Suppose a world where the CAPM holds, i.e. stocks with higher beta have higher expected returns. What would be in this world the implication for Sharpe Ratios? Would stocks with higher beta also have higher sharpe ratios or should sharpe ratios be equal?

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    $\begingroup$ Hint: Review the Capital Market Line en.wikipedia.org/wiki/Capital_market_line $\endgroup$ – noob2 Mar 1 '18 at 18:28
  • $\begingroup$ I am fully aware of what the CML implies. It implies that the market portfolio should have the highest attainable sharpe ratio. It does not tell me anything about how sharpe ratios line up with betas or not. $\endgroup$ – phdstudent Mar 1 '18 at 18:32
  • $\begingroup$ A portfolio with a single stock has undiversified risk that you are not being rewarded for, so the sharpe ratio will be less than the sharpe ratio of the market portfolio.You need to diversify to attain that ideal sharpe ratio. $\endgroup$ – noob2 Mar 1 '18 at 18:49
  • $\begingroup$ Again that does not answer the question of what are the theory implications for the relation between betas and sharpe ratios. $\endgroup$ – phdstudent Mar 1 '18 at 18:51
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    $\begingroup$ I'll make 1 more attempt: If and only if a portfolio is fully diversified, then the Sharpe ratio does not depend on Beta and is equal to the Sharpe ratio of the market portfolio. (higher beta gives higher return but also higher $\sigma$ and the two exactly cancel out). But all single stock portfolios are undiversified and attain a worse Sharpe Ratio due to excessive σ (the denominator of the s.r.) So for a single stock it does not even make sense to compute a shrape ratio, it is going to be low. $\endgroup$ – noob2 Mar 1 '18 at 19:11

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