CAT 2007 — QA Question 6
Answer the next 2 questions based on the information given below.
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:
Answer & solution
- A
0.25%
- B
0.10%
0.20%
- D
0.15%
- E
0.30%
Let Shabnam have Rs. 100 to invest. Let Rs. x, Rs. y and Rs. z be invested in option A, B and C respectively.
∴ 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 should be such that regardless of whether the market rises or falls, they give the same return, which is the maximum guaranteed return.
∴ 0.001x + 0.05y – 0.025z = 0.001x – 0.03y + 0.02z
∴ y/z = 9/16
Now, consider different possible values of x, y and z. The returns are as follows:
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We see that as the values of y and z increase, the returns increase.
∴ The returns are maximum when x = 0%, y = 36% and z = 64% (Note that the values of y and x are multiples of 9 and 16.)
The maximum returns are 0.2%.
Hence, option (c).