= Solution
The <capital asset pricing model> gives
$$
\mathbb Er_i=r_f+\beta_i(\mathbb Er_M-r_f),\qquad
\beta_i=\frac{\operatorname{Cov}(r_i,r_M)}{\operatorname{Var}(r_M)}.
$$
Thus it has the same affine relation between <expected returns> and a single systematic exposure. When the factor is the <market portfolio>'s excess return, the loadings are the <beta of an asset>, $\lambda_0=r_f$, and $\lambda_1=\mathbb Er_M-r_f$. More generally, for a nondegenerate exact one-factor model and a <market portfolio> with loading $b_M\ne0$, $\beta_i=b_i/b_M$, and the pricing relation can be rewritten using that exposure.
The interpretations and assumptions differ. The <CAPM> is an equilibrium relation obtained with a <mean-variance optimization> framework, common beliefs, and suitable borrowing/lending and market-clearing assumptions. <Arbitrage pricing theory> uses absence of <arbitrage>, factor structure, and in realistic models <diversification>; it does not identify a generic factor with the <market portfolio>. Moreover the <CAPM> permits asset-specific risk, whereas the exact model in part (a) has no residual risk. \b[The two formulas coincide for a suitable market factor, but no-arbitrage factor pricing by itself does not establish the CAPM's equilibrium assumptions.]
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