questions

What is the holding period return formula in NISM X-A?

HPR = (Ending value − Beginning value + Income) ÷ Beginning value. Income means dividends, interest or other cash received during the holding period. The result covers the whole period and is not an annual rate.

What is the difference between CAGR and XIRR?

CAGR uses only a beginning value, an ending value and the number of years, so it suits a single lump-sum investment. XIRR handles several dated cash flows, such as SIP instalments or withdrawals. Both give an annualised rate.

What is the difference between time-weighted and money-weighted return?

Time-weighted return removes the effect of the timing and size of deposits and withdrawals, so it measures the manager's performance. Money-weighted return, such as XIRR, includes those effects, so it measures the investor's actual experience.

How do I calculate portfolio return when there are cash flows?

For the manager's performance, split the period at each cash flow, find each sub-period return and compound them. For the investor's return, find the rate that makes the dated cash flows net to zero, which is XIRR.