Investment choices for surplus cash

CAT 2007 Slot 1 · QA · Medium · Maxima and Minima

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Passage / data set

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 of 2

The maximum guaranteed return to Shabnam is

A.
0.25%
B.
0.10%
C.
0.20%
D.
0.15%
E.
0.30%

Answer

Explanation

Let $b$ be fraction in B and $c$ be fraction in C. If market rises: return is $5b - 2.5c$ . If market falls: return is $-3b + 2c$ . To guarantee maximum return independent of market, set $5b - 2.5c = -3b + 2c \implies 8b = 4.5c \implies \frac{b}{c} = \frac{9}{16}$ . So $b = 36\%$ , $c = 64\%$ . Return $= 5(0.36) - 2.5(0.64) = 1.8 - 1.6 = 0.20\%$ .

Question 2 of 2

What strategy will maximize the guaranteed return to Shabnam?

A.
100% in option A
B.
36% in option B and 64% in option C
C.
64% in option B and 36% in option C
D.
1/3 in each of the three options
E.
30% in option A, 32% in option B and 38% in option C

Answer

Explanation

The optimal allocation is $36\%$ in B and $64\%$ in C.

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