Chapter 20: Performance Measurement and Evaluation of Portfolio Managers
20.1 Rate of Return Computation: Time-Weighted Rate of Return (TWRR) vs. Money-Weighted Rate of Return (MWRR / IRR)
The Core Problem in Performance Measurement
Evaluating the authentic investment skill of a Portfolio Manager requires calculating the true rate of return earned by the portfolio while isolating the performance from external cash inflows (client capital injections) and outflows (client withdrawals) over which the manager exercises no discretion.
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| TWRR VS. MWRR (IRR) COMPARISON |
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| Metric | Time-Weighted Rate of Return (TWRR)| Money-Weighted Rate of Return (MWRR / IRR)|
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| Core Philosophy | Measures pure investment manager | Measures actual financial growth of the |
| | skill; ELIMINATES cash flow bias | investor's capital account |
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| Cash Flow Impact | Neutralized by breaking horizon | Highly sensitive to the timing and scale |
| | into sub-periods at each cash flow| of client cash inflows and withdrawals |
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| Regulatory Status | MANDATED by SEBI for all PMS | Used for private equity / closed-end funds|
| | performance disclosures and audits| where manager controls capital calls |
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Time-Weighted Rate of Return (TWRR) Formulation
TWRR calculates the compounded rate of growth of an initial rupee invested in the portfolio over the evaluation period by dividing the total evaluation horizon into $k$ sub-periods whenever an external cash flow occurs:
$$R_{\text{TWRR}} = \left[ (1 + R_1) \times (1 + R_2) \times \dots \times (1 + R_k) \right] - 1$$ Where the holding period return for each sub-period $t$ is: $$R_t = \frac{V_{\text{end}, t} - (V_{\text{start}, t} + C_t)}{V_{\text{start}, t} + C_t}$$ (assuming cash inflow $C_t$ occurs at the start of sub-period $t$).
Why SEBI Mandates TWRR for PMS Reporting:
Consider an investor who deposits ₹1 Crore at inception. The manager achieves a +50% return in Year 1 (portfolio reaches ₹1.5 Crore). Impressed, the client injects ₹10 Crore at the start of Year 2. In Year 2, the market declines by -10% (portfolio drops to ₹10.35 Crore).
- Under MWRR, because the client deposited massive capital right before the drawdown, the overall IRR is negative!
- Under TWRR, the manager's compounded skill is $(1 + 0.50) \times (1 - 0.10) - 1 = +35.0%$! TWRR correctly isolates the manager's genuine stock-picking skill from the client's poor cash flow timing.
Money-Weighted Rate of Return (MWRR / IRR)
The Money-Weighted Rate of Return is the internal rate of return (IRR) that equates the present value of all cash inflows to the present value of all cash outflows plus ending portfolio value:
$$\text{Initial Value} = \sum_{t=1}^T \frac{C_t}{(1 + r)^t} + \frac{\text{Ending Value}}{(1 + r)^T}$$ MWRR is appropriate when the manager controls the timing and magnitude of capital deployment (such as in Private Equity / AIF drawdown funds), but is fundamentally flawed for evaluating liquid open-ended PMS managers.
20.2 Risk-Adjusted Performance Ratios: Sharpe, Treynor, Jensen's Alpha, Sortino Ratio, and Information Ratio
The Need for Risk-Adjusted Evaluation
Evaluating an investment strategy solely on nominal return is dangerous because higher returns can simply reflect excess risk-taking (higher leverage, excessive small-cap exposure, or concentrated illiquid bets). Modern portfolio management evaluates managers on Risk-Adjusted Performance:
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| SUMMARY OF RISK-ADJUSTED PERFORMANCE RATIOS |
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| Metric | Mathematical Formula | Target Application |
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| Sharpe Ratio | (R_p - R_f) / sigma_p | Total Risk (Standard Deviation) |
| | | Best for evaluating complete portfolios |
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| Treynor Ratio | (R_p - R_f) / beta_p | Systematic Risk (Beta) |
| | | Best for evaluating diversified sub-funds |
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| Jensen's Alpha | R_p - [R_f + beta_p(R_m - R_f)] | CAPM Abnormal Return (Intercept) |
| | | Quantifies manager's pure value add |
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| Sortino Ratio | (R_p - MAR) / sigma_downside | Downside Risk (Penalizes only losses) |
| | | Superior for asymmetric / option returns |
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| Information Ratio | (R_p - R_b) / Tracking_Error | Active Return per unit of Active Risk |
| | | Evaluates skill relative to a benchmark |
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1. Sharpe Ratio vs. Treynor Ratio
- Sharpe Ratio: Uses total standard deviation $\sigma_p$ in the denominator. If a portfolio contains significant unhedged idiosyncratic risk, its Sharpe ratio will be penalized.
- Treynor Ratio: Uses systematic market risk (Beta $\beta_p$). Appropriate when the PMS portfolio is one of many components within a client's broader multi-asset wealth allocation.
2. Sortino Ratio and Downside Deviation
The Sharpe ratio treats upside volatility (unexpected massive gains) identically to downside volatility (painful capital losses). The Sortino Ratio replaces standard deviation with Downside Deviation ($\sigma_{\text{downside}}$) calculated relative to a Minimum Acceptable Return (MAR, often $R_f$ or 0):
$$\text{Sortino Ratio} = \frac{R_p - \text{MAR}}{\sigma_{\text{downside}}}$$ $$\sigma_{\text{downside}} = \sqrt{\frac{\sum_{t=1}^T \left[ \min(0, R_{pt} - \text{MAR}) \right]^2}{T}}$$ A strategy that delivers strong positive upside with strict capital preservation on the downside will achieve an exceptional Sortino ratio.
3. Information Ratio (IR)
Measures the consistency of an active manager's alpha per unit of tracking risk: $$\text{IR} = \frac{\bar{R}_p - \bar{R}b}{\text{Tracking Error}} = \frac{\alpha}{\sigma{(R_p - R_b)}}$$ An Information Ratio exceeding 0.50 denotes good active management; exceeding 1.00 reflects elite institutional performance.
20.3 Performance Attribution (Brinson-Fachler Model), Valuation Standards, and Global Investment Performance Standards (GIPS®)
Performance Attribution: Deconstructing the Sources of Alpha
Performance attribution seeks to explain why a portfolio outperformed or underperformed its designated benchmark. The most widely deployed institutional framework is the Brinson-Fachler Model, which decomposes total active return into three distinct components:
$$\Delta R = R_p - R_b = \text{Allocation Effect} + \text{Selection Effect} + \text{Interaction Effect}$$
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| BRINSON-FACHLER ATTRIBUTION COMPONENTS |
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| Allocation Effect | Return generated by over-weighting or under-weighting specific sectors |
| | relative to the benchmark: |
| | Alloc = sum (w_pi - w_bi) * (R_bi - R_b) |
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| Selection Effect | Return generated by picking superior stocks within a sector: |
| | Select = sum w_bi * (R_pi - R_bi) |
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| Interaction Effect| Joint impact of simultaneous sector weighting and stock selection decisions: |
| | Interact = sum (w_pi - w_bi) * (R_pi - R_bi) |
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Valuation Standards for PMS Portfolios
Under SEBI guidelines, portfolio managers must adhere to strict, objective valuation principles:
- Traded Equities: Valued at the official closing price on the primary stock exchange (NSE; secondary fallback to BSE).
- Illiquid / Thinly Traded Equities: If not traded for over 30 days, valued based on fair value guidelines (independent valuation by registered valuer using book value, earnings capitalization, and peer multiples).
- Debt Securities: Traded debt securities valued at clean traded prices plus accrued interest. Non-traded or illiquid bonds valued using matrix pricing benchmarks published by AMFI-approved rating agencies (CRISIL / ICRA).
Global Investment Performance Standards (GIPS®)
Created by the CFA Institute, GIPS® is an ethical standard for investment performance presentation used globally by institutional asset managers to ensure fair representation and full disclosure:
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| KEY PILLARS OF GIPS® COMPLIANCE |
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| Composites Construction | - All actual, fee-paying, discretionary portfolios must be |
| | included in at least one composite defined by mandate |
| | - Prevents 'cherry-picking' high-performing client accounts |
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| Complete Historical Record | - Minimum 5 years of compliant performance (or since inception|
| | if younger), building up to a 10-year compliant track record|
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| Survivorship Bias Elimination | - Terminated portfolios must be included in historical |
| | composites up to the last full period of management |
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| Valuation & Total Return | - Mandates trade-date accounting and Time-Weighted Returns |
| | including full dividend and interest reinvestment (TRI) |
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