पोर्टफोलियो प्रदर्शन का मापन एवं मूल्यांकन · NISM-Series-X-A: Investment Adviser (Level 1) Certification Examination
What this chapter covers
Measuring and judging performance: return measures (HPR, TWRR, MWRR/IRR, arithmetic versus geometric mean, gross versus net, pre- and post-tax, CAGR, cash-drag adjustment, alpha and beta returns), risk measures (standard deviation, semi-variance, tracking error, beta) and risk-adjusted ratios (Sharpe, Treynor, Sortino, information ratio, M²), benchmarking and attribution.
पोर्टफोलियो प्रदर्शन — HPR, TWRR, MWRR, CAGR, बीटा, CAPM, अल्फा, शार्प, ट्रेनॉर, सोर्टिनो, इन्फॉर्मेशन रेशियो और M²।
What to master before the exam
- HPR = (income + ending value − beginning value) ÷ beginning value; TWRR chain-links sub-period returns (the workbook example: 6.02%) and is required for discretionary PMS disclosures; MWRR is the IRR of the cash flows (15.15% in the same example).
- The geometric mean is below the arithmetic mean unless all returns are equal (−50% then +100%: AMR 25%, GMR 0%); post-tax return = pre-tax × (1 − tax rate); CAGR = (A ÷ P)^(1/t) − 1.
- CAPM required return = Rf + β(Rm − Rf); Jensen's alpha = actual − CAPM return (25% − [5% + 1.5 × 10%] = 5%); portfolio beta is the weighted average of the individual betas.
- Sharpe = (Rp − Rf) ÷ σp; Treynor = (Rp − Rf) ÷ βp; Sortino uses semi-standard deviation; information ratio = (Rp − Rb) ÷ tracking error; M² levers the portfolio to the market's volatility before comparing returns.
- Gross versus net return after fees, hurdle and exit load (the workbook example: 20% gross, 13.88% net); cash-drag adjustment; currency-converted returns (15% in USD became 6.79% in rupees when the rupee rose from 70 to 65).
Exam tip: The most formula-dense chapter in Module 5 (20 marks). Expect Sharpe, Treynor, Jensen alpha, TWRR or CAGR sums in both MCQs and caselets — use the formula sheet, and know when Treynor is better than Sharpe (for a well-diversified investor).
Sample questions from this chapter
Five of the 40 questions in our free bank. Open the answer to see the explanation — every question in the mock test has one, in English and Hindi.
Question 1
A portfolio worth ₹2,00,000 at the beginning of the year is worth ₹2,30,000 at the end, and it received ₹6,000 as dividend and interest income during the year. What is its holding period return?
वर्ष की शुरुआत में ₹2,00,000 का एक पोर्टफोलियो वर्ष के अंत में ₹2,30,000 का है, और वर्ष के दौरान इसे ₹6,000 डिविडेंड और ब्याज आय मिली। इसका holding period return क्या है?
- 15.00%15.00 प्रतिशत
- 18.00%18.00 प्रतिशत
- 3.00%3.00 प्रतिशत
- 12.00%12.00 प्रतिशत
Show answer & explanation
Answer: B — 18.00%
HPR = (I + (E − B))/B = (6,000 + (2,30,000 − 2,00,000))/2,00,000 = 36,000/2,00,000 = 18%.
HPR = (I + (E − B))/B = (6,000 + (2,30,000 − 2,00,000))/2,00,000 = 36,000/2,00,000 = 18%।
Question 2
An investment of ₹50,000 is worth ₹46,000 at the end of the holding period, with no income received. Its holding period return is:
₹50,000 का एक निवेश होल्डिंग अवधि के अंत में ₹46,000 का है और कोई आय प्राप्त नहीं हुई। इसका holding period return है:
- −8.00%−8.00 प्रतिशत
- 8.00%8.00 प्रतिशत
- −8.70%−8.70 प्रतिशत
- −4.00%−4.00 प्रतिशत
Show answer & explanation
Answer: A — −8.00%
HPR = (E − B)/B = (46,000 − 50,000)/50,000 = −4,000/50,000 = −8%. The denominator is always the beginning value.
HPR = (E − B)/B = (46,000 − 50,000)/50,000 = −4,000/50,000 = −8%। हर (denominator) हमेशा प्रारंभिक मूल्य होता है।
Question 3
A portfolio with external cash flows at the start of each year has annual sub-period returns of 12%, −8% and 15% over three years. What is its time-weighted rate of return (TWRR)?
हर वर्ष की शुरुआत में बाहरी नकदी प्रवाह वाले एक पोर्टफोलियो के तीन वर्षों के वार्षिक उप-अवधि रिटर्न 12%, −8% और 15% हैं। इसका time-weighted rate of return (TWRR) क्या है?
- 6.33%6.33 प्रतिशत
- 18.50%18.50 प्रतिशत
- 6.17%6.17 प्रतिशत
- 5.82%5.82 प्रतिशत
Show answer & explanation
Answer: D — 5.82%
Wealth relatives 1.12 × 0.92 × 1.15 = 1.18496 (cumulative); TWRR = 1.18496^(1/3) − 1 ≈ 5.82%. TWRR chain-links sub-period returns, so it is not affected by the timing of cash flows.
Wealth relatives 1.12 × 0.92 × 1.15 = 1.18496 (संचयी); TWRR = 1.18496^(1/3) − 1 ≈ 5.82%। TWRR उप-अवधि रिटर्न को chain-link करता है, इसलिए नकदी प्रवाह के समय से प्रभावित नहीं होता।
Question 4
A fund returns +30% in year 1 and −10% in year 2. What is its arithmetic mean return (AMR)?
एक फंड पहले वर्ष +30% और दूसरे वर्ष −10% रिटर्न देता है। इसका arithmetic mean return (AMR) क्या है?
- 10.00%10.00 प्रतिशत
- 8.17%8.17 प्रतिशत
- 20.00%20.00 प्रतिशत
- 17.00%17.00 प्रतिशत
Show answer & explanation
Answer: A — 10.00%
AMR is the simple average: (30% + (−10%))/2 = 10%.
AMR साधारण औसत है: (30% + (−10%))/2 = 10%।
Question 5
For the same fund (+30% in year 1, −10% in year 2), what is the geometric mean return (GMR)?
उसी फंड (पहले वर्ष +30%, दूसरे वर्ष −10%) का geometric mean return (GMR) क्या है?
- 10.00%10.00 प्रतिशत
- 17.00%17.00 प्रतिशत
- 8.17%8.17 प्रतिशत
- 8.50%8.50 प्रतिशत
Show answer & explanation
Answer: C — 8.17%
GMR = ((1.30 × 0.90)^(1/2)) − 1 = 1.17^(1/2) − 1 ≈ 8.17%, lower than the 10% arithmetic mean because the yearly returns are unequal.
GMR = ((1.30 × 0.90)^(1/2)) − 1 = 1.17^(1/2) − 1 ≈ 8.17%, जो 10% के arithmetic mean से कम है क्योंकि वार्षिक रिटर्न असमान हैं।
Aumsetu
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