# Can I deduce a portfolio is inefficient by compare is Sharpe ratio to the on the one the tangent portfolio?

If I have a portfolio with a Sharpe ratio lower than the Sharpe ratio of the tangent portfolio, can I conclude something about whether or not it is efficient?

If so, how/why?

Sure you can. Sharpe Ratio is defined as: $$SR=\frac{E(R)-R_f}{\sqrt{Var(R)}}$$ When you have a risk-free asset, the efficient frontier becomes linear (i.e. the line that passes from the $R_f$ and the tangent portfolio), named Capital Market Line (CML) and $SR$ denotes its slope. So lower $SR$ means that your portfolio does not lie on the efficient frontier and hence it is not efficient.

• Note that this is only true if you are allowed to leverage your portfolio (i.e. borrow at the risk-free rate to invest extra). If you have a long-only portfolio, then portfolios more risky than then tangent portfolio will have lower Sharpe ratios.
– SRKX
Commented Jun 18, 2016 at 13:09
• You are perfectly right. In this case, the efficient frontier is not linear after the tangent portfolio. Nice point! Commented Jun 19, 2016 at 14:11