Mutual fund XYZ offers schemes where one can invest for a period of 30 days.SCHEME A: It invests the money in debt funds and gives a steady return of 1.2%SCHEME B: It takes the bearish view of the market and short sells itand offers a return of -6%if the market goes up and 9% return if themarket goes downSCHEME C:It takes the bullish views of the market and buys into it and gives a 13% returnif market goes up and -7%return if the market goes down.Find the max guaranteed return that any person can expect if he invested in one or more of these scheme.

1) 13/7 %
2) 15/7%
3) 16/7%
4) 17/7%

• Answer=15/7 %
  
  Explanation:
  Scheme A: fixed return of 1.2%
  
  But for Scheme B && Scheme C:
  if Market goes up then: -6% +13%
  if Mkt goes down then: +9% -7%
  
  Now, Suppose one invests "100b" in Scheme B & "100c" in Scheme C: then return will be as follows:
  
  Case:1> If Market goes up
  then, RETURN=13a-6b
  
  Case2>If Market goes down:
  then, RETURN=9b-7c
  
  Now, equating the returns obtained in both the cases (in order to neutralise the market fluctuations & to see the assured return)
  
  => 13c-6b=9b-7c =>20c=15b => 4c=3b => b:c = 4:3.
  
  Therefore, if one invests in the ratio 4:3 in scheme B & C respectively; one would obtain the same return regardless of the market fluctuations.
  
  Now, finding the value of that assured return (also to check whether this assured return% > than the one being offered in schemeA)
  
  Let the investments be 400 & 300 in Scheme B & C respectively. Then the returns will be:
  
  CASE1> If Market goes up:
  then Return= 39-24 => 15
  
  Case2: If Market goes down:
  then RETURN=36-21 =>15
  
  Therefore, the value of this guaranteed return% = (Return/Investment)* 100
  which is =(15/700)*100 => 15/7 %
  
  & this Return% is also greater than the return being offered by Scheme A.
  
  So, Answer= 15/7 %.
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