= Solution
Form a <portfolio> with weights $\beta$ in the first factor-exposure asset, $\gamma$ in the second, and $1-\beta-\gamma$ in the <risk-free asset>. Its total initial investment is one. Its two factor exposures match those of asset $k$, so subtracting its return from $r_k$ leaves a constant. Any nonzero constant difference would allow a zero-cost long-short position with a strictly positive certain payoff after choosing its direction, an <arbitrage>. Under absence of <arbitrage>, the returns must therefore have the same <expectation>. Thus
$$
\boxed{\mathbb E r_k=1.05+0.05\beta+0.10\gamma.}
$$
The coefficients are the two factor <risk premiums> relative to the risk-free return, not the expected factor levels themselves. This reasoning permits negative weights, as assumed in the unconstrained <arbitrage pricing theory> model.
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