NISM V-C Scheme Evaluation — Practice Questions
Questions on evaluating and comparing schemes — risk-adjusted returns, Sharpe, Treynor and alpha, tracking error, benchmarks, fund manager and AMC assessment, and the historical returns of asset classes.
46 questions on Scheme Evaluation in the ScoreSetu bank — each with a detailed explanation and, where useful, a memory hook.
What this topic covers
- Sharpe, Treynor and alpha
- Tracking error and benchmarks
- Assessing fund manager and AMC
- Historical asset class returns
Free sample questions
1. A distributor is comparing two large-cap equity schemes for a client. Over the last three years Scheme X returned 14% a year with a standard deviation of 20% and a beta of 1.2. Scheme Y returned 11% a year with a standard deviation of 12% and a beta of 0.8. The risk-free rate over the period was 6% and the benchmark index returned 12% a year. The client already holds a broadly diversified equity portfolio and wants to add one of the two schemes to it.
What are the Sharpe ratios of Scheme X and Scheme Y?
- A. X: 0.70, Y: 0.92
- B. X: 0.40, Y: 0.42 ✅
- C. X: 0.42, Y: 0.40
- D. X: 6.67, Y: 6.25
Answer: B — X: 0.40, Y: 0.42
Why: Sharpe ratio = (scheme return − risk-free rate) ÷ standard deviation. For X: (14 − 6) ÷ 20 = 0.40. For Y: (11 − 6) ÷ 12 = 0.417, about 0.42. Y earned slightly more excess return per unit of total risk despite the lower headline return.
💡 Sharpe = (Rp − Rf) / SD. X = 8/20 = 0.40; Y = 5/12 = 0.42.
2. A distributor is comparing two large-cap equity schemes for a client. Over the last three years Scheme X returned 14% a year with a standard deviation of 20% and a beta of 1.2. Scheme Y returned 11% a year with a standard deviation of 12% and a beta of 0.8. The risk-free rate over the period was 6% and the benchmark index returned 12% a year. The client already holds a broadly diversified equity portfolio and wants to add one of the two schemes to it.
What are the Treynor ratios of the two schemes?
- A. X: 6.67, Y: 6.25 ✅
- B. X: 0.40, Y: 0.42
- C. X: 11.67, Y: 13.75
- D. X: 6.25, Y: 6.67
Answer: A — X: 6.67, Y: 6.25
Why: Treynor ratio = (scheme return − risk-free rate) ÷ beta. For X: (14 − 6) ÷ 1.2 = 6.67. For Y: (11 − 6) ÷ 0.8 = 6.25. On this measure X wins, because it divides the excess return by market risk only rather than by total risk.
💡 Treynor = (Rp − Rf) / BETA. X = 8/1.2 = 6.67; Y = 5/0.8 = 6.25.
3. A distributor is comparing two large-cap equity schemes for a client. Over the last three years Scheme X returned 14% a year with a standard deviation of 20% and a beta of 1.2. Scheme Y returned 11% a year with a standard deviation of 12% and a beta of 0.8. The risk-free rate over the period was 6% and the benchmark index returned 12% a year. The client already holds a broadly diversified equity portfolio and wants to add one of the two schemes to it.
The Sharpe and Treynor rankings disagree. Which measure is more relevant to this client, and why?
- A. Sharpe, because it uses the larger denominator
- B. Treynor, because the client's portfolio is already diversified and only systematic (beta) risk matters at the margin ✅
- C. Sharpe, because standard deviation is easier to compute
- D. Neither — the client should simply pick the higher return
Answer: B — Treynor, because the client's portfolio is already diversified and only systematic (beta) risk matters at the margin
Why: Standard deviation captures total risk, including the unsystematic risk that diversification removes. For an investor whose portfolio is already well diversified, the scheme's contribution to risk is its beta, so Treynor is the appropriate yardstick. Sharpe suits an investor for whom the scheme is the whole portfolio.
💡 Diversified investor -> TREYNOR (beta). Scheme is whole portfolio -> SHARPE (SD).
Practise all 46 Scheme Evaluation questions
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