Scheme Evaluation is one of the three heaviest units in NISM Series V-C, and it is where the 2-mark questions cluster. The exam does two things with it: asks you to compute a measure, and asks you to choose the right measure for a given investor. Both are worked below.
The workbook's starting point: a mutual fund is a relative-return product. Its performance means nothing in isolation — it must be compared with a benchmark or a peer group, over a period suited to the asset class (weeks for a liquid fund; years for equity).
Two measures of risk
Standard deviation is the degree to which short-term returns scatter around the long-term average. Lower means more consistent. It measures total volatility, both sides, and is an absolute number. Its square is the variance.
Beta measures volatility relative to the market. The benchmark's beta is 1. A fund with beta 0.9 is less volatile than the market; 1.1 is more. Two flexi-cap funds with betas of 1.1 and 1.2 are both more volatile than the benchmark, and the second more so than the first.
The distinction the exam tests: standard deviation captures risk that diversification can remove; beta captures only the risk that it cannot.
Sharpe ratio
Sharpe = (Rp − Rf) ÷ σ — excess return over the risk-free rate, per unit of total risk.
Scheme X: return 14%, standard deviation 20%, risk-free rate 6%. Sharpe = (14 − 6) ÷ 20 = 0.40.
Scheme Y: return 11%, standard deviation 12%. Sharpe = (11 − 6) ÷ 12 = 0.42.
Y wins on Sharpe despite the lower headline return: it earned more per unit of risk.
Treynor ratio
Treynor = (Rp − Rf) ÷ β — the same excess return, per unit of market risk.
Scheme X, beta 1.2: (14 − 6) ÷ 1.2 = 6.67. Scheme Y, beta 0.8: (11 − 6) ÷ 0.8 = 6.25.
X wins on Treynor. The rankings disagree — and that disagreement is the exam's favourite question.
Which measure for which investor
- The scheme is the investor's whole portfolio → total risk matters → Sharpe.
- The investor already holds a diversified portfolio → only the scheme's contribution to market risk matters → Treynor.
For a diversified HNI adding one scheme, X is the better choice on Treynor even though Y looked better on Sharpe.
Jensen's alpha
Alpha = Rp − [Rf + β × (Rm − Rf)] — what the scheme returned over what CAPM says its beta deserved.
Scheme X, market return 12%: expected = 6 + 1.2 × (12 − 6) = 13.2%; actual 14%; alpha = +0.8%. Scheme Y: expected = 6 + 0.8 × 6 = 10.8%; actual 11%; alpha = +0.2%.
The trap: the 2-percentage-point gap between X and the benchmark is not alpha, because X took more market risk than the index. Alpha adjusts for that.
Tracking error
For an index fund the question is not "did it beat the index" but "how closely did it follow it". Tracking error is the standard deviation of the difference between the fund's return and the index's. Lower is better. A large tracking error means the fund is not doing the one job an index fund has.
What makes a credible benchmark
The workbook lists the tests: the benchmark should be in sync with the scheme's investment objective and asset allocation, representative of the kind of portfolio the scheme holds, calculated by an independent agency transparently and published regularly. A large-cap fund against a small-cap index fails the first test, however flattering the comparison.
How the exam sets this
- Compute Sharpe / Treynor / alpha from given numbers — 2 marks, and the numbers are usually chosen so that Sharpe and Treynor disagree.
- Which measure suits this investor? — diversified means Treynor.
- Which of two funds is less volatile? — read the betas and standard deviations separately; they are different questions.
- A distractor — a risk-free rate offered in a simple-return question, where it is irrelevant.
Practise the unit free, then see how it fits the three-week V-C plan.