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Unit ko samjho · NISM Series X-A

Portfolio Performance Measurement and Evaluation

25 questions is unit mein

Sawaal aur jawaab English mein hain, kyunki NISM ka exam paper bhi English mein hota hai.

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Practice bank se · 1

A portfolio is worth ₹100 lakh before an additional ₹20 lakh contribution is made immediately at the start of the measurement period. It ends the period at ₹132 lakh, with no later cash flows or distributions. What is the investment return on the capital invested throughout the period?

The full-period capital base is ₹120 lakh and its investment gain is ₹12 lakh, giving 10%. Opening invested capital is ₹100 lakh + ₹20 lakh = ₹120 lakh because the contribution occurs before the measurement period’s returns. With no later flows, investment gain is ₹132 lakh − ₹120 lakh = ₹12 lakh. Return = ₹12 lakh / ₹120 lakh = 10%. The timing assumption matters. A contribution made midway through the period would require a method that handles cash-flow timing rather than simply using this full-period opening base. Remember: Distinguish money added by the investor from money earned by the investments.

Hint Common mistake: Counting external contributions as portfolio performance.

X-A-201

Practice bank se · 2

A portfolio’s correctly cash-flow-adjusted returns are +10% in the first subperiod and −5% in the next. What is the cumulative time-weighted return over both subperiods?

Linking growth factors gives 1.10 × 0.95 − 1 = 0.045, or 4.5%. Convert the returns to growth factors: a 10% gain is 1.10 and a 5% loss is 0.95. Their product is 1.045. A unit of capital following both returns would therefore end at 1.045 units, a cumulative gain of 4.5%. The 5% loss acts on the amount after the first gain. That interaction explains why the cumulative return differs from 10% − 5%. The question asks for a cumulative, not annualised, result. Remember: Link adjusted subperiod returns multiplicatively to obtain a cumulative time-weighted return.

Hint Common mistake: Adding subperiod percentage returns when a compounded total is required.

X-A-202

Practice bank se · 3

An investor puts in ₹100 lakh now and another ₹100 lakh after one year, and receives ₹231 lakh after two years. What is the annual money-weighted return?

At 10%, the first contribution grows to ₹121 lakh and the second to ₹110 lakh, totalling ₹231 lakh. The initial ₹100 lakh is invested for two years, whereas the second ₹100 lakh is invested for one year. Test r = 0.10: 100 × 1.10² + 100 × 1.10 = 121 + 110 = 231 lakh. Thus 10% satisfies the specified equation. The equation is increasing in 1+r when r is above −100%, so this is the unique solution in the stated domain. A simple profit divided by total contributions ignores the differing durations. Remember: Date every contribution before solving for a money-weighted rate.

Hint Common mistake: Averaging gains over years without accounting for when the money entered.

X-A-203

Practice bank se · 4

An investment earns +20% in year one and −20% in year two, with no cash flows. Its arithmetic average annual return is 0%. What is the geometric average annual return, rounded to two decimals?

The two-year growth factor is 1.20 × 0.80 = 0.96. Its square root minus one is approximately −2.02%. An initial ₹100 becomes ₹120 after the gain and ₹96 after the subsequent 20% loss. The two-year growth factor is therefore 0.96. The annual compound factor is √0.96, giving √0.96 − 1 = −0.020204. The geometric annual return is −2.02%. Equal positive and negative percentage returns do not cancel in wealth because the loss applies to a different starting balance. Remember: Use geometric averaging to describe multi-period wealth growth when there are no external flows.

Hint Common mistake: Assuming equal percentage gains and losses produce zero cumulative change.

X-A-204

Practice bank se · 5

A portfolio earns 3% over one quarter. For a mathematical annualisation only, assume the same return is earned and reinvested in each of four quarters. What is the compounded annualised rate, rounded to two decimals?

Four quarterly growth factors give 1.03⁴ − 1, approximately 12.55%. A 3% quarterly return has growth factor 1.03. Four equal quarters imply a one-year growth factor of 1.03 raised to the fourth power. 1.03⁴ = 1.12550881. Subtract one and convert to percent to obtain 12.550881%, rounded to 12.55%. The simple annual multiple, 4 × 3% = 12%, is a different convention. The question explicitly asks for compound annualisation with reinvestment. Remember: State the annualisation convention and the number of compounding periods.

Hint Common mistake: Presenting an annualised short-period rate as an assured future annual return.

X-A-205

Practice bank se · 6

A portfolio starts at ₹10 lakh and earns a gross 10% return over the year. A hypothetical fee of 2% of the gross closing portfolio value is then deducted. There are no other cash flows or charges. What is the investor’s net return?

Gross closing value is ₹11 lakh. The 2% fee is ₹22,000, leaving ₹10.78 lakh and a 7.8% net gain. Gross closing assets = ₹10 lakh × 1.10 = ₹11 lakh. The closing-value-based fee is 0.02 × ₹11 lakh = ₹22,000. Net closing assets = ₹11,00,000 − ₹22,000 = ₹10,78,000. Divide the ₹78,000 net gain by the ₹10,00,000 opening value. Net return is 7.8%, equivalently 1.10 × 0.98 − 1. These are hypothetical fee terms rather than a current product charge or legal limit. Remember: Calculate net ending wealth using the actual fee base before converting to a return.

Hint Common mistake: Subtracting headline fee and return percentages without checking their denominators.

X-A-206

Practice bank se · 7

A portfolio holds 80% in a risky asset that returns 15% during a period and 20% in cash that returns 3%. With fixed beginning weights and no flows, how much lower is portfolio return than a hypothetical 100% investment in the risky asset over the same period?

Portfolio return is 12.6%, which is 2.4 percentage points below the 15% fully invested comparator. Actual portfolio return = 0.80 × 15% + 0.20 × 3% = 12% + 0.6% = 12.6%. The stated comparator earns 15%. The difference is 15% − 12.6% = 2.4 percentage points, also 0.20 × (15% − 3%). This historical scenario does not establish that holding cash was an error. Cash may serve or risk objectives, and in another period it could outperform the risky asset. Remember: Measure cash’s return contribution and opportunity difference without ignoring its portfolio purpose.

Hint Common mistake: Treating all cash as earning zero or assuming cash must always reduce performance.

X-A-207

Practice bank se · 8

The covariance between a portfolio and the market is 0.018 and the market's variance is 0.0225. What is the portfolio's beta?

0.018 divided by 0.0225 equals 0.80. The squared-return units cancel. Use the stipulated formula β = Cov(portfolio, market) / Var(market), keeping the same observation period and return units. β = 0.018 / 0.0225 = 0.80. Since numerator and denominator have the same squared-return units, beta is dimensionless. A beta of 0.80 describes the estimated relationship to this benchmark. It does not mean every market move produces exactly an 80%-as-large portfolio move, nor does it eliminate company-specific variation. Remember: Match beta’s covariance and variance inputs to the same benchmark, period and units.

Hint Common mistake: Confusing market sensitivity with total standard deviation or a guaranteed movement ratio.

X-A-208

Practice bank se · 9

The risk-free rate is 5%, the expected market return is 11% and a portfolio's beta is 1.2. What is its required return under CAPM?

The market premium is 6%. Multiply it by 1.2 and then add the 5% risk-free component. Market risk premium = 11% − 5% = 6 percentage points. This is the expected compensation above the risk-free component. Beta-adjusted premium = 1.2 × 6% = 7.2%. Add the 5% risk-free rate to obtain 12.2%. This is a result conditional on the supplied model and hypothetical inputs. It is not a promise about realised performance or a statement of the current risk-free rate in India. Remember: Subtract the risk-free rate before multiplying the market premium by beta.

Hint Common mistake: Scaling the full market return and then adding the risk-free rate again.

X-A-209

Practice bank se · 10

A portfolio returned 14% in a year. The risk-free rate was 5%, the market returned 11% and the portfolio's beta is 1.2. What is its Jensen's alpha?

The model return is 12.2%, so the excess over it is 14% − 12.2% = 1.8 percentage points. Calculate the comparison first: 5% + 1.2 × 6% = 12.2%. This uses the same annual period as the portfolio return. Subtract the comparison from actual return: 14% − 12.2% = +1.8 percentage points. Positive measured alpha for this year does not prove persistent manager skill. Model choice, estimation uncertainty, costs and chance can affect the interpretation. The question asks only for this specified difference. Remember: Name the model and return basis before interpreting an alpha number.

Hint Common mistake: Treating every outperformance figure as the same type of alpha.

X-A-210

Practice bank se · 11

A portfolio's mean return is 14%, the risk-free rate is 6% and its standard deviation is 20%. What is its Sharpe ratio?

The 8-percentage-point excess mean return divided by 20% standard deviation gives 0.40. Annual excess mean return = 14% − 6% = 8%. The annual standard deviation is 20%. Sharpe ratio = 0.08 / 0.20 = 0.40. Using 8/20 also works because both numbers are in percentage-point units. The result is a dimensionless ratio, not a 40% investment return. Comparing it with other ratios requires consistent return definitions, observation periods and risk-free assumptions. Remember: Subtract the risk-free return and match units before dividing by total volatility.

Hint Common mistake: Using raw return instead of excess return, or calling the resulting ratio a percentage profit.

X-A-211

Practice bank se · 12

A portfolio's mean return is 14%, the risk-free rate is 6% and its beta is 1.25. What is its Treynor ratio, in percentage points per unit of beta?

The annual excess mean return is 8 percentage points. Dividing by 1.25 gives 6.4. Treynor ratio = 8 / 1.25 = 6.4 percentage points per unit of beta, equivalently 0.064 when returns are entered as decimals. The positive beta makes this straightforward calculation interpretable as specified. A beta-based measure does not by itself describe all portfolio risks, and unusual or unstable beta values require care. Remember: Identify whether a risk-adjusted measure uses total volatility, beta or another risk denominator.

Hint Common mistake: Interchanging beta and standard deviation because both are called risk measures.

X-A-212

Practice bank se · 13

A portfolio's mean return is 12%. The minimum acceptable return is 5% and the downside deviation is 7%. What is its Sortino ratio?

The return above the chosen target is 7%. Dividing by the matching 7% downside deviation gives 1.00. The minimum acceptable return is explicitly 5%. Mean return above it is 12% − 5% = 7%. Downside deviation is supplied as 7%, already calculated relative to the same annual target. The ratio is therefore 0.07 / 0.07 = 1.00. No separate downside-deviation convention needs to be invented because the statistic is given. Comparisons still require compatible targets, periods and calculation methods. The ratio is not a guaranteed future outcome. Remember: Use the same target in both the excess-return numerator and downside-risk measurement.

Hint Common mistake: Replacing the specified minimum acceptable return with a different rate without justification.

X-A-213

Practice bank se · 14

Quarterly active returns are +2, 0, −2 and 0 percentage points. Using the sample standard deviation (n − 1), what is the quarterly tracking error, to two decimals?

Mean active return is zero, and √[(4 + 0 + 4 + 0)/3] is approximately 1.63. The four active returns sum to zero, so their sample mean is zero percentage points. Squared deviations are 4, 0, 4 and 0 in squared percentage-point units. Sample variance = 8/(4−1) = 8/3. The square root is 1.632993 percentage points, rounded to 1.63. The question requests quarterly tracking error, so do not multiply by a square-root-of-four annualisation factor. Remember: Separate average active return from the dispersion of active returns, and use the requested frequency.

Hint Common mistake: Calling tracking error zero just because average outperformance is zero.

X-A-214

Practice bank se · 15

A portfolio's mean return is 11%, its benchmark's is 8% and the tracking error is 4%. What is its information ratio?

Mean active return is 3%. Dividing by the 4% tracking error gives 0.75. Mean active return is 11% − 8% = 3 percentage points using matching annual return measures. Divide by annual tracking error: 0.03/0.04 = 0.75. The numerator and denominator share return units, giving a dimensionless ratio. A risk-free rate is not needed for this stated formula. The selected benchmark and consistent measurement conventions matter, and the historical result does not ensure future outperformance. Remember: Match each performance ratio with its own return comparison and risk denominator.

Hint Common mistake: Substituting risk-free excess return or total volatility into an information-ratio calculation.

X-A-215

Practice bank se · 16

A portfolio returns 14% with a standard deviation of 20%. The risk-free rate is 4% and the benchmark's standard deviation is 12%. What is the portfolio's M² risk-adjusted return, as a return level?

The portfolio Sharpe ratio is 0.50. Scaling it by 12% gives 6% excess return, then adding 4% gives 10%. Portfolio excess return is 14% − 4% = 10%. Dividing by 20% standard deviation gives a Sharpe ratio of 0.50. Normalised excess return = 0.50 × 12% = 6%. Add the 4% risk-free component to obtain a 10% return level. A difference from benchmark return would require subtracting that separate return, which is neither requested nor supplied. Keep the normalised return level and any benchmark-relative spread distinct. Remember: State whether M² means a normalised return level or a difference from a benchmark before calculating.

Hint Common mistake: Reporting only the excess-return component when the requested measure includes the risk-free rate.

X-A-216

Practice bank se · 17

A portfolio’s reported return includes investment income. Its manager compares it with a price-only index that excludes dividends, then attributes the entire difference to security-selection skill. What should be corrected before accepting that attribution?

The current comparison mixes an income-inclusive portfolio return with an index that omits income. Identify the inconsistent treatment of income: the portfolio includes it, while the chosen index excludes dividends. A suitably matched total-return index can address this feature, alongside checks on asset universe, currency, period, fees and other relevant conventions. Even a corrected active-return difference is not automatically pure selection skill. Allocation, risk exposures, costs and chance may also contribute and require separate analysis. Remember: Align the return basis before interpreting benchmark outperformance.

Hint Common mistake: Crediting a manager with skill for a difference partly caused by inconsistent income treatment.

X-A-217

Practice bank se · 18

A hypothetical five-fund peer group has annual returns of 12%, 10%, 8%, −5% and −10%. A database drops the last two funds after they close and reports the equally weighted average of only the remaining three. By how many percentage points does this raise the reported average compared with retaining all five?

The full group averages 3%, while the retained three average 10%, creating a 7-point increase. Average for all five = (12 + 10 + 8 − 5 − 10)/5 = 15/5 = 3%. Average for the three survivors = (12 + 10 + 8)/3 = 30/3 = 10%. The reported increase is 10% − 3% = 7 percentage points. The numerical direction follows from these stated omitted returns. The lesson is to define the comparison universe consistently, not to assume that every fund closure has the same cause or performance effect. Remember: Keep the original eligible universe in view when interpreting a peer-group performance average.

Hint Common mistake: Comparing only surviving products and treating that subset as the full historical investment opportunity.

X-A-218

Practice bank se · 19

A portfolio holds 60% equity and 40% debt. Its benchmark holds 50% of each. Benchmark returns are 12% for equity and 4% for debt. What is the allocation effect?

The equity overweight contributes +1.2 points and the debt underweight contributes −0.4 points, for +0.8. Equity weight difference = 0.60 − 0.50 = +0.10. Its contribution is 0.10 × 12% = +1.2 percentage points. Debt difference = 0.40 − 0.50 = −0.10. Its contribution is −0.10 × 4% = −0.4 percentage points. Sum = +0.8. This measures only the defined allocation component. It does not include the portfolio’s within-segment selection results or establish the manager’s total active return without further information. Remember: Use the attribution formula supplied and distinguish allocation effects from security-selection effects.

Hint Common mistake: Reporting the raw segment return spread without applying the difference in portfolio weights.

X-A-219

Practice bank se · 20

A benchmark holds 60% equity and 40% debt. The portfolio's equity and debt returned 15% and 5%, against benchmark returns of 12% and 4%. What is the selection effect?

The equity contribution is 0.60 × 3% = 1.8 points and the debt contribution is 0.40 × 1% = 0.4 points. Equity segment difference = 15% − 12% = 3%. Weighting by 60% gives 1.8 percentage points. Debt segment difference = 5% − 4% = 1%. Weighting by 40% gives 0.4 percentage points. Together they give 2.2 percentage points. Other attribution conventions may separate interaction differently. This answer applies only the explicit formula. It does not assume that selection alone equals all of the portfolio’s benchmark-relative performance. Remember: Keep segment returns, segment excess returns and the specified attribution weights separate.

Hint Common mistake: Adding within-segment excess returns without weighting them by the stated exposure basis.

X-A-220

Practice bank se · 21

CASE: An investor puts in ₹100 lakh. After one year it is worth ₹120 lakh, and the investor adds ₹80 lakh. After the second year the portfolio is worth ₹180 lakh. What is the two-year time-weighted return?

Year one: 120 ÷ 100 = +20%. Year two: 180 ÷ 200 = −10%. 1.20 × 0.90 = 1.08, so the return is +8%. Remember: Measure each subperiod on the capital present during that subperiod before linking its return.

Hint Common mistake: Using a portfolio value after a contribution as if it were all investment growth.

X-A-221

Practice bank se · 22

CASE: A portfolio returns +20% in year one and −10% in year two. What is its annualised time-weighted return?

Two-year factor = 1.20 × 0.90 = 1.08. Annual = √1.08 − 1 = 3.92%. Remember: Annualise a multi-year linked return with a root of its growth factor.

Hint Common mistake: Dividing a cumulative compound return by the number of years.

X-A-222

Practice bank se · 23

CASE: An investor puts in ₹100 lakh, adds ₹80 lakh after one year and takes out ₹180 lakh after two years. What is the annual money-weighted return?

The investor put in ₹180 lakh and got back exactly ₹180 lakh, so the money-weighted return is 0%. Check: 100 × 1² + 80 × 1 = 180. Remember: Use amounts and dates, not just yearly percentage returns, to evaluate the investor’s money-weighted experience.

Hint Common mistake: Assuming TWR and MWR must coincide even when there is a substantial interim contribution.

X-A-223

Practice bank se · 24

CASE: An investor's ₹100 lakh grows to ₹120 lakh in year one. The investor adds ₹80 lakh, and the ₹200 lakh then falls to ₹180 lakh in year two. The time-weighted return is +8% but the money-weighted return is 0%. Which explanation is best?

Year one gained ₹20 lakh on ₹100 lakh. Year two lost ₹20 lakh on ₹200 lakh. Time-weighting counts each year equally. Money-weighting counts how much money was in. Remember: Different capital amounts can make the same sequence of percentage returns produce a different investor experience.

Hint Common mistake: Concluding that a legitimate TWR–MWR difference proves an error or manager misconduct.

X-A-224

Practice bank se · 25

CASE: A portfolio's two-year time-weighted return is +8%. A benchmark earns 4% in each of the two years, reinvested. What is the portfolio's cumulative return minus the benchmark's?

Benchmark = 1.04² − 1 = 8.16%. Portfolio minus benchmark = 8% − 8.16% = −0.16 percentage points. Remember: Align horizons and return methods, then distinguish a percentage-point spread from a relative-wealth ratio.

Hint Common mistake: Comparing cumulative, annualised and money-weighted results as though they were interchangeable.

X-A-225

Is topic ka lesson padho

Liquidity

Liquidity describes how easily a given quantity can be traded.

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