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Daily Test Prep
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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