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Question of the Day
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%

The maximum guaranteed return to Shabnam is
(1) 0.25%
(2) 0.10%
(3) 0.20%
(4) 0.15%
(5) 0.30%


Solution
Let Shabnam have Rs. 100 to invest. Let Rs. x, Rs. y and Rs. z be invested in option A, B and C respectively.
Therefore, x + y + z = 100 ... (I)
If there is a rise in the stock market, returns = 0.001x + 0.05y 0.025z
If there is a fall in the stock market, returns = 0.001x 0.03y + 0.02z
Now, x, y and z are such that regardless of whether the market rises or falls, they give the same return, which is the maximum guaranteed return.
Therefore, 0.001x + 0.05y 0.025z = 0.001x 0.03y + 0.02z
Therefore, y/z = 9/16
Now, consider different possible values of x, y and z.

We see that as the values of y and z increase, the returns increase.
Therefore, The returns are maximum when x = 0%, y = 36% and z = 64%
The maximum returns are 0.2%.
Hence, option 3

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