Performance with an external contribution
Series X-A case study · set 1, case 8 of 9 · 5 questions · 2 marks each
Question 1 of 5Case practice
0 right · 0 wrong · 5 to go
The case · stays here for all 5 questions
A portfolio begins the year at ₹10 lakh. At the end of six months it is worth ₹11 lakh immediately before the client adds ₹5 lakh. There are no earlier contributions or withdrawals. After that contribution the portfolio starts the second half at ₹16 lakh and ends the year at ₹15.2 lakh. There are no later cash flows, distributions, taxes or fees. The two half-year periods are equal in length. The adviser wants a time-weighted return that removes the effect of the client’s contribution. Do not count the contributed ₹5 lakh as investment profit.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Learn these topics
The written-out answers on this page are hidden while your timed set runs.
The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A portfolio begins the year at ₹10 lakh. At the end of six months it is worth ₹11 lakh immediately before the client adds ₹5 lakh. There are no earlier contributions or withdrawals. After that contribution the portfolio starts the second half at ₹16 lakh and ends the year at ₹15.2 lakh. There are no later cash flows, distributions, taxes or fees. The two half-year periods are equal in length. The adviser wants a time-weighted return that removes the effect of the client’s contribution. Do not count the contributed ₹5 lakh as investment profit.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What is the return in the first half-year?
Option A. 60%
Why it is wrong: This incorrectly includes the later contribution.
Option B. 5%
Why it is wrong: This understates the ₹1 lakh gain on ₹10 lakh.
Option C. 10% — Correct answer
Option D. 11%
Why it is wrong: This treats the ending value as a percentage.
Answer: C. (₹11 lakh ÷ ₹10 lakh − 1) × 100 = 10%. Remember: Split performance periods immediately around external cash flows.
Hint, shown before you answer in practice mode: Use the value just before the contribution.
XA-S1-C08-Q1mediumnumerical
Q2What is the second half-year return?
Option A. 38.18%
Why it is wrong: This compares the ending value with the pre-contribution value.
Option B. −5% — Correct answer
Option C. −0.80%
Why it is wrong: This treats the rupee loss as a percentage.
Option D. 5%
Why it is wrong: This reverses the sign of the loss.
Answer: B. (₹15.2 lakh ÷ ₹16 lakh − 1) × 100 = −5%. Remember: Each subperiod uses the capital actually present during that period.
Hint, shown before you answer in practice mode: The second period begins after the ₹5 lakh arrives.
XA-S1-C08-Q2mediumnumerical
Q3What is the linked time-weighted return for the full year?
Option A. 4.50% — Correct answer
Option B. 2.50%
Why it is wrong: This is the arithmetic average of the two half-year returns.
Option C. 52.00%
Why it is wrong: This counts the external contribution as profit.
Option D. 5.00%
Why it is wrong: This adds 10% and −5% instead of linking growth factors.
Answer: A. (1.10 × 0.95 − 1) × 100 = 4.50%. Remember: Time-weighted return geometrically links cash-flow-free subperiods.
Hint, shown before you answer in practice mode: Multiply the two growth factors and subtract one.
XA-S1-C08-Q3hardnumerical
Q4What is the investment gain in rupees over the year, after removing the contribution?
Option A. −₹80,000
Why it is wrong: This includes only the second-half loss.
Option B. ₹5,20,000
Why it is wrong: This includes the client’s ₹5 lakh contribution.
Option C. ₹20,000 — Correct answer
Option D. ₹45,000
Why it is wrong: This applies time-weighted return only to opening capital.
Answer: C. ₹15,20,000 − ₹10,00,000 − ₹5,00,000 = ₹20,000. The money arrived at different dates, so this rupee gain is not the time-weighted percentage. Remember: Rupee gain and time-weighted return answer different questions.
Hint, shown before you answer in practice mode: Ending wealth less opening wealth less external contributions gives the rupee gain.
XA-S1-C08-Q4mediumnumerical
Q5Why is a simple ending-value/opening-value calculation misleading here?
Option A. It treats the client’s contribution as if it were investment growth. — Correct answer
Option B. It is required to equal the average half-year return.
Why it is wrong: No such equality applies.
Option C. It must always produce a negative number.
Why it is wrong: Its sign is not the issue.
Option D. It ignores a dividend that was paid.
Why it is wrong: The case states that no distribution occurred.
Answer: A. The account increased partly because ₹5 lakh was added. A calculation that does not adjust for it overstates investment performance. Remember: Separate external cash flows from gains earned on investments.
Hint, shown before you answer in practice mode: Identify the non-performance source of money entering the account.
XA-S1-C08-Q5mediumapplication
Advice, consent and an undisclosed incentive
The next case in this set. Read its story first, then answer.
Next casePaper Trading Try it on the practice trading desk