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Formula sheet/NISM Series X-A: Investment Adviser (Level 1)/Portfolio Construction, Performance Monitoring and Evaluation
[ PORTFOLIO CONSTRUCTION, PERFORMANCE MONITORING AND EVALUATION ]

Time-Weighted (TWRR) vs. Money-Weighted Rate of Return (MWRR)

TWRR(Geometric Linking):Cumulative Wealth Relative=∏(1+Rt)  ⇒  TWRR=[∏(1+Rt)]1/n−1TWRR (\text{Geometric Linking}): \text{Cumulative Wealth Relative} = ∏ ( 1 + R_{t} ) \;\Rightarrow\; TWRR = [ ∏ ( 1 + R_{t} ) ]^{1/n} - 1
MWRR(IRR):Solve for r in:∑[Ct/(1+r)t]=0MWRR (IRR): \text{Solve for r in}: \sum [ C_{t} / (1 + r)^{t} ] = 0
Excel: =XIRR(values, dates)
Arithmetic(AMR)vs.Geometric Mean(GMR):AMR=∑Rt/n∣GMR=[∏(1+Rt)]1/n−1(GMR≤AMR)Arithmetic (AMR) vs. \text{Geometric Mean} (GMR): AMR = \sum R_{t} / n\quad\Big|\quad GMR = [ ∏ (1 + R_{t}) ]^{1/n} - 1 (GMR \le AMR)
Variables

SEBI mandates TWRR for evaluating PMS fund manager performance as it eliminates the distortion of client cash inflow/outflow timings. RtR_{t}: Sub-period return; n: Number of periods; CtC_{t}: Cash flow at time t; r: IRR being solved for.

Worked examples
Time-Weighted Rate of Return (TWRR) vs. MWRR (IRR)

An investor begins with Rs 5,000 in Year 0. In Year 1, the portfolio drops by -5.0% (Value = Rs 4,750). At the start of Year 2, she adds Rs 10,000 (Total = Rs 14,750), and portfolio earns -15.2% (Value = Rs 12,508). In Year 3, she adds Rs 15,000 (Total = Rs 27,508) and earns +8.1% (Value = Rs 29,736). In Year 4, she adds Rs 20,000 and earns +30.75% (Value = Rs 65,030). In Year 5, she adds Rs 25,000 and earns +17.65% (Ending Value = Rs 1,05,920.31). Calculate the 5-year TWRR and compare with MWRR.

Advanced Risk-Adjusted Ratios (Sortino & Modigliani-Modigliani M^2)

A fund delivers an annualized return of 18.0% with total Standard Deviation of 16.0%, downside semi-standard deviation (loss volatility) of 8.0%, and Beta of 1.20. The market index returns 14.0% with market standard deviation of 12.0%, and risk-free rate is 6.0%. Calculate Sharpe Ratio, Sortino Ratio, and the Modigliani-Modigliani (M^2) measure.

Cash-Drag & Foreign Exchange Currency Adjustment

An Indian investor allocates $100,000 to a US Tech Fund. Over 1 year, the US fund gains 15.0% in USD terms. Concurrently, the USD appreciates against INR from Rs 82.00 to Rs 86.10 (+5.0% USD appreciation). If the investor also kept 10% in an INR cash balance earning 6.0% p.a., calculate the Total INR Return in the international fund and the overall Cash-Drag Adjusted Portfolio Return.