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State the original Y-on-X fit
Asset return is the response and benchmark the explanatory series. Centered cross-product is 21, benchmark squared sum 10 and asset squared sum 45.3 in percentage-point units. Forward slope is 21/10=2.1.
Change the response direction
Regressing benchmark on asset divides the same cross-product by 45.3, giving 70/151≈0.463576. Its residuals are in benchmark-return units, so it minimises a different squared-error criterion.
Reconcile the two slopes
Their product is (21/10)×(70/151)=147/151, equal to squared correlation in this simple intercept setup. Only under a perfect nonconstant linear fit does that product become one and the slopes become reciprocals.
Retain the intended question
A forward beta estimate answers how asset returns are fitted against the chosen benchmark. Reversing the equation changes the estimation question; algebraically solving a fitted line for X is not the same as refitting X on Y.