What is the risk free rate in the economy what are the, Financial Management

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What is the risk free rate in the economy what are the

There are three assets with returns r1, r2, r3, whose variation is completely explained by two factors F1 and F2:

r1 = 0.04+2F1-F2

r2 = 0.11+3F1

r3 = 0.08-6F1+3F2

Suppose that the factors are demeaned (E(F1) = E(F2) = 0) and uncorrelated.

1. Construct two portfolios with the three assets that have factor loadings (1,0) and (0,1) respectively (one portfolio has exposure only to F1, and the second has exposure only to F2)? What is the portfolios expected return?

2. Construct a portfolio with the three assets that have factor loadings (0, 0).

3. What is the risk free rate in the economy? What are the portfolios risk premia?

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