Performance Measurement — the ground floor

Return alone tells half the story

People love to talk about return. "My PMS made 25% last year." Very few ask the next question: how much risk was taken to get it?

The workbook opens this chapter with exactly that warning. The human tendency is to focus on return "with little regard to the risk involved". Proper performance measurement must recognise both return and risk.

Many ways to measure return

The workbook says rate of return has many possible definitions, but one right definition for each purpose. So first decide why you are measuring. Then pick the measure.

Holding period return (HPR)

The simplest measure. Also called total return or point-to-point return.

It is the income earned plus the change in value, divided by the beginning value.

• Portfolio worth ₹1,00,000 on 1 April 2018 and ₹1,20,000 on 31 March 2019 → HPR 20%.
• Add ₹5,000 of dividend and interest received during the year → HPR 25%.

Its limitation: it assumes all income is received at the end of the year. Even so, it is widely used and is called the starting point of performance measurement.

Money-weighted versus time-weighted return

Now the investor adds money over several years. Two very different questions can be asked.

Money-weighted rate of return (MWRR) is simply the IRR of the investor's cash flows. It answers: what did my money actually earn? It depends on the timing of the cash flows.

The workbook's example: an investor puts in ₹5,000, ₹10,000, ₹15,000, ₹20,000 and ₹25,000 at the start of 2015 to 2019 — ₹75,000 in all. The yearly returns are −5.00%, −15.20%, 8.10%, 30.75% and 17.65%. The money grows to ₹1,05,920.31. MWRR = 15.15%.

Now reverse the order — ₹25,000 first, ₹5,000 last. Same ₹75,000, same yearly returns. The ending value becomes ₹1,07,900.97 and MWRR drops to 10.21%. Nothing about the manager changed. Only the investor's timing did.

Time-weighted rate of return (TWRR) strips that timing out. The portfolio is valued every time there is an external cash flow, a return is worked out for each sub-period, and the sub-period returns are chain-linked. For the same five years the TWRR is 6.021% — and it is the same whichever order the money came in.

The GIPS glossary says TWRR "removes the effects of external cash flows, which are generally client driven, and best reflects the portfolio manager's ability to manage assets according to a specified strategy or objective."

What SEBI requires on TWRR

• SEBI (Portfolio Managers) Regulations, 2020 require discretionary portfolio managers to disclose performance using TWRR for the immediately preceding three years.
• Portfolio managers shall disclose the performance of benchmark indices in the periodical reports to clients.
• They may pick any index that suits the client's objective. The workbook's examples are BSE Sensex, CNX Nifty, BSE 100, BSE 200 and CNX 500. Any later change of benchmark must be recorded and justified.
• They may show more than one index, and may add their own view on performance.
• The Boards of portfolio managers may review each client's performance separately and should take corrective action where needed.

SEBI has also clarified that portfolio managers shall:

1. Include all cash holdings and investments in liquid funds when calculating performance.
2. Report performance net of all fees and all expenses (including taxes).
3. Clearly disclose in marketing material any change in investment approach that may affect performance.
4. Ensure performance in marketing material and on the website is the same as reported to SEBI.
5. Ensure firm-level performance equals the combined performance of all portfolios managed.
6. Carry a disclaimer that performance information is not verified by SEBI.

Arithmetic versus geometric mean

Two portfolios, ₹1,00,000 each.

Choice 1 "averages" 25% and made nothing. Choice 2 averages 10% and made ₹21,000. The investor is clearly better off with Choice 2.

• The arithmetic mean is the simple average. It is the best estimate of a single future year's return.
• The geometric mean is the compound rate. It depends only on the starting and ending values, not the path. It is the only way to compare long-term accumulations.
• For one year both are identical. Over longer periods geometric is always lower than arithmetic, unless every yearly return is exactly the same.

Gross, net, pre-tax, post-tax

• Gross return is before fees, expenses and commissions. Net return is after them — it is what the investor actually makes. Focusing on gross return can be misleading.
• Pre-tax return is how performance is normally communicated, because investors sit in different tax brackets. Post-tax return is what really matters to the investor.
• Post-tax = Pre-tax × (1 − tax rate). The workbook's example: 5% pre-tax with 15% capital gains tax gives 4.25% post-tax.

CAGR and annualising

CAGR is the constant yearly growth rate that takes the opening value to the closing value. It assumes income is reinvested at that day's market price. Formula: (A ÷ P)^(1/t) − 1.

Annualising reports returns on a yearly basis so they can be compared. The workbook says the method is the same as CAGR or geometric mean. One rule to remember: if the measurement period is less than a year, it is inadvisable to annualise, because that extrapolates a part-year to a full year.

Cash drag

Managers do not always invest all the money. The workbook notes that some portfolio managers were ignoring the cash component when computing returns. That mis-states the return.

Example: ₹100 lakh given, ₹75 lakh in equity earning ₹7.5 lakh, ₹25 lakh in liquid funds earning 4%. Ignoring the cash, return looks like 10%. Counting it honestly, it is 8.5% on ₹100 lakh.

Alpha and beta return

The CAPM splits risk into systematic (cannot be diversified) and unsystematic (can be diversified). Investors are paid only for systematic risk, measured by beta.

Required return = Rf + β × (Rm − Rf)

Alpha is what the portfolio earns above that required return. This is also called Jensen alpha. Beta return is a reward for bearing market risk. Alpha return is a reward for bearing non-market risk.

Some professionals use "alpha" for something simpler — portfolio return minus benchmark return. Know both uses.

Portfolio return is the weighted average of the returns of the securities in it.

Measuring risk

The workbook calls risk a decisive factor in selecting a portfolio manager. Risk can mean two things:

• Total risk — variability around the expected return. Measured by variance and standard deviation.
• Downside risk — only the bad outcomes. Measured by semi-variance / semi-standard deviation and target semi-variance.

Standard deviation

The square root of variance. Higher standard deviation means higher risk. It is the most widely used risk measure and works the same way for bonds, growth stocks or anything else.

The workbook's reading of it, for a portfolio with expected monthly return 2% and standard deviation 3.27%:

Semi-variance looks only at returns below the mean. Target semi-variance looks at returns below a target. It is not popular in practice: for symmetric returns it adds nothing, and asymmetric distributions are very hard to forecast.

Portfolio risk is not a simple average

Portfolio standard deviation is not the weighted average of individual standard deviations — except when the assets are perfectly positively correlated, which is practically impossible. It depends on the weights, the individual standard deviations and, most importantly, the correlation between them. The poorer the correlation, the lower the portfolio risk.

Systematic risk, unsystematic risk and beta

Systematic risk comes from common factors — interest rates, exchange rates, commodity prices. It cannot be diversified away, though it can be hedged. It is measured by beta.

Unsystematic risk is sector- or company-specific. It can be diversified away.

Beta = Covariance(market return, portfolio return) ÷ Variance(market return). It needs data over a reasonably long period, say 3 to 5 years.

• Beta above 1 → more volatile than the index.
• Beta below 1 → less volatile than the index.
• Portfolio beta is the weighted average of individual betas. Stocks with betas 1.2 and 1.1 held 60:40 give a portfolio beta of 1.16.

Notice the contrast: beta averages linearly; standard deviation does not.

Tracking error

Tracking error is the standard deviation of the difference between portfolio return and benchmark return. Lower tracking error means the portfolio hugs the index more closely. It is always calculated against the Total Returns Index (which includes dividends). It arises mainly from mismatches between the portfolio's risk profile and the benchmark's.

Risk-adjusted return: five ratios

A few points the workbook stresses:

• Sharpe is named after William Sharpe and measures reward to variability. It is the simplest to compute and most widely used. Its disadvantage: it ignores the diversification potential of the portfolio.
• For a completely well-diversified portfolio, Sharpe and Treynor give identical rankings. Any difference in ranking comes from differences in diversification.
• Higher is better for Sharpe, Treynor and Sortino.
• M² was derived by Franco Modigliani and his granddaughter Lea Modigliani (1997). They lever or de-lever the portfolio until its risk matches the market's, then compare returns directly.

Evaluating performance: benchmarks and peers

Performance evaluation is a relative concept. It tells an investor whether the manager beat what a passive indexed strategy could have given, and whether the fees are justified.

GIPS defines a benchmark as "an independent rate of return (or hurdle rate), forming an objective test of the effective implementation of investment strategy."

A good benchmark:

1. Has clearly defined constituents and weights.
2. Is investable — you could hold it passively.
3. Is consistent with the portfolio's investment approach (blue-chip portfolio → blue-chip benchmark; value style → value benchmark).
4. Has the same risk-return profile as the portfolio.
5. Is measurable.

When no market index fits, a customised benchmark can be built from the manager's own investment universe. Advantage: it meets the tests of a valid benchmark. Disadvantage: much higher cost to construct and maintain than paying for a market index.

Managers' universe analysis (peer group analysis) uses the median portfolio of managers with a similar approach as the yardstick.

Performance attribution

This is the second phase of evaluation. The dominant framework is the one propounded by Fama. It splits the extra return into:

• Allocation effect — overweighting segments that did well, underweighting those that did badly.
• Selection effect — picking better securities within a segment.
• Interaction effect — the part caused by doing both at once.

The goal: find out whether the extra return came from skill or luck.

Foreign investments and currency risk

An Indian investor in foreign securities must convert returns back to rupees. The workbook's example: ₹50 lakh into a US equity fund at ₹70 per dollar. The fund returns 15%. The rupee appreciates to ₹65. The rupee return is only 6.79%, not 15%. The gap is roughly the rupee's appreciation. This is currency risk.

Reporting to the investor

Under SEBI's Portfolio Managers regulations, the portfolio manager must send a periodic report as agreed in the contract, but not exceeding three months, and whenever the client asks. It must contain:

• (a) composition and value of the portfolio, securities, goods, cash balance and aggregate value
• (b) transactions during the period, with dates and purchase/sale details
• (c) benefits received — interest, dividend, bonus shares, rights shares
• (d) expenses incurred in managing the portfolio
• (e) risks foreseen by the portfolio manager
• (f) defaults in coupons or payments on debt securities and downgrades to default rating
• (g) commission paid to distributors for that client

Two presentation rules:

• When advertising or publishing performance of an investment approach: show TWRR of the investment approach with the trailing return of the selected benchmark.
• When reporting to an investor: show XIRR for each investment approach the investor is in, with the minimum, maximum and median XIRR across all investors in that approach, plus the approach's TWRR and benchmark return separately — and a disclaimer that the investor's performance may differ because of (a) timing of inflows and outflows and (b) differences in portfolio composition due to restrictions and constraints.

Valuation

APMI (Association of Portfolio Managers in India) prescribes standardised valuation norms. Debt and money market securities must be valued as per these norms, using only APMI-empanelled valuation agencies. But the ultimate responsibility for fair valuation stays with the portfolio manager.

Choosing a portfolio manager

Due diligence means quantitative and qualitative analysis of reputation, key people and operations. The workbook's order: first draft the investment policy statement and decide the asset allocation, then pick the manager who offers the best means to implement it. Judge philosophy, approach, process, style, past performance against a benchmark or peers, contract terms — and fees and costs.

GIPS

The Global Investment Performance Standards (GIPS®) are ethical standards for firms presenting performance to prospective clients. They bring uniformity and comparability regardless of geography. Firms claiming compliance must follow rules on both calculation and display. GIPS mandates TWRR — and SEBI's 2020 regulations also prescribe TWRR.

The GIPS Advertising Guidelines do not replace the full standards. They apply only to firms that already comply firm-wide and claim it. They set the minimum disclosures for an advert carrying a compliance claim — firm description, how to get a compliant presentation, the compliance statement, strategy description, period-to-date results, 1-, 3- and 5-year annualised returns or 5 years of annual returns, gross/net of fees, benchmark total return, currency, leverage and derivatives use, and non-compliant periods before 1 January 2000. Periods of less than one year must not be annualised.