# global minimum variance portfolio vs all-bond portfolio

I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if risk free bonds (i.e, gvt bonds) is included as selectable asset.

Would anyone please confirm that the global MVP is actuallay all-bond portfolio in this case?

If that is true, then it will contradict the power of diversification which states that there exists a diversified portfolio which has the same risk as bond but higher return. Could anyone please help clarify that?

• Why should the global MVP only contain bonds? You can compute the efficient frontier from any set of $N$ assets, these assets may not even include any bonds. Mar 2, 2021 at 23:55
• thanks. I updated my question. Mar 3, 2021 at 0:04
• If a risk-free asset is allowed, then this asset lies on the $\sigma=0$ axis. This asset will be the MVP and indeed it is a zero risk portfolio. Your efficient frontier is then the capital market line. This straight line is tangent to the efficient frontier shown in your plot and starts at the risk-free asset for $\sigma=0$. The CML dominates all currently attainable portfolios in your plot. An investor only holds portfolios on the CML. But you are right: if a risk-free asset exists, then (by definition!) the MVP only invests in this risk-free asset. Mar 3, 2021 at 1:26
• Nitpicking: A rational investor only holds... Mar 3, 2021 at 8:23
• Hahaha, good (and important) point by @BobJansen! In my world and models, there are only rational investors. To be even more precise, an investor holds portfolios on the CML if and only if all Markowitz assumptions are true (this includes rationality but also that the investor only cares about the first two moments, etc.) Mar 3, 2021 at 10:26