# Are heuristic portfolios efficient portfolios?

Markowitz's definition of an efficient portfolio is one that minimizes portfolio risk for a given level of expected return. He therefore calls portfolios along the efficient frontier "frontier portfolios" as well as "efficient portfolios".

There also exist well-performing strategies called heuristic portfolios including the equally-weighted (1/N) portfolio, and inverse-volatility portfolio (IVP). I know the 1/N portfolio doesn't lie on the efficient frontier, but is known to often outperform all frontier (efficient) portfolios out-of-sample. There's also no comment about the IVP being efficient. Can we call these two heuristic portfolios efficient portfolios?

optional question: Are the following strategies also efficient portfolios or no?

• hierarchical risk parity portfolio (HRP)
• maximum diversification portfolio (MDP)
• maximum decorrelation portfolio
• Some of these are efficient under special assumptions, for ex. Minimum Variance (which you did not mention) is efficient if expected returns are the same, 1/N is efficient if in addition the covariance matrix is the identity, MDP is efficient if excess returns on assets are proportional to their volatility, etc. I don't have a complete listing of the required conditions, but it would be interesting. – noob2 Jul 17 at 13:47
• the min variance portfolio is one of Markowitz' efficient portfolios that lie on the frontier so i knew already it was efficient. but you did answer the question on heuristic portfolios: to confirm, are you saying that if the 1/N (or MDP) is made efficient by having an identity covariance matrix (or having asset excess returns that are proportional to their volatility, in the case of MDP), then it is efficient because the said condition minimizes that portfolio's risk? (in other words, Markowitz's definition of efficiency = low risk, is upheld even for the heuristics) – develarist Jul 17 at 14:31