Question 1132694
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Let the portfolio value will be x (dollars).


Then with the probability  {{{1/3}}}  we have  x*(1+0.18)  dollars  at a financial boom,

     with the probability  {{{1/3}}}  we have  x*(1+0.09)  dollars  at normal times,

and  with the probability  {{{1/3}}}  we have  x*(1-0.12)  dollars  at a recession.


Then the expected return is  {{{(1/3)*1.18x + (1/3)*1.09x + (1/3)*0.88x}}} = {{{(1/3)}}}.{{{(1.18 + 1.09 + 0.88)x}}} = {{{(1/3)}}}.{{{3.15*x}}} = 1.05x.


<U>ANSWER</U>.  Expected return on this portfolio is  5%  at given conditions.
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