Unit study guide · NISM Series V-D
Risk, Return and Performance of Funds
5 questions in this unit
What this unit covers
- A unit is purchased at ₹20 and sold one year later at ₹22. The investor also receives a ₹1 cash distribution during the year, which is not reinvested. Ignore taxes and charges. What is the holding-period total return? Assumptions: One unit is held for the whole period. The distribution is not reinvested.
- A lump-sum investment rises from ₹1,00,000 to ₹1,33,100 in exactly three years with no intermediate cash flows. What is its compound annual growth rate? Assumptions: No contributions, withdrawals or distributions occur.
- A debt portfolio has modified duration of 4.0. Using the first-order approximation and ignoring convexity, what is the estimated percentage price change for a parallel yield rise of 0.50 percentage points? Assumptions: The yield shift is parallel. Modified duration stays constant and convexity is ignored.
- What does a fund’s beta primarily describe in relation to a chosen market benchmark?
- A teaching example has three equally weighted annual returns: −10%, 10% and 30%. Use population standard deviation: the square root of the average squared deviation from the mean. What is the standard deviation, rounded to two decimals? Assumptions: Use population standard deviation and equally weighted observations, as explicitly stated.
Key ideas
From the practice bank · 1
A unit is purchased at ₹20 and sold one year later at ₹22. The investor also receives a ₹1 cash distribution during the year, which is not reinvested. Ignore taxes and charges. What is the holding-period total return? Assumptions: One unit is held for the whole period. The distribution is not reinvested.
Total gain is ₹22 − ₹20 + ₹1 = ₹3. Dividing by the initial ₹20 gives 15%. Remember: Total return includes distributed cash as well as price or NAV changes.
Hint Include both the change in unit value and the cash received.
V-D-049From the practice bank · 2
A lump-sum investment rises from ₹1,00,000 to ₹1,33,100 in exactly three years with no intermediate cash flows. What is its compound annual growth rate? Assumptions: No contributions, withdrawals or distributions occur.
= (1,33,100/1,00,000)^(1/3) − 1 = 10%. A 1.10 factor applied for three years produces 1.331. Remember: CAGR converts a multi-year growth factor into an equivalent compound annual rate.
Hint Find the annual growth factor whose cube equals 1.331.
V-D-050From the practice bank · 3
A debt portfolio has modified duration of 4.0. Using the first-order approximation and ignoring convexity, what is the estimated percentage price change for a parallel yield rise of 0.50 percentage points? Assumptions: The yield shift is parallel. Modified duration stays constant and convexity is ignored.
The decimal yield change is 0.005. Estimated price change = −4.0 × 0.005 × 100 = −2.00%. This is a first-order estimate rather than an exact valuation. Remember: Keep basis points, percentage points and decimal yields consistent.
Hint Percentage price change is approximately minus modified duration times the decimal yield change.
V-D-051From the practice bank · 4
What does a fund’s beta primarily describe in relation to a chosen market benchmark?
Beta estimates how the fund’s returns move with the selected benchmark. It is distinct from standard deviation, which measures the variability of the fund’s own returns. Remember: A risk statistic must be interpreted according to what it measures.
Hint Beta links the fund’s returns to a market return series.
V-D-052From the practice bank · 5
A teaching example has three equally weighted annual returns: −10%, 10% and 30%. Use population standard deviation: the square root of the average squared deviation from the mean. What is the standard deviation, rounded to two decimals? Assumptions: Use population standard deviation and equally weighted observations, as explicitly stated.
Population variance = (400 + 0 + 400)/3 = 266.6667 squared percentage points. Its square root is 16.33 percentage points. The supplied population convention avoids confusing the result with sample standard deviation. Remember: State the statistical convention and distinguish average return from variability.
Hint The mean is 10%. Deviations are −20, 0 and +20 percentage points.
V-D-053CAGR expresses the change between a starting value and an ending value as a single constant annual rate.
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