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XXI-A · Chapter 10 of 12

Performance measurement and evaluation of PMS

Absolute vs CAGR, TWRR vs XIRR with a worked example, Sharpe, Treynor, alpha, information ratio, and SEBI/APMI…

9 min read+20 XP when done3-question check

Clients compare managers on returns, so the way a return is calculated decides who looks good. SEBI standardised PMS performance reporting precisely because managers used to pick the method that flattered them. This chapter gives you the methods, the SEBI rules and the risk-adjusted measures the exam asks you to compute.

Absolute, annualised and the two kinds of rate of return

An absolute return is the plain percentage change: ₹1 crore to ₹1.3 crore is 30%. An annualised return (CAGR) converts that to a yearly rate: over three years, (1.3)^(1/3) − 1 = 9.14% a year, not 10%, because compounding is at work. The simple average of yearly returns overstates growth whenever returns fluctuate; always use CAGR for multi-year figures.

The real complication is cash flow. When a client adds or withdraws money mid-period, two different questions arise. Money-weighted rate of return (MWRR, or XIRR) asks what the client actually earned on her rupees, so it is affected by the timing and size of her contributions. Time-weighted rate of return (TWRR) asks how the manager's decisions performed, so it strips out the effect of cash flows by chaining the returns of each sub-period between flows.

Formula
TWRR = [(1 + r1) × (1 + r2) × … × (1 + rn)] − 1, where each r is the return of a sub-period between cash flows
Worked example: TWRR versus simple return with a mid-year inflow
Opening value, 1 April₹1,00,00,000
Value on 30 September, before inflow₹1,10,00,000
Sub-period 1 return+10.0%
Client adds ₹50 lakh on 30 September; value becomes₹1,60,00,000
Value on 31 March₹1,52,00,000
Sub-period 2 return (152 ÷ 160 − 1)−5.0%
TWRR = 1.10 × 0.95 − 1+4.5%
Simple return on total money in: (152 − 150) ÷ 150+1.33%
Money-weighted return (XIRR), for comparison≈ +1.6%

The manager earned 4.5% on the money entrusted over the year; the client earned about 1.6% because she added a large sum just before the fall. Both numbers are true. SEBI requires portfolio managers to report TWRR, because it measures the manager; a client reconciling her own statement should look at XIRR.

Risk-adjusted performance

A 15% return at twice the market's volatility is not the same as 15% at half of it. The exam uses four measures:

  • Sharpe ratio = (Portfolio return − Risk-free rate) ÷ Standard deviation. Excess return per unit of total risk.
  • Treynor ratio = (Portfolio return − Risk-free rate) ÷ Beta. Excess return per unit of market risk; suits a diversified portfolio.
  • Jensen's alpha = Portfolio return − [Risk-free rate + Beta × (Market return − Risk-free rate)]. Return above what the market exposure alone would explain.
  • Information ratio = (Portfolio return − Benchmark return) ÷ Tracking error, where tracking error is the standard deviation of the difference between the two.
Worked example: portfolio 15%, risk-free 6%, standard deviation 18%, beta 1.1, market 12%
Excess return (15 − 6)9%
Sharpe ratio (9 ÷ 18)0.50
Treynor ratio (9 ÷ 1.1)8.18%
Expected return from CAPM: 6 + 1.1 × (12 − 6)12.6%
Jensen's alpha (15 − 12.6)+2.4%

Maximum drawdown (the worst peak-to-trough fall) and the Sortino ratio (which penalises only downside volatility) are also used in PMS factsheets. A high Sharpe with a deep drawdown usually means a short track record.

Alpha is the number a PMS is ultimately selling, so check how it was produced. A beta of 1.4 that lifted returns in a rising market is not skill; alpha isolates the part that market exposure does not explain. Over short periods alpha is noisy, which is why three- and five-year figures matter more than one-year figures, and why the exam asks for the CAPM step before the subtraction.

SEBI and APMI rules on reporting performance

The rules a distributor must know:

  • Performance is reported using TWRR, net of all fees and expenses charged to clients, including taxes and charges on transactions.
  • It is reported for each investment approach, aggregated across all clients in that approach, not from a model portfolio and not from a chosen set of accounts; firm-level performance is disclosed separately.
  • Trailing periods (one, three and five years and since inception) are shown against the benchmark, which must be chosen from the list APMI prescribes for the strategy's category and cannot be switched to suit results.
  • Any marketing material that cites performance must carry the same figures as the disclosure document and the standard disclaimer that past performance does not indicate future results; no guaranteed or assured returns may be mentioned.
  • Investment approach performance is also published through APMI, so clients can compare managers on a like-for-like basis.

A manager who shows you a model portfolio chart, a gross-of-fee number or a hand-picked period is not following the rules; treat it as a red flag, not a selling point.

Evaluating a PMS for a client

Returns are the beginning of due diligence, not the end. Look at consistency across periods, drawdown in bad years, dispersion between clients of the same approach, turnover (which drives tax and brokerage), style drift relative to the stated approach, and the fee drag under the fee illustration. Compare net TWRR with the benchmark's total return index, because price-only indices ignore dividends and flatter the manager. Finally, translate the number for the client: a 3% annual outperformance on ₹1 crore over ten years is roughly ₹70 lakh or more of extra wealth, and that is the scale against which a performance fee should be judged.

Exam trap
Exam trap. TWRR is what SEBI prescribes for the manager; XIRR or MWRR is what the client personally earned. Do not annualise a 30% three-year return as 10%; use the compound root. And compare against a total return index, since the benchmark's dividends count too.

If you can chain sub-period returns and compute Sharpe, Treynor and alpha from a short table, you have this chapter. The rules then tell you which number a manager is allowed to show.

Remember

  1. Annualise multi-year returns with CAGR = (End ÷ Start)^(1/n) − 1, never by simple division.
  2. TWRR chains sub-period returns between cash flows and measures the manager; XIRR/MWRR measures what the client earned.
  3. SEBI requires PMS performance in TWRR, net of all fees and expenses, aggregated across all clients of each investment approach.
  4. Sharpe = excess return ÷ SD; Treynor = excess return ÷ beta; alpha = return − [Rf + β(Rm − Rf)]; information ratio = active return ÷ tracking error.
  5. Benchmarks come from APMI's prescribed list per strategy category; compare against total return indices and show standard periods.
  6. Judge a PMS on consistency, drawdown, dispersion, turnover and fee drag, not on the best trailing number.
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