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Unit study guide · NISM Series V-A

Risk, Return and Performance

21 questions in this unit

What this unit covers

Key ideas

From the practice bank · 1

An investor made SIP contributions on different dates, missed one instalment and then redeemed the holding. Which measure best captures the investor’s annualised return using the amounts and actual dates of all these cash flows?

This answer incorporates the size and date of each contribution and the final redemption. Earlier contributions and later contributions have different holding periods. Combining them into a fictional first-day investment changes the problem. uses the dates and amounts of cash flows to find an annualised money-weighted return. Contributions and redemption must be entered with opposite signs. The scheme’s own return history does not, by itself, capture this investor’s contribution timing. Remember: Use a dated cash-flow measure for the investor’s experience, not a lump-sum shortcut.

Hint Common mistake: Using on total SIP contributions as though they all entered on the first day.

VA-017

From the practice bank · 2

An investor sees a scheme’s Riskometer category in its disclosure. What does that category primarily communicate?

The Riskometer is a scheme-level risk label. It helps the investor assess fit alongside their own circumstances. The label appears in a scheme disclosure, so its subject is the scheme’s potential risk. It does not know the individual investor’s goals, finances or willingness to bear a loss. Those must be assessed separately. The label is also not a return forecast or a contractual limit on the loss an investor may experience. Remember: Compare scheme risk with investor suitability, rather than treating one as a substitute for the other.

Hint Common mistake: Reading a product-risk category as a personalised recommendation, a promised return or a maximum-loss guarantee.

VA-018

From the practice bank · 3

A simplified annual illustration starts with ₹1,00,000. Gross investment gains are 13% of that amount and total expenses are ₹1,800. With no other cash flows or charges, what is the net return on the opening amount?

This answer divides the ₹11,200 net gain by the ₹1,00,000 opening amount. Gross gain = ₹1,00,000 × 13% = ₹13,000. Net gain = ₹13,000 − ₹1,800 = ₹11,200. Net return = ₹11,200 ÷ ₹1,00,000 × 100 = 11.20%. The explicit rupee expense makes the result exact for this illustration. It is not a claim that subtracting an annual TER always reproduces an exact real-world return. Remember: Use the stated expense amount and denominator, and distinguish exact cash arithmetic from a TER approximation.

Hint Common mistake: Treating an annualised expense ratio as though its cash-flow base and timing never matter.

VA-019

From the practice bank · 4

Across 252 observed trading days, an index fund’s daily return is exactly 0.10 percentage points below its benchmark’s daily return on every day. What is the annualised tracking error for this dataset?

All daily differences equal their mean, so their standard deviation is zero. Every daily return difference is −0.10 percentage points. Their mean is therefore also −0.10 percentage points. Each deviation from that mean is zero. The variance and standard deviation of the differences are zero. Annualising a zero standard deviation still gives zero. The fund nevertheless trails its benchmark every day in this hypothetical dataset. This is a limiting example that separates variability from a persistent return gap. It is not a forecast of index-fund performance. Remember: A fund can have very low tracking error while consistently lagging its benchmark.

Hint Common mistake: Confusing tracking error with the average or cumulative return shortfall.

VA-026

From the practice bank · 5

Two schemes have the same average annual return over the same observation period. Scheme X has a return standard deviation of 6% and Scheme Y of 12%, calculated on the same basis. What do these figures establish?

This answer makes the valid comparison without inventing a probability or loss bound. The measurements use the same return frequency and period, so their dispersion can be compared. The higher standard deviation indicates wider observed variation. The figures alone do not provide the full return distribution or a guaranteed range of outcomes. Remember: Read standard deviation as variability, and keep it separate from return and downside probability.

Hint Common mistake: Interpreting “twice the standard deviation” as “twice the chance of losing”.

VA-042

From the practice bank · 6

An investment grows from ₹1,00,000 to ₹1,33,100 in exactly three years, with no contributions, withdrawals or distributions. What is its CAGR?

Compounding ₹1,00,000 at 10% for three years gives ₹1,33,100. CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1. Substitute: (₹1,33,100 ÷ ₹1,00,000)^(1/3) − 1 = 1.331^(1/3) − 1. Since 1.10 × 1.10 × 1.10 = 1.331, CAGR = 0.10 = 10.00% per year. The answer does not imply that each actual year earned exactly 10%. It is the equivalent compounded rate. Remember: For a single initial amount and a final value, annualise multiplicatively rather than dividing the total gain.

Hint Common mistake: Using simple annualisation where the question asks for compound growth.

VA-043

From the practice bank · 7

Over the same one-year period, an equity growth plan returns 8%. Its designated benchmark’s price return is 7% and total return is 9%. On a total-return comparison, the plan:

The fund’s 8% return is 1 percentage point below the benchmark’s 9% total return. The requested comparison uses the benchmark’s 9% total return, not its 7% price-only return. Relative result = 8% − 9% = −1 percentage point. The 2-percentage-point difference between the benchmark’s own two versions is not the fund’s performance difference. Remember: Compare returns over the same period and on the same return basis.

Hint Common mistake: Creating apparent outperformance by choosing the benchmark’s price-only version.

VA-044

From the practice bank · 8

A ₹20 lakh debt portfolio has 40% of its market value in bonds with modified duration 2 and 60% in bonds with modified duration 5. For a parallel yield rise of 0.50 percentage points, what is the approximate immediate change in portfolio value? Ignore convexity, accrued income and other changes.

Portfolio modified duration is 0.40 × 2 + 0.60 × 5 = 3.8. A 0.005 yield increase gives an approximate return of −3.8 × 0.005 = −1.9%, or a ₹38,000 fall. Calculate the value-weighted duration: 0.40 × 2 + 0.60 × 5 = 0.8 + 3 = 3.8. Convert the yield change: 0.50 percentage points = 0.005 in decimal form. Approximate fractional price change = −modified duration × yield change = −3.8 × 0.005 = −0.019, or −1.9%. Value change = ₹20,00,000 × (−0.019) = −₹38,000. The negative sign denotes a fall. This is a first-order immediate price estimate under the stated exclusions, not a forecast of the portfolio’s full holding-period return. Remember: Weight durations by value, convert the yield change to a decimal and retain the minus sign.

Hint Common mistake: Using equal weights, confusing percentage points with decimals, or adding coupon income to an immediate price-only estimate.

VA-067

From the practice bank · 9

Using comparable annual inputs, Scheme X has return 11%, standard deviation 10% and beta 1.2. Scheme Y has return 10%, standard deviation 12.5% and beta 0.5. With a 5% risk-free rate, which ranking follows from the Sharpe and Treynor measures?

Sharpe is 0.60 for X and 0.40 for Y. Treynor is 0.05 for X and 0.10 for Y when returns are decimals. The measures therefore rank the schemes differently. Excess returns are 11% − 5% = 6% for X and 10% − 5% = 5% for Y. Sharpe divides excess return by standard deviation. X = 0.06 / 0.10 = 0.60. Y = 0.05 / 0.125 = 0.40. X is higher. Treynor divides excess return by beta. X = 0.06 / 1.2 = 0.05. Y = 0.05 / 0.5 = 0.10. Y is higher. The different ranking reflects total volatility versus market sensitivity. It is not an arithmetic contradiction and does not by itself establish universal suitability for every investor. Remember: Use standard deviation for Sharpe and beta for Treynor, with the same-period excess return in both numerators.

Hint Common mistake: Comparing raw returns alone, omitting the risk-free rate or swapping the two risk denominators.

VA-068

From the practice bank · 10

For the same period and benchmark, Scheme A has beta 0.7 and return standard deviation 20%. Scheme B has beta 1.1 and standard deviation 14%. Which conclusion is supported by these statistics?

A’s beta is lower, while its standard deviation is higher. The two statistics describe different aspects of risk. Compare the betas: 0.7 is below 1.1, so A has the lower measured sensitivity to the stated benchmark. Compare the standard deviations: 20% is above 14%, so A has greater total return variability over the measurement period. The statistics can coexist because total variability also reflects movements not captured by the benchmark relationship. These are measured characteristics, not a guarantee about the next market movement or a complete suitability assessment. Remember: Read beta and standard deviation separately rather than treating them as interchangeable risk rankings.

Hint Common mistake: Assuming that a fund with beta below one must be less volatile overall than every fund with beta above one.

VA-069

From the practice bank · 11

A corporate bond in a debt fund falls in market value after the issuer’s credit outlook weakens. The issuer has missed no payment, and the question excludes a general interest-rate move, currency change or trading-liquidity shock. Which risk best explains the fall?

The stated cause is a deterioration in the issuer’s perceived ability to meet its obligations. Credit-related price loss can occur before an actual payment default. Identify the stated trigger rather than inferring one from the fact that the holding is a bond. The issuer’s credit outlook has weakened. Investors may require greater compensation for bearing that issuer’s risk, reducing the price of its existing bond. The question expressly excludes the principal competing explanations in the options, leaving credit deterioration as the supported cause. No default is needed for the mark-to-market price loss described. A no-missed-payment history therefore does not disprove credit risk. Remember: Distinguish a credit-related valuation loss from an actual default event.

Hint Common mistake: Treating credit risk as relevant only after a coupon or principal payment has already been missed.

VA-070

From the practice bank · 12

Which event is the clearest example of company-specific risk that a diversified equity portfolio can reduce?

The recall is specific to one company. Spreading exposure across different companies can limit the portfolio’s dependence on that event. The key distinction is whether the source of risk is confined to a company or is a common influence on many companies. The product recall is expressly confined to one investee company. A portfolio with different company exposures need not depend entirely on that company’s outcome. The other events are economy-wide or market-wide shocks, so they can affect many holdings at once. Reducing company-specific exposure does not mean the diversified portfolio has no possibility of loss. Remember: Diversification reduces concentration in company-specific events but does not remove market-wide shocks.

Hint Common mistake: Treating the presence of many securities as proof that every kind of risk has been diversified away.

VA-071

From the practice bank · 13

A scheme earns 13% over a year. The benchmark earns 11%, the risk-free rate is 5% and the scheme’s beta against that benchmark is 1.2. Using the stated CAPM inputs, what is Jensen alpha for the year?

CAPM-required return is 5% + 1.2 × (11% − 5%) = 12.2%. Actual return of 13% exceeds that by 0.8 percentage points. Calculate the market risk premium: 11% − 5% = 6 percentage points. Calculate the scheme’s beta-adjusted premium: 1.2 × 6 = 7.2 percentage points. Add the risk-free rate to get the CAPM-required return: 5% + 7.2% = 12.2%. Jensen alpha = actual return − required return = 13% − 12.2% = 0.8 percentage points. The positive result describes performance relative to the specified model and period. It does not prove future outperformance or isolate skill with certainty. Remember: For Jensen alpha, subtract the risk-free rate and the beta-adjusted market premium from actual return.

Hint Common mistake: Confusing alpha with raw benchmark outperformance or applying beta to the full benchmark return.

VA-075

From the practice bank · 14

A debt portfolio has 20% of its market value in securities maturing in 0.5 years, 50% in securities maturing in 2 years and 30% in securities maturing in 5 years. What is its value-weighted average maturity?

The stated value weights give 0.10 + 1.00 + 1.50 = 2.60 years. Use the supplied market-value weights, which sum to 100%. Weighted average maturity = 0.20 × 0.5 + 0.50 × 2 + 0.30 × 5. The contributions are 0.10, 1.00 and 1.50 years. Their sum is 2.60 years. This describes average remaining maturity. It is not automatically the portfolio’s modified duration or a promise of a fixed investor holding period. Remember: For weighted average maturity, multiply each remaining maturity by its portfolio-value weight and add.

Hint Common mistake: Giving a small holding the same influence as a large holding by using a simple average.

VA-081

From the practice bank · 15

A gilt fund mainly holds long-dated, fixed-rate Government of India securities. Market yields rise sharply, with no default or other change assumed. Which immediate effect is most likely?

A bond-price decline caused by higher required yields can reduce the fund’s NAV. The existing securities have fixed cash flows. A rise in the market’s required yield makes those cash flows less valuable today. Their market prices can therefore decline, even without a payment default. The fund’s NAV reflects portfolio values. Long-dated fixed-rate holdings can make the effect material, although the exact change needs further information. Remember: Do not confuse low default risk with low interest-rate risk.

Hint Common mistake: Treating a government-security portfolio as immune to a decline in NAV.

VA-086

From the practice bank · 16

An unhedged overseas holding is worth USD 1,000 when the exchange rate is ₹80 per USD. It rises to USD 1,080 while the exchange rate falls to ₹76 per USD. Ignoring distributions, costs and taxes, what is the return in rupees?

The two currency conversions produce a ₹2,080 gain on ₹80,000, or 2.60%. Initial rupee value = USD 1,000 × ₹80 per USD = ₹80,000. Final rupee value = USD 1,080 × ₹76 per USD = ₹82,080. Gain = ₹82,080 − ₹80,000 = ₹2,080. Rupee return = ₹2,080 ÷ ₹80,000 × 100 = 2.60%. Equivalently, the value multiplier is 1.08 × (76 ÷ 80) = 1.026. The stronger rupee offsets part of the foreign-asset gain. Remember: Value the foreign holding in rupees at both endpoints before calculating its rupee return.

Hint Common mistake: Adding the asset and currency percentage changes instead of multiplying their value factors.

VA-087

From the practice bank · 17

A debt scheme’s stated mandate is to maintain short maturity and high credit quality. Which approach is most appropriate when choosing a benchmark for evaluating its performance?

Maturity and credit-risk alignment makes the comparison relevant to the stated debt-investment mandate. The stated mandate identifies two important characteristics: short maturity and high credit quality. A benchmark with a materially different maturity or credit profile can experience different market effects, making a simple performance comparison less informative. Matching the benchmark to the mandate is more appropriate than picking a return after observing recent results. A suitable benchmark does not have to hold exactly the same securities as the scheme. Remember: Select a performance benchmark for mandate and risk relevance, not for a convenient recent return.

Hint Common mistake: Choosing a benchmark after seeing which comparison makes the scheme look best.

VA-091

From the practice bank · 18

An investment rises by 25% in the first year and falls by 25% in the second. With no cash flows or charges, what is its cumulative two-year return?

Multiplying 1.25 by 0.75 gives 0.9375, or a 6.25% cumulative loss. Use a notional starting value of ₹100. After the first year it is ₹100 × 1.25 = ₹125. The second-year fall is 25% of ₹125, leaving ₹125 × 0.75 = ₹93.75. The cumulative return is (₹93.75 ÷ ₹100 − 1) × 100 = −6.25%. A zero arithmetic average of the two annual percentages is not a zero cumulative holding-period return. Remember: Multiply successive return factors when no money enters or leaves the investment.

Hint Common mistake: Using the arithmetic average of annual returns as the cumulative return.

VA-092

From the practice bank · 19

A fund holds fixed-coupon bonds. Existing coupon amounts are unchanged, but future coupon receipts can now be reinvested only at lower rates than previously expected. Which risk does this change most directly illustrate?

The investor or fund earns less on future reinvestment of coupon cash than had been assumed. The existing bonds continue to pay their fixed contractual coupons in this example. The question does not describe a missed payment. The change is the lower return available on cash received in the future and then reinvested. That is reinvestment risk. The current market price of a bond may respond to rates separately, but that is not the effect being asked about. Remember: Fixed coupons do not fix the rate that will be earned when those coupons are reinvested.

Hint Common mistake: Confusing a fixed contractual coupon with a fixed compounded outcome for all future reinvestments.

VA-116

From the practice bank · 20

A practice dataset contains four equally weighted returns: 0%, 2%, 4% and 6%. Treat these four observations as the complete population and do not annualise. What is the population standard deviation, rounded to two decimal places?

The square root of the population variance of five is approximately 2.24 percentage points. Mean return = (0 + 2 + 4 + 6) ÷ 4 = 3%. Work in percentage-point units throughout. Deviations from the mean are −3, −1, +1 and +3 percentage points. Their squares are 9, 1, 1 and 9. Population variance = (9 + 1 + 1 + 9) ÷ 4 = 5 squared percentage points. Population standard deviation = √5 = 2.2360679 percentage points, which rounds to 2.24. The denominator is four because the stem explicitly specifies the population convention. Remember: Check both the denominator convention and the units before calculating standard deviation.

Hint Common mistake: Using the sample denominator automatically or reporting the variance without taking its square root.

VA-117

From the practice bank · 21

Two investors each start with ₹1,00,000 and withdraw ₹10,000 immediately after year 1. X earns +20% in year 1 and −20% in year 2. Y earns −20% first and +20% second. There are no other cash flows, taxes or costs. What are their invested balances at the end of year 2?

The balances follow the separate year-by-year cash-flow calculations. For X, year 1 ends at ₹1,00,000 × 1.20 = ₹1,20,000. After withdrawal, ₹1,10,000 remains. Year 2 ends at ₹1,10,000 × 0.80 = ₹88,000. For Y, year 1 ends at ₹1,00,000 × 0.80 = ₹80,000. After withdrawal, ₹70,000 remains. Year 2 ends at ₹70,000 × 1.20 = ₹84,000. Without the withdrawal, each path would end at ₹96,000. With the specified withdrawal, X has ₹4,000 more left invested. The answer reports the remaining invested balances only. It does not add back the identical ₹10,000 each investor has already received. Remember: The timing of withdrawals can make return sequence important even when the same annual returns occur.

Hint Common mistake: Applying the two-year compounded return first and then subtracting an earlier withdrawal.

VA-144

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