NISM Series X-A · Chapter 16: Portfolio Performance Measurement and Evaluation

L1 · Foundation

Foundation — Holding period return, TWRR versus MWRR, and geometric versus arithmetic mean

Why performance must recognise both return and risk, the holding period return as the starting point, the difference between time weighted and money weighted returns and why SEBI mandates TWRR for portfolio managers, and why the geometric mean is the honest number over long periods.

26 min read · Worth 4% of the paper · Written from pages 266–289 of the official NISM workbook · Updated 11 September 2026

16.1 The two parameters — risk AND return

The chapter opens with a diagnosis of a very human failing:

Keep that sentence in mind for the whole chapter. Sections 16.2 measure return, section 16.3 measures risk, and section 16.4 puts them together into risk-adjusted return measures. The structure of the chapter is the argument of the chapter.

16.2 Rate of return measures — one definition per purpose

This is the sanest sentence in the chapter. There is no single "correct" return. There is a correct return for a stated purpose. Gross return answers one question, net return another; time weighted answers one, money weighted another. The examiner will often give you the purpose and ask for the measure.

16.2.1 Holding period return — the starting point

Learn all three names — questions use them interchangeably.

The two equations:

Equation 1 (no income): HPR = (E − B) / B

Equation 2 (with income): HPR = (I + (E − B)) / B

where HPR = holding period return; I = Income; E = Ending Value; B = Beginning Value.

The workbook's example. If the market value of an investor's portfolio on 1 April 2018 is Rs 1,00,000, and on 31 March 2019 it stands at Rs 1,20,000:

HPR = (1,20,000 − 1,00,000) / 1,00,000 = 20%

Now assume that during the same period the investor received Rs 5,000 by way of dividend and interest income:

HPR = (5,000 + (1,20,000 − 1,00,000)) / 1,00,000 = 25%

Two closing points, both examinable:

This measure assumes that all income distributions are made at the END OF THE YEAR. That is its limitation — a dividend received in April is treated as though it arrived the following March, earning nothing in between.
In spite of this limitation, Holding Period Return is widely used and a generally accepted indicator of performance. This is considered as the STARTING POINT of the performance measurement exercise.

16.2.2 Time weighted versus money weighted rate of return

Now to multiple periods, where the interesting problem lives. Suppose a portfolio generated these annual holding period returns:

Year	HPR for the year
2015	−5.00%
2016	−15.20%
2017	8.10%
2018	30.75%
2019	17.65%

And suppose the investor invested Rs 75,000 in total, by making contributions at the beginning of each year:

Year	Investment (Rs)
2015	5,000
2016	10,000
2017	15,000
2018	20,000
2019	25,000

At the end of 2019 the investments would have grown to Rs 1,05,920.31, built up as follows:

Year	Invested at start	Return for year	Return in Rs	Portfolio value at start	Portfolio value at end
2015	5,000	−5.00%	−250	5,000	4,750.00
2016	10,000	−15.20%	−2,242	14,750	12,508.00
2017	15,000	8.10%	2,228.15	27,508	29,736.15
2018	20,000	30.75%	15,293.87	49,736.15	65,030.01
2019	25,000	17.65%	15,890.30	90,030.01	1,05,920.31

What is the rate of return generated during the period of five years? There are two honest answers, and the whole point of this section is that they answer different questions.

Money weighted rate of return

By discounting the terminal value of the investment, Rs 1,05,920.31, and the cash flow contributions made, the internal rate of return can be calculated.

Solving that equation gives IRR = 15.15%.

That last sentence is the key. Look at the pattern of this investor's contributions: small money in the two bad years, big money in the two good years. He put Rs 5,000 in when the portfolio fell 5 per cent and Rs 25,000 in when it rose 17.65 per cent. The bulk of his money experienced the good years. His personal outcome — 15.15 per cent — is excellent, and it reflects his timing decisions, not the manager's skill.

Time weighted rate of return

The method in four steps.

Step 1 — compute each sub period return using Equation 1, (E − B) / B. With five contributions there are five sub periods:

Year	Value at start	Value at end	Sub period return
2015	5,000.00	4,750.00	−5.00%
2016	14,750.00	12,508.00	−15.20%
2017	27,508.00	29,736.15	8.10%
2018	49,736.15	65,030.01	30.75%
2019	90,030.01	1,05,920.31	17.65%

Step 2 — convert each to a wealth relative. Wealth relative is the ending value of one unit of money. So add one to each period return:

Year	Return	Wealth relative
2015	−0.05	0.9500
2016	−0.152	0.8480
2017	0.081	1.0810
2018	0.3075	1.3075
2019	0.1765	1.1765

Step 3 — chain link by multiplying them together.

Cumulative wealth relative = 0.95 × 0.848 × 1.081 × 1.3075 × 1.1765 = 1.3396

Cumulative wealth relative tells us what one rupee has grown to over a period of time. Here one rupee has become Rs 1.3396 in five years.

Step 4 — annualise.

TWRR = (1.3396 ^ (1/5)) − 1 = 6.021%

The two numbers side by side

	MWRR	TWRR
Answer	15.15%	6.021%
What it is	The rate at which cumulative contributions grow	The compound rate of growth of the portfolio
Affected by timing of cash flows?	YES	NO
Also known as	IRR	Geometric return
Whose performance it reflects	The investor's	The manager's

Both are correct. Neither is wrong. The gap of nine percentage points is entirely the value of the investor's own contribution pattern — money that happened to arrive before the good years.

Two more points the workbook makes:

What SEBI requires, and why

The workbook then explains the industry practice in four crisp observations, all examinable:

In Mutual Funds, there is a NAV every working day, hence the investor or adviser can calculate returns in any manner as he or she wants.
In PMS, since portfolios are CUSTOMISED and there is NO NAV, SEBI has mandated TWRR for fund managers.
Wealth manager software systems and adviser excel reporting on client returns are on MWRR BASIS, as money flows multiple times over a long holding period.
At the end of the day the client is bothered about how much he or she is taking home; TWRR is FOR THE FUND MANAGER, for UNIFORMITY IN REPORTING AND COMPARING.

Fix that last line. TWRR exists for comparability between managers. MWRR exists because it tells the client what actually happened to his money. Both have a job.

16.2.3 Geometric mean versus arithmetic mean return

The workbook poses a question that settles the matter better than any definition.

Suppose there are two portfolio choices available for investing Rs 1,00,000.

The first produces a holding period return of −50 per cent in year one and +100 per cent in year two.
The second produces 10 per cent in year one and 10 per cent in year two.

Which one would you suggest?

Work it through. In the first scheme, Rs 1,00,000 falls by half to Rs 50,000, then doubles back to Rs 1,00,000. The value of the portfolio is the same as it was two years ago — yet the average annual return on the portfolio is 25 per cent.

In the second scheme, Rs 1,00,000 becomes Rs 1,10,000 and then Rs 1,21,000 — an average annual 10 per cent gain in value.

A "25 per cent average" that leaves you exactly where you started, against a "10 per cent average" that makes you Rs 21,000 richer. Something is wrong with the first average — and that something is the arithmetic mean.

Arithmetic mean return

First choice: AMR = (−50% + 100%) / 2 = 25%
Second choice: AMR = (10% + 10%) / 2 = 10%

So when is the arithmetic mean the right tool? The workbook is specific, and this is examinable:

Geometric mean return

And the property that makes it honest:

GMR is based on an EXPONENTIAL FUNCTION, which represents periodic compounding.

The process of calculating the GMR is the SAME AS TWRR. We are required to calculate wealth relatives for each HPR, then link these sub period returns. In the above example the evaluation period is two years, hence to calculate annualised return the cumulative wealth ratio is raised to (1/2), n being the number of years.

First choice: GMR = (((1 − 50%) × (1 + 100%)) ^ (1/2)) − 1 = (0.5 × 2.0)^0.5 − 1 = 1 − 1 = 0%
Second choice: GMR = (((1 + 10%) × (1 + 10%)) ^ (1/2)) − 1 = (1.21)^0.5 − 1 = 10%

The geometric mean gives the honest answer the arithmetic mean hid: the first scheme earned nothing at all.

The relationship between the two — memorise this

Verify with the second choice: returns of 10 per cent and 10 per cent are identical, and indeed AMR = GMR = 10 per cent. With the first choice, the returns differ wildly, and the gap between 25 per cent and 0 per cent is correspondingly huge. The bigger the variability, the bigger the gap.

Why this matters for judging a manager

The summary table you should carry into the hall:

Use the...	When you want to...
Arithmetic mean	Estimate next year's return — the best guess for the holding period return in a given year, and the expected return over a multiyear horizon conditioned on past experience
Geometric mean	Analyse the long-run return on assets, compare long-term accumulations, and estimate the probability distribution of terminal wealth

Think of it like this

The batsman who scored a century and a duck

Two batsmen average 50. One scored 50 and 50; the other 100 and 0. The arithmetic mean cannot tell them apart. In investing, the difference is not academic: a portfolio that goes 100 → 50 → 100 shows an arithmetic average of 25 per cent while the investor is exactly where he started. The geometric mean reports what really happened: zero.

Grading the coach or grading the player

TWRR grades the coach — it strips out when the student joined and how much he put in, so you can compare coaches fairly. MWRR grades the student's own result — it is the rate at which his contributions actually grew, and it depends on the timing of the cash flow. Both are true. SEBI mandates TWRR for discretionary portfolio managers precisely so that coaches can be compared with each other.

Why PMS has no NAV

A mutual fund has a NAV every working day, so anyone can compute returns however they wish. A PMS portfolio is customised and has no NAV — every client holds something different — so SEBI mandated TWRR to give a common yardstick. Meanwhile the adviser's own spreadsheet reports MWRR, because that is what the client takes home.

The dividend that arrives in April but is counted in March

The holding period return assumes that all income distributions are made at the end of the year. A dividend banked in April is treated as though it arrived eleven months later, earning nothing in between. It is a real limitation — and in spite of it, HPR remains widely used and generally accepted, and is the starting point of the performance measurement exercise.

One rupee, five years, and a chain of links

A wealth relative is the ending value of one unit of money — add one to each period return. Multiply them and you get the cumulative wealth relative: here 0.95 × 0.848 × 1.081 × 1.3075 × 1.1765 = 1.3396, meaning one rupee became Rs 1.3396 in five years. Raise it to the power of one-fifth, subtract one, and you have the annual compound rate: 6.021 per cent.

The lucky SIP investor

This investor put Rs 5,000 into the year that fell 5 per cent and Rs 25,000 into the year that rose 17.65 per cent. His MWRR of 15.15 per cent hugely exceeds the portfolio's TWRR of 6.021 per cent — and the whole nine-point gap belongs to his contribution pattern, not the manager's skill. Reverse the contributions and the MWRR would collapse while the TWRR stayed exactly where it is.

The path does not matter, only the ends

A characteristic of the compound return is that it depends only on the initial and final values of the portfolio, not on the path by which that value was realised. Whether the journey from Rs 1 lakh to Rs 1.34 lakh was smooth or violent, the geometric return is the same. That is exactly why it cannot be flattered by volatility — and why a fund manager can always increase the average annual ARITHMETIC return by increasing risk.

One definition for each purpose

Asking "what was the return?" is like asking "how far is it?" without saying by road, by rail or as the crow flies. Rate of return has many possible definitions; however, there is one possible definition for each purpose. Get clear about the purpose first — comparing managers, reporting to a client, estimating next year — and the right measure follows.

Key terms in this chapter

Allocation effect: Differential return from being overweight a sector that outperformed the benchmark or underweight an asset category that underperformed it.
Alpha return: The return generated by a portfolio over the required rate of return as per CAPM, also called Jensen alpha. It is a reward for bearing non-market or unsystematic risk.
Arithmetic Mean Return: The simple average of a series of returns, obtained by summing all returns and dividing by the number of values. It is the best estimate of a future year's return.
Benchmark: Defined by GIPS as an independent rate of return or hurdle rate forming an objective test of the effective implementation of investment strategy, representing the investment characteristics and approach of the portfolio.
Beta: The measure of systematic risk, relating the return of a stock or portfolio to the return on a market index. Portfolio beta is the weighted average of individual betas; above one means more volatile than the index.
Beta return: Beta multiplied by the market risk premium. It is a reward for bearing market risk.
Capital Asset Pricing Model: The most popular asset pricing model, holding that investments should be priced only for non-diversifiable market risk measured by beta. Required return equals the risk free rate plus beta times the market risk premium.
Cash drag adjusted return: Return computed on the entire capital contribution rather than only the deployed portion. Ignoring the drag that uninvested cash exerts mis-states the return, and the manager must report on the entire portfolio.
Compounded Annual Growth Rate: A measure of annual growth with compounding, computed as closing wealth divided by opening wealth, raised to the power of one over the number of years, minus one. It assumes income is reinvested in the same investment at that day's market price.
Credit risk: The risk that the borrower is not able to repay amounts on time to the lender, arising in the case of debt instruments following a deterioration in financial condition.
Currency risk: The risk that fluctuations in currency values enhance or reduce returns on foreign currency denominated investments. Rupee appreciation reduces rupee returns; in most cases the rupee depreciates and adds to returns.
Customised benchmark: A benchmark built from the manager's own investment universe when market-based indices do not meet the criteria. It meets the requirement of a valid benchmark but costs much more to construct and maintain.
Downside risk: Risk limited to losses or worse than expected outcomes only, captured by semi-variance or semi-standard deviation and their target versions.
Geometric Mean Return: The compound rate at which the initial sum accumulates to the final sum. It depends only on the initial and final values, not on the path, and is the only way to compare long-term accumulations.
Gross return: The total return generated on an investment before deduction of any fees, expenses or commissions, stated for a specified period.
Holding period return: Also called total return or point-to-point return. The income generated plus the change in value over the period, divided by the beginning value. It assumes all income distributions are made at the end of the year.
Hurdle rate: The threshold return above which a performance fee becomes payable. In the workbook example the required portfolio value is the capital contribution compounded at the hurdle rate.
Information Ratio: Also called the appraisal ratio. Portfolio return less benchmark return, divided by the standard deviation of those differences. It tests whether an observed alpha is due to skill or chance; the denominator, active risk, is nothing but tracking error.
Liquidity risk: The uncertainty introduced by the secondary market of an investment. Liquidity is the ease of converting an asset into cash at close to its economic worth; Treasury bills have almost none, while a piece of art has much.
Managers universe analysis: Peer group analysis, in which the median portfolio or the universe of investments with similar approach and strategies is the yardstick. Tracking firms rank similar portfolios on a risk-adjusted return measure.
Market timing: The ability of the fund manager to anticipate developments in the market and invest to take advantage of them. Most studies have shown it is not the factor resulting in better performance.
Modigliani and Modigliani measure: The M-squared measure of Franco and Lea Modigliani (1997), which levers or de-levers the portfolio to match the market standard deviation and then compares the adjusted return directly with the market return.
Money Weighted Rate of Return: The annual rate of return at which cumulative contributions grow over the measurement period. It is the same as the internal rate of return and depends on the timing of the cash flow.
Net return: Return calculated after adjusting gross return for fees, expenses and commissions. It is the return the investor actually makes.
Net selectivity: Fama's absolute measure of performance: the annualised fund return less the risk free yield, reduced by the standardised expected market premium times the total risk of the portfolio.
Performance attribution: The second phase of performance evaluation, dissecting return into that driven by the benchmark and the differential return, and establishing whether the difference was driven by the manager's skill or by luck.
Post-tax return: Pre-tax return multiplied by one minus the tax rate. Performance is communicated pre-tax because investors belong to different tax brackets, but what really matters to the investor is the post-tax return.
Selectivity: The ability of the fund manager to select securities that will generate extra returns. Study results on selectivity are mixed, with some managers having the ability.
Semi variance: A measure of the dispersion of returns below the mean return, identifying the variability of negative returns. It is not popularly used because it is proportional to variance for symmetric returns and asymmetric distributions are hard to forecast.
Sharpe Ratio: Portfolio return less the risk free return, divided by the portfolio standard deviation. Named after William Sharpe, it measures reward to variability, uses total risk, is the simplest and most widely used measure, but ignores diversification potential.
Sortino Ratio: Portfolio return less the risk free return, divided by the semi standard deviation. It adjusts excess return for downside risk and appeals to investors who view risk as the chance of losing money.
Systematic risk: Risk due to common factors such as interest rates, exchange rates and commodity prices. It cannot be diversified away though it can be hedged, and is measured by beta.
Time Weighted Rate of Return: The compound rate of growth over the stated period, computed by valuing the portfolio at every external cash flow and chain linking the sub period returns. It is unaffected by the timing of cash flows and equals the geometric return.
Total risk: Risk defined as variability in the expected return, captured by the variance and standard deviation of the estimated distribution of expected returns.
Tracking difference: The layman's approach, being simply the point-to-point difference between index return and fund return.
Tracking error: The standard deviation of the difference between the portfolio and its target benchmark total return, always calculated against the Total Returns Index. It arises from mismatches between the portfolio and benchmark risk profiles.
Treynor Ratio: Portfolio return less the risk free return, divided by portfolio beta. It measures return per unit of systematic risk and suits investors whose wealth is already well diversified.
Unsystematic risk: Risk due to sector specific or company specific factors, which can be diversified away. Alpha return is a reward for bearing it.
Wealth relative: The ending value of one unit of money, obtained by adding one to a period return. Multiplying the wealth relatives gives the cumulative wealth relative.

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Original explanatory writing based on the official NISM workbook for Series X-A, which is published and copyrighted by NISM. Check figures against the current edition at nism.ac.in.

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