Rebalancing a portfolio with a cash withdrawal
Series X-A case study · set 1, case 7 of 9 · 5 questions · 2 marks each
Question 1 of 5Case practice
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The case · stays here for all 5 questions
Asha’s investment policy targets 60% equity and 40% debt. Her current portfolio is worth ₹12 lakh: equity ₹8 lakh and debt ₹4 lakh. She must first withdraw ₹2 lakh from debt for a planned expense. This amount is no longer investible. She then wants to rebalance the remaining portfolio to the same target, without adding money. For a separate forward-looking comparison, assume equity has an expected return of 12% and debt 6%, with no claim that these forecasts are certain. Ignore taxes and transaction costs. No emergency reserve is included in the portfolio, and the planned expense must not be financed by borrowing.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
Asha’s investment policy targets 60% equity and 40% debt. Her current portfolio is worth ₹12 lakh: equity ₹8 lakh and debt ₹4 lakh. She must first withdraw ₹2 lakh from debt for a planned expense. This amount is no longer investible. She then wants to rebalance the remaining portfolio to the same target, without adding money. For a separate forward-looking comparison, assume equity has an expected return of 12% and debt 6%, with no claim that these forecasts are certain. Ignore taxes and transaction costs. No emergency reserve is included in the portfolio, and the planned expense must not be financed by borrowing.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1How much remains investible after the withdrawal?
Option A. ₹12 lakh
Why it is wrong: This ignores the planned withdrawal.
Option B. ₹10 lakh — Correct answer
Option C. ₹14 lakh
Why it is wrong: This adds rather than subtracts the withdrawal.
Option D. ₹8 lakh
Why it is wrong: This incorrectly removes all debt.
Answer: B. ₹12 lakh − ₹2 lakh = ₹10 lakh remains. Remember: Allocation targets apply to the actual investible portfolio.
Hint, shown before you answer in practice mode: Remove the planned cash need before setting target weights.
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Q2What equity value should the remaining portfolio hold at the target?
Option A. ₹7.20 lakh
Why it is wrong: This applies 60% to the pre-withdrawal value.
Option B. ₹4 lakh
Why it is wrong: This is the target debt value.
Option C. ₹8 lakh
Why it is wrong: This retains the current equity amount.
Option D. ₹6 lakh — Correct answer
Answer: D. 60% × ₹10 lakh = ₹6 lakh in equity. Remember: Withdrawals change the rupee amounts behind target weights.
Hint, shown before you answer in practice mode: Apply 60% to the post-withdrawal portfolio.
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Q3What trade restores the target after the withdrawal?
Option A. Sell ₹0.80 lakh of equity and buy debt.
Why it is wrong: This targets the old ₹12 lakh portfolio.
Option B. Sell ₹2 lakh of debt and buy equity.
Why it is wrong: This increases an already excessive equity weight.
Option C. Sell ₹2 lakh of equity and buy ₹2 lakh of debt. — Correct answer
Option D. Make no trade because ₹8 lakh equity is below ₹12 lakh.
Why it is wrong: The relevant comparison is equity’s weight, not the total amount.
Answer: C. Reducing equity from ₹8 lakh to ₹6 lakh releases ₹2 lakh, which raises debt from ₹2 lakh to ₹4 lakh. Remember: Rebalancing transfers value between asset classes without changing total wealth.
Hint, shown before you answer in practice mode: After the withdrawal, equity is ₹8 lakh and debt is ₹2 lakh.
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Q4What expected annual return does the restored allocation imply?
Option A. 10.80%
Why it is wrong: This corresponds to an 80/20 allocation.
Option B. 9.60% — Correct answer
Option C. 18.00%
Why it is wrong: This adds asset returns without weights.
Option D. 9.00%
Why it is wrong: This uses equal weights.
Answer: B. 0.60 × 12% + 0.40 × 6% = 9.60%. Forecast returns remain uncertain. Remember: Portfolio expected return is a weighted average of asset expected returns.
Hint, shown before you answer in practice mode: Weight each forecast by its target allocation.
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Q5Which statement best explains the equity sale?
Option A. It eliminates all investment risk.
Why it is wrong: Both asset classes retain risks.
Option B. It proves equity prices will fall next month.
Why it is wrong: Rebalancing is not a short-term price forecast.
Option C. It restores the agreed risk allocation after a withdrawal changed the portfolio weights. — Correct answer
Option D. It guarantees the 9.60% return.
Why it is wrong: Expected returns are not guaranteed.
Answer: C. The action follows the chosen 60/40 policy. It reduces the unintended 80% equity exposure after the debt withdrawal. Remember: A rebalancing decision can be policy-driven rather than forecast-driven.
Hint, shown before you answer in practice mode: Use the policy and the changed weights, not a market prediction.
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