The big picture
A return percentage is useful only when its inputs and meaning are clear. Investors often compare a broker balance, an index movement and a fund return as though they were the same measure. This topic builds a consistent calculation chain from transaction records to a reproducible result. All numerical examples are mathematical teaching illustrations, not actual PSX returns, prices or investment promises.
Core concepts
Learning objectives
- Separate price change, income and external contributions.
- Calculate cumulative and annualised returns correctly.
- Choose a method that recognises deposits and withdrawals.
- Compare results with a suitable benchmark and purchasing-power measure.
Define the return question
1.1 Price, income and total return
A price return measures the change in a security’s price. Total return also includes cash distributions under a stated reinvestment convention. A portfolio balance includes more: contributions, withdrawals, charges and possibly unsettled cash. Before using a percentage, define the owner, period, currency and included cash flows. Otherwise two correct-looking calculations may answer entirely different questions.
1.2 Balance growth is not investment return
For one holding without external flows, a simple holding-period return is (ending value − beginning value + distributions) ÷ beginning value. Match quantities and adjust consistently for splits, rights and other corporate actions. If distributions have already been included in ending cash, adding them again double-counts income. An increase created by a fresh deposit must be separated from investment performance.
Step-by-step method
- Write the return definition and measurement dates.
- Reconcile opening quantity, corporate actions and closing quantity.
- Identify whether distributions are already included.
Illustration: an investment worth PKR 100,000 becomes PKR 110,000 and pays PKR 5,000 held outside it. Before costs and tax, total return is 15%; the price-value change alone is 10%.
Calculate costs and spendable results
2.1 Gross and net return
Gross performance and investor experience differ because brokerage, market charges, spreads, fund expenses and taxes may apply. Start from the actual contract notes and statements. Some costs are paid separately; others are reflected in a quoted net asset value or reported return. Deducting an expense twice understates the result, while overlooking entry and exit costs overstates it.
2.2 Tax records and consistent treatment
Keep investment performance separate from legal taxable gain. The tax calculation may use prescribed basis and matching rules rather than your preferred economic method. For a net-return comparison, use actual attributable deductions or clearly labelled estimates awaiting verification. Do not assume one tax percentage covers every acquisition cohort, product or investor. State which taxes are included and which remain unresolved.
Step-by-step method
- Reconcile charges to documentary evidence.
- Identify costs already reflected in reported returns.
- Calculate a separate after-cost result with an explicit tax scope.
If a published fund return is already net of recurring expenses, do not subtract its expense ratio again. Entry loads and investor-specific taxes may still need separate treatment.
Compound returns across time
3.1 Geometric growth and CAGR
Returns compound multiplicatively. Multiply each period’s growth factor, then subtract one. Adding annual percentages ignores the changing capital base. The compound annual growth rate, or CAGR, is (ending value ÷ beginning value) raised to 1/years, minus one, when there are no intervening external flows. It gives an equivalent smooth annual rate, not the actual experience in each year.
3.2 Recovery after a loss
Volatility creates an important asymmetry: a percentage loss requires a larger percentage gain to recover. A 20% loss leaves 80% of the original capital; returning to the starting point requires 25% on that reduced base. This arithmetic does not predict market recovery. Annualising a very short period can also produce an impressive number unsupported by a durable record.
Step-by-step method
- Use growth factors for each period.
- Apply CAGR only with compatible dates and cash-flow assumptions.
- Show drawdowns and annual variation alongside annualised return.
Illustration: +20% followed by −20% changes PKR 100,000 to PKR 96,000. The two-year cumulative result is −4%, despite an arithmetic average of zero.
Account for deposits and withdrawals
4.1 Time-weighted return
When external cash enters or leaves, the simple beginning-to-ending formula can mislead. A time-weighted approach values the portfolio around external flows, computes subperiod returns and links the growth factors. It is useful for evaluating the investment process while reducing the effect of the investor’s contribution timing. Accurate valuations around flows are necessary; a rough month-end shortcut should be labelled.
4.2 Money-weighted return and cash-flow dates
A money-weighted return finds the rate consistent with the amounts and dates invested and withdrawn. Dated internal-rate-of-return methods can describe the investor’s actual cash experience. Their sign convention and date inputs must be correct, and unusual flow patterns can create multiple or unstable solutions. Report the method rather than presenting one percentage as the only possible definition of performance.
Step-by-step method
- List every external cash flow with its date.
- Keep dividends inside performance, not automatically as new contributions.
- Choose and disclose time-weighted or money-weighted measurement.
A large deposit near year end can double an account balance without doubling investment wealth. Date the deposit and use an appropriate cash-flow-aware calculation.
Compare fairly and communicate the result
5.1 Benchmarks, inflation and currency
A benchmark should match the asset exposure, dates, currency and dividend convention. A dividend-inclusive portfolio is not directly comparable with a price-only index without explanation. Real return adjusts purchasing power: (1 + nominal return) ÷ (1 + inflation) − 1. Foreign-currency obligations require a further currency-matched view. Do not mix a calendar-year return with a different inflation interval.
5.2 A reproducible performance report
Finish with opening and ending values, dated external flows, income, costs, taxes, method and source references. Include drawdown and concentration context because the same return can come with very different risks. Separate verified outcomes from forecasts and teaching examples. A reader should be able to reproduce the working and see unresolved records instead of accepting a screenshot as proof.
Step-by-step method
- Match benchmark assumptions and dates.
- Calculate real return with a compatible inflation measure.
- Publish the inputs, method and important risk context.
A return statement labels the result “after brokerage, before personal tax,” includes cash-flow dates and identifies its benchmark. That description is more informative than an unexplained annual percentage.
Compounding: equal percentage moves do not cancel
| Measure | Value |
|---|---|
| Starting capital | 100,000 PKR |
| After +20% | 120,000 PKR |
| After subsequent −20% | 96,000 PKR |
Reference table
| Question | Measure |
|---|---|
| What did price do? | Price return |
| What did ownership earn including distributions? | Total return |
| What remains after specified deductions? | Net return |
| How did the strategy perform across flows? | Time-weighted return |
| What did my dated cash investment earn? | Money-weighted return |
Glossary of key terms
- Annualisation
- Expressing a period’s result as an equivalent annual rate under stated assumptions.
- Benchmark
- A relevant reference portfolio or index for comparison.
- CAGR
- Equivalent compounded annual growth rate between compatible endpoints.
- Drawdown
- Decline from an earlier portfolio peak.
- External flow
- A contribution or withdrawal crossing the portfolio boundary.
- Money-weighted return
- Return reflecting invested amounts and the timing of external flows.
- Time-weighted return
- Linked subperiod return designed to reduce the effect of external-flow timing.
Frequently asked questions
Is a rising balance always profit?
No. New contributions can raise the balance without producing investment gains.
Can annual percentages be added?
Use multiplied growth factors for cumulative performance. Addition usually ignores the changing base.
Is CAGR the return in every year?
No. It is an equivalent smooth rate and can hide substantial volatility.
Which method is best?
Choose the method suited to the question and disclose it; manager evaluation and personal cash experience differ.
Common pitfalls
| Common mistake | A better approach |
|---|---|
| Double-counting dividends | Check whether ending value already includes the distribution. |
| Ignoring external cash flows | Record dates and use a compatible method. |
| Comparing unlike benchmarks | Match income, currency, exposure and period. |
| Presenting gross return as spendable | Show costs and tax scope explicitly. |
Your learner task
Build a return worksheet from a small set of your own verified records. Reconcile opening capital, external flows, income, charges and ending value. Show a cumulative result, an annualised figure when appropriate, and a clear explanation of limitations.
Sources & verification
Use the linked documents to check the factual and regulatory context. Source dates and limitations are stated where relevant. Educational examples and analytical frameworks are not personalised recommendations.
- PSX · Guide to investors ↗
Market institutions and investor process; verify current rules for the selected account.
- PSX · Data Portal and issuer disclosures ↗
Official filings for company research; current market values are not reproduced here.
Editorial review: 22 October 2026