On 1 January 2012, Meera invested ₹10,00,000 across four asset classes: 40% in Equity, 30% in Debt, 20% in Gold and 10% in Real estate. She made no further investments or withdrawals, and all gains were reinvested in the same asset class (that is, each holding simply grows or shrinks by its annual return). Unless stated otherwise, she did not move money between asset classes.
The annual returns of the four asset classes were:
| Year | Equity | Debt | Gold | Real estate |
|---|---|---|---|---|
| 2012 | +20% | +8% | +10% | +5% |
| 2013 | −10% | +8% | +20% | +10% |
| 2014 | +30% | +7% | −10% | +10% |
| 2015 | +5% | +8% | 0% | −5% |
The return of the portfolio in a year is the percentage change in its total value over that year.
The annual returns of the four asset classes were:
| Year | Equity | Debt | Gold | Real estate |
|---|---|---|---|---|
| 2012 | +20% | +8% | +10% | +5% |
| 2013 | −10% | +8% | +20% | +10% |
| 2014 | +30% | +7% | −10% | +10% |
| 2015 | +5% | +8% | 0% | −5% |
The return of the portfolio in a year is the percentage change in its total value over that year.
Question 1
Single correct option
What was the value of Meera's Equity holding at the end of 2015?
- A. ₹5,80,000
- B. ₹5,89,680
- C. ₹5,61,600
- D. ₹6,04,800
Show answer and solution
Answer: (B) ₹5,89,680
Equity started at 40% of ₹10,00,000 = ₹4,00,000.
4,00,000 × 1.20 × 0.90 × 1.30 × 1.05 = 4,00,000 × 1.4742 = ₹5,89,680.
Trap: adding the returns (20 − 10 + 30 + 5 = 45%) gives ₹5,80,000, which ignores compounding.
Year-end holdings (₹):
| End of | Equity | Debt | Gold | Real estate | Total | Year's return |
|---|---|---|---|---|---|---|
| 2012 | 4,80,000 | 3,24,000 | 2,20,000 | 1,05,000 | 11,29,000 | 12.90% |
| 2013 | 4,32,000 | 3,49,920 | 2,64,000 | 1,15,500 | 11,61,420 | 2.87% |
| 2014 | 5,61,600 | 3,74,414 | 2,37,600 | 1,27,050 | 13,00,664 | 11.99% |
| 2015 | 5,89,680 | 4,04,368 | 2,37,600 | 1,20,698 | 13,52,345 | 3.97% |
4,00,000 × 1.20 × 0.90 × 1.30 × 1.05 = 4,00,000 × 1.4742 = ₹5,89,680.
Trap: adding the returns (20 − 10 + 30 + 5 = 45%) gives ₹5,80,000, which ignores compounding.
Year-end holdings (₹):
| End of | Equity | Debt | Gold | Real estate | Total | Year's return |
|---|---|---|---|---|---|---|
| 2012 | 4,80,000 | 3,24,000 | 2,20,000 | 1,05,000 | 11,29,000 | 12.90% |
| 2013 | 4,32,000 | 3,49,920 | 2,64,000 | 1,15,500 | 11,61,420 | 2.87% |
| 2014 | 5,61,600 | 3,74,414 | 2,37,600 | 1,27,050 | 13,00,664 | 11.99% |
| 2015 | 5,89,680 | 4,04,368 | 2,37,600 | 1,20,698 | 13,52,345 | 3.97% |
Question 2
Single correct option
In which year did Meera's portfolio earn its highest return?
- A. 2012
- B. 2013
- C. 2014
- D. 2015
Show answer and solution
Answer: (A) 2012
Track the portfolio year by year (it is not rebalanced, so weights drift):
| End of | Equity | Debt | Gold | Real estate | Total | Year's return |
|---|---|---|---|---|---|---|
| 2012 | 4,80,000 | 3,24,000 | 2,20,000 | 1,05,000 | 11,29,000 | 12.90% |
| 2013 | 4,32,000 | 3,49,920 | 2,64,000 | 1,15,500 | 11,61,420 | 2.87% |
| 2014 | 5,61,600 | 3,74,414 | 2,37,600 | 1,27,050 | 13,00,664 | 11.99% |
| 2015 | 5,89,680 | 4,04,368 | 2,37,600 | 1,20,698 | 13,52,345 | 3.97% |
2012: 11,29,000/10,00,000 − 1 = 12.90%; 2014: 13,00,664/11,61,420 − 1 ≈ 11.99%. So 2012 is highest, just ahead of 2014.
Trap: 2014 has the biggest equity return (+30%), but gold (−10%) had grown to a larger weight after 2013, dragging the portfolio return below 2012's.
| End of | Equity | Debt | Gold | Real estate | Total | Year's return |
|---|---|---|---|---|---|---|
| 2012 | 4,80,000 | 3,24,000 | 2,20,000 | 1,05,000 | 11,29,000 | 12.90% |
| 2013 | 4,32,000 | 3,49,920 | 2,64,000 | 1,15,500 | 11,61,420 | 2.87% |
| 2014 | 5,61,600 | 3,74,414 | 2,37,600 | 1,27,050 | 13,00,664 | 11.99% |
| 2015 | 5,89,680 | 4,04,368 | 2,37,600 | 1,20,698 | 13,52,345 | 3.97% |
2012: 11,29,000/10,00,000 − 1 = 12.90%; 2014: 13,00,664/11,61,420 − 1 ≈ 11.99%. So 2012 is highest, just ahead of 2014.
Trap: 2014 has the biggest equity return (+30%), but gold (−10%) had grown to a larger weight after 2013, dragging the portfolio return below 2012's.
Question 3
Numerical answer
What was the total value of Meera's portfolio at the end of 2014, in ₹ thousand? (Round to the nearest integer.)
Show answer and solution
Answer: 1301
Compute each holding to the end of 2014:
- Equity: 4,00,000 × 1.2 × 0.9 × 1.3 = 5,61,600
- Debt: 3,00,000 × 1.08 × 1.08 × 1.07 = 3,74,414
- Gold: 2,00,000 × 1.1 × 1.2 × 0.9 = 2,37,600
- Real estate: 1,00,000 × 1.05 × 1.1 × 1.1 = 1,27,050
Total = ₹13,00,664 ≈ 1301 thousand.
- Equity: 4,00,000 × 1.2 × 0.9 × 1.3 = 5,61,600
- Debt: 3,00,000 × 1.08 × 1.08 × 1.07 = 3,74,414
- Gold: 2,00,000 × 1.1 × 1.2 × 0.9 = 2,37,600
- Real estate: 1,00,000 × 1.05 × 1.1 × 1.1 = 1,27,050
Total = ₹13,00,664 ≈ 1301 thousand.
Question 4
Single correct option
Suppose instead that, at the start of every year from 2013 onwards, Meera rebalanced her portfolio back to 40% Equity, 30% Debt, 20% Gold and 10% Real estate (with no costs). Approximately what would her portfolio have been worth at the end of 2015?
- A. ₹13.72 lakh
- B. ₹13.52 lakh
- C. ₹13.20 lakh
- D. ₹14.05 lakh
Show answer and solution
Answer: (A) ₹13.72 lakh
With yearly rebalancing, the portfolio return each year is the weighted average of the four returns with fixed weights 0.4, 0.3, 0.2, 0.1:
- 2012: 0.4(20) + 0.3(8) + 0.2(10) + 0.1(5) = 12.9%
- 2013: −4 + 2.4 + 4 + 1 = 3.4%
- 2014: 12 + 2.1 − 2 + 1 = 13.1%
- 2015: 2 + 2.4 + 0 − 0.5 = 3.9%
Value = 10,00,000 × 1.129 × 1.034 × 1.131 × 1.039 ≈ ₹13,71,806 ≈ ₹13.72 lakh.
Compare with ₹13.52 lakh without rebalancing — rebalancing helped because it trimmed gold before its 2014 fall and topped up equity before its 2014 rise.
- 2012: 0.4(20) + 0.3(8) + 0.2(10) + 0.1(5) = 12.9%
- 2013: −4 + 2.4 + 4 + 1 = 3.4%
- 2014: 12 + 2.1 − 2 + 1 = 13.1%
- 2015: 2 + 2.4 + 0 − 0.5 = 3.9%
Value = 10,00,000 × 1.129 × 1.034 × 1.131 × 1.039 ≈ ₹13,71,806 ≈ ₹13.72 lakh.
Compare with ₹13.52 lakh without rebalancing — rebalancing helped because it trimmed gold before its 2014 fall and topped up equity before its 2014 rise.
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