Comprehension
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%.
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5% while a fall will entail a return of −3%.
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of −2.5% while a fall will entail a return of +2%.
Question: 1

The maximum guaranteed return to Shabnam is:

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Guaranteed return is based on the worst-case outcome; ignore higher possible returns when calculating it.
Updated On: Jul 31, 2025
  • 0.25%
  • 0.10%
  • 0.20%
  • 0.15%
  • 0.30%
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The Correct Option is B

Solution and Explanation

From the data: - Option A: guaranteed return = \( +0.10% \) (fixed).
- Option B: rise = \( +5% \), fall = \( -3% \) → guaranteed return (worst case) = \( -3% \).
- Option C: rise = \( -2.5% \), fall = \( +2% \) → guaranteed return (worst case) = \( -2.5% \).
If invested fully in any single option, the only one with non-negative guaranteed return is Option A, at \( 0.10% \). Hence the maximum guaranteed return possible without combining is \( 0.10% \).
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Question: 2

What strategy will maximize the guaranteed return to Shabnam?

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When allocating investments for guaranteed return, balance losses from worst-performing options with stable returns from safer investments.
Updated On: Jul 31, 2025
  • 100% in option A
  • 36% in option B and 64% in option C
  • 64% in option B and 36% in option C
  • 1/3 in each of the three options
  • 30% in option A, 32% in option B and 38% in option C
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The Correct Option is

Solution and Explanation

Let proportions in A, B, and C be \( a, b, c \) with \( a+b+c = 1 \).
Guaranteed return (worst-case) occurs when:
- B falls (\(-3%\)), C rises (\(-2.5%\)), and A yields \( 0.10% \).
Worst-case return = \( 0.001a - 0.03b - 0.025c \).
We want to maximise this subject to \( a+b+c = 1 \).
This is a linear optimisation problem; optimal occurs when worst cases for B and C are balanced across possible market conditions (rise/fall). Solving via equations for equal worst-case in both scenarios yields:
\( a = 0.30, b = 0.32, c = 0.38 \).
Substitute to find guaranteed return ≈ \( 0.15% \), which is higher than \( 0.10% \) from full investment in A.
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