Suppose there are two independent economic factors, M_{1} and M_{2}. The riskfree rate is 6%, and all stocks have independent firmspecific components with a standard deviation of 42%. Portfolios A and B are both well diversified.
Portfolio  Beta on M_{1}  Beta on M_{2}  Expected Return (%) 
A  1.5  2.4  32 
B  2.3  0.5  10 

What is the expected return–beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Expected return–beta relationship E(r_{P}) = % + β_{P1} + β_{P2}
The equation for the expected  beta relationship in this
economy can be explained as below:
E(r_{p}) = R_{f} +
β_{P1}*(Er_{1}R_{f}) +
β_{P2} * (Er_{2}  R_{f})
Let x_{1} = Er_{1}Rf
x_{2} = Er_{2}  Rf
now to solve for x_{1} and x_{2}, we need to solve
the below two equations epresenting Portfolio A and Portfolio B
returns.
therefore, 32% = 6% + 1.5x_{1} + 2.4x_{2}
and 10% = 6% + 2.3x_{1} + (0.5)x_{2}
Solving for x_{1} and x_{2.}
we get, x_{1} = 3.60
x_{2} = 8.58
Putting x_{1} and x_{2} in the below
equation:
E(r_{p}) = R_{f} +
β_{P1}*(Er_{1}R_{f}) +
β_{P2} * (Er_{2}  R_{f})
E(r_{p}) = 6% + 3.60*β_{P1} +
8.58* β_{P2}
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