Performance Measurement and Evaluation of Portfolio Managers

1Measure risk as well as return

People tend to look only at the return and ignore the risk taken to earn it. Proper evaluation looks at both return and risk.

2Holding period return

HPR (total or point-to-point return) = (income + ending value − beginning value) ÷ beginning value.

Example A portfolio grows from ₹1,00,000 to ₹1,20,000. HPR = 20%. If ₹5,000 of dividends and interest were also received, HPR = (5,000 + 20,000) ÷ 1,00,000 = 25%.

HPR assumes income arrives at the end of the period. Even so, it is the widely accepted starting point for measuring performance.

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3Money-weighted vs time-weighted return

The workbook uses one five-year example for both measures:

• annual returns of −5%, −15.2%, +8.1%, +30.75% and +17.65%;
• contributions of ₹5,000, ₹10,000, ₹15,000, ₹20,000 and ₹25,000 at the start of each year;
• a final value of ₹1,05,920.

MWRR (money-weighted rate of return) is the IRR of all the contributions and the final value. Here it is ≈ 15.15%. It depends on the timing and size of cash flows. In this case it is high because most of the money arrived before the strong years.

TWRR (time-weighted rate of return) removes the effect of cash flows:

1. Value the portfolio at every external cash flow.
2. Calculate each sub-period return.
3. Convert each return to a wealth relative (1 + r).
4. Multiply the wealth relatives together.
5. Annualise the product.

Example 0.95 × 0.848 × 1.081 × 1.3075 × 1.1765 = 1.3396. TWRR = 1.3396^(1/5) − 1 ≈ 6.02%. This is the geometric return. Sub-periods shorter or longer than a year need annualising.

Who uses which

• SEBI PMS Regulations, 2020: discretionary portfolio managers must report performance using TWRR for the preceding three years. PMS portfolios are customised and have no NAV, so TWRR keeps reporting uniform.
• Mutual funds publish a daily NAV, so returns can be calculated either way.
• Adviser and wealth-management software usually reports MWRR, because clients add and withdraw money many times.
• TWRR judges the manager; MWRR shows what the client actually earned.

Exam trap TWRR is unaffected by when the investor added or withdrew money. MWRR is affected.

Remember

• MWRR = IRR, which depends on cash flows.
• TWRR = chain-linked geometric return; SEBI requires it for discretionary PMS.

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4Arithmetic vs geometric mean

Example Choice 1 returns −50% then +100%. Choice 2 returns +10% then +10%.

• Arithmetic mean (AMR): 25% vs 10%.
• Geometric mean (GMR): 0% vs 10%.

₹1,00,000 ends at ₹1,00,000 under choice 1 and at ₹1,21,000 under choice 2. Choice 2 is clearly better.

• AMR is the simple average of yearly returns. It is the best estimate of a single future year's return.
• GMR is the compound rate that turns the starting value into the ending value. It depends only on the start and end values, not the path in between. It is the right measure for long-term accumulation.
• Over one year the two are equal. Over longer periods GMR < AMR, unless every year's return is the same.
• A manager can raise the arithmetic average by taking more risk without improving the final result.

The workbook says GMR is the measure for estimating terminal wealth.

Remember

• Geometric ≤ arithmetic.
• Use geometric for multi-year performance.

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5Gross vs net, and pre-tax vs post-tax

Gross return is before fees, expenses and commissions. Net return is after them, and it is what the investor actually earns.

Example (PMS): ₹1 crore earns 20%, giving ₹1.2 crore gross. The charges:

• other expenses 0.5% of gross value: ₹60,000;
• fixed fee 1.5% on the average of the opening and closing values (₹1.1 crore): ₹1.65 lakh;
• performance fee 20% of value above a 10% hurdle, no catch-up: 20% × (₹1.1775 crore − ₹1.10 crore) = ₹1.55 lakh;
• exit load 2%: ₹2.324 lakh.

Net value = ₹1,13,87,600. Gross return 20%; net return 13.88%.

Pre-tax vs post-tax

• Performance is reported pre-tax, because investors are in different tax brackets. Advisers convert it for each client.
• Post-tax return = pre-tax return × (1 − tax rate). Pre-tax return = post-tax ÷ (1 − tax rate).
• For example, a 5% pre-tax return with 15% tax gives 4.25% post-tax.
• Investors decide on the basis of post-tax returns.

Remember

• The net return is what the investor keeps.
• Post-tax = pre-tax × (1 − t).

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6CAGR and annualising

CAGR = (closing value ÷ opening value)^(1/t) − 1. It assumes income is reinvested at the market price on the day it is received.

Example ₹1,00,000 grows to ₹1,33,960 in 5 years, using the same returns as the TWRR example. CAGR = 6.02%, which is the same as the TWRR.

Annualising: chain-link the period returns, then raise the product to 1 ÷ number of years.

Example Returns of +15.5%, +9.5% and −6.9% turn 100 into 117.75. Annualised return = 1.1775^(1/3) − 1 ≈ 5.60%.

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7Cash drag

Returns must be calculated on the whole capital contributed, including any money left uninvested.

Example ₹100 lakh is contributed. ₹75 lakh goes into equity and earns ₹7.5 lakh (10%). ₹25 lakh sits in a liquid fund earning 4% (₹1 lakh).

• Ignoring cash drag: 7.5 ÷ 75 = 10%.
• Correct figure: (₹7.5 lakh + ₹1 lakh) ÷ ₹100 lakh = 8.5%.

The workbook gives the rupee total as "₹85,000". It should be ₹8.5 lakh.

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8Alpha, beta and portfolio return

CAPM splits risk into two parts:

• systematic risk, which cannot be diversified and is measured by beta;
• unsystematic risk, which can be diversified away and so earns no reward.

Required return = Rf + β × (Rm − Rf).

Jensen's alpha = actual return − CAPM required return.

Example A portfolio returns 25%. The market returns 15%, β = 1.5 and Rf = 5%.

• Risk-free part: 5%.
• Beta return: 1.5 × (15 − 5) = 15%.
• Alpha: 25 − (5 + 15) = 5%.

Some people call the simple excess over the benchmark (25 − 15 = 10%) "alpha".

Beta return rewards market risk; alpha rewards non-market risk (the manager's active bets).

Portfolio return is the weighted average of the securities' returns. For example: 15%×0.3 + 10%×0.2 + 12%×0.2 + 18%×0.3 = 14.3%.

Remember

• Jensen's alpha is the return above CAPM's required return.
• Beta return = β × market risk premium.

9Risk measures

Total vs downside risk

• Total risk is all variability around the expected return. It is measured by variance and standard deviation.
• Downside risk counts only bad outcomes. It is measured by semi-variance or semi-SD (dispersion below the mean) and target semi-variance (dispersion below a target return).

Portfolio risk is not the weighted average of individual SDs, except when correlation is perfectly +1. It depends on the weights, the individual SDs and, above all, the correlations. Covariance = correlation × σ₁ × σ₂. The lower the correlations, the lower the portfolio risk.

Market risk affects all investments. It is measured by beta and can be hedged but not diversified away.

Interpreting volatility

• Standard deviation is the most widely used risk measure. It works for any asset type and lets you compare funds with similar objectives over the same period.
• Semi-variance adds nothing when returns are symmetric, and asymmetric distributions are hard to forecast, so it is used less.

Tracking error is the standard deviation of the difference between portfolio and benchmark returns. It is always measured against the Total Return Index, which includes dividends. Lower tracking error means the portfolio stays closer to the index. It mainly arises from differences in risk profile between the portfolio and the benchmark.

Tracking difference is the simple point-to-point gap between the fund's return and the index's return.

Systematic vs unsystematic risk

• Systematic: common factors such as interest rates, exchange rates and commodity prices. Measured by beta; can only be hedged.
• Unsystematic: sector- or company-specific. It can be diversified away; alpha is the reward for bearing it.

Beta measures a portfolio's sensitivity to the market index. Portfolio beta is the weighted average of the individual betas. For example, 0.6×1.2 + 0.4×1.1 = 1.16.

• β > 1: more volatile than the market.
• β < 1: less volatile than the market.

Other risks

• Liquidity risk: how hard it is to convert to cash near fair value. A T-bill is nearly instant; art can take a long time and sell well below its worth.
• Credit risk: the borrower fails to repay on time. It applies to debt.

Exam trap Tracking error is the SD of return differences. Tracking difference is the simple gap in returns.

Remember

• Portfolio beta is a weighted average; portfolio SD is not.

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10Risk-adjusted ratios

Higher is better for every ratio. All the inputs must cover the same period, usually annualised.

Example (Sharpe and Treynor): Rp = 10.5%, Rf = 5.5%, σ = 6.5%, β = 1.

• Sharpe = 5 ÷ 6.5 ≈ 0.77.
• Treynor = 0.05 ÷ 1 = 0.05, i.e. 5 percentage points of excess return per unit of beta.

Example (M²): Portfolio return 35%, SD 42%. Market return 28%, SD 30%. Rf = 6%.

• Put 30 ÷ 42 = 0.714 in the portfolio and 0.286 in T-bills, so the mix has the market's 30% SD.
• Return of the mix = 0.714×35% + 0.286×6% ≈ 26.7%.
• That is 1.3% below the market, so the portfolio underperformed on a risk-adjusted basis.

Sharpe vs Treynor: for a fully diversified portfolio the two give the same ranking, because total risk then equals systematic risk. For a poorly diversified portfolio, Treynor can rank it higher, because it ignores unsystematic risk. Any difference in rankings reflects differences in diversification.

Remember

• Sharpe uses SD; Treynor uses beta; Sortino uses downside SD; the information ratio uses tracking error.

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11Benchmarking and peer groups

Performance evaluation is relative. It asks whether the manager added value beyond a passive index and whether the fees are justified.

GIPS defines a benchmark as an independent rate of return (or hurdle) that objectively tests how well the strategy has been implemented.

A good benchmark:

• has clearly defined constituents and weights;
• is investable, so passive exposure to it is possible;
• is consistent with the portfolio's approach (blue-chip vs blue-chip, value vs value);
• has the same risk–return profile as the portfolio;
• is measurable.

Customised benchmarks are built from the manager's own investment universe when no market index fits. They are valid but costly to build and maintain. NSE and BSE keep launching new indices, and custom benchmarks can be obtained from index providers.

Benchmarking errors

• using an unrepresentative index;
• not changing the benchmark when the style changes;
• using an index that is not investable;
• using an index whose constituents change too often;
• lacking data, especially Total Return Index data.

Manager universe (peer group) analysis compares the portfolio with the median of portfolios that share a similar approach. Tracking firms rank peers on risk-adjusted measures.

Remember

• Benchmark tests: defined, investable, consistent, same risk profile, measurable.

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12Performance attribution

Performance attribution splits the return into benchmark return plus differential return, then finds where the differential came from, to tell skill from luck.

• Allocation effect: being overweight in sectors or assets that beat the benchmark, or underweight in those that lagged.
• Selection effect: holding stocks that did better than the benchmark, or avoiding those that did worse.
• Market timing vs selectivity: most studies find market timing does not explain superior performance; evidence on selectivity is mixed, with some managers showing skill.
• Fama's net selectivity is an absolute measure: (fund return − Rf) minus the market premium scaled by the portfolio's total risk. It is the excess return that could not have been earned from the market portfolio.

Currency effect on overseas investments

Example ₹50 lakh is invested at ₹70/$, buying $71,428.57. The US fund returns 15%, so the holding grows to $82,142.86. Meanwhile the rupee appreciates to ₹65/$, making the holding worth ₹53.39 lakh. The rupee return is 6.79%, not 15%. The gap is roughly the rupee's appreciation.

The rupee usually depreciates, which adds to returns on foreign assets. Gold returns in rupees, for example, combine the international gold price with rupee depreciation.

Remember

• Attribution = allocation + selection.
• A stronger rupee cuts returns on foreign assets.

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13How PMS performance must be reported

To stop managers showing only their best accounts or hypothetical "model" returns, SEBI has standardised PMS performance reporting:

• Returns are calculated using the time-weighted rate of return (TWRR), which removes the effect of the client's own deposits and withdrawals, so it measures the manager's skill.
• Returns are reported net of all fees and expenses, and include cash and liquid fund holdings.
• Performance is reported for each investment approach, covering all client portfolios in it, including portfolios of clients who have since left.
• Each investment approach is compared with a benchmark chosen from a set of broad-based benchmarks for its strategy (equity, debt, hybrid or multi-asset) selected by APMI. APMI publishes the performance of investment approaches against these benchmarks, so clients can compare managers.
• Firm-level performance figures are audited every year.

The money-weighted return (IRR or XIRR) still matters to the client, because it shows the return on the client's actual cash flows, but it reflects the client's timing as well as the manager's skill.

Exam trap TWRR judges the manager. Money-weighted return (XIRR) shows the investor's own experience.

Remember

• PMS reporting: TWRR, net of all fees, all portfolios in the approach, APMI-selected benchmark.

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