It has appeared couple of time in exams, just like to understand it better

**Unconstrained Black - Litterman (UBL)**

- Uses market cap weight of asset classes in a global benchmarks -
**Neutral starting point** - Adjust up/downward to reflect investors opinion (according to Bayesian procedure)
- Unconstrained (I guess no negative weights here)

**Advantages -** Well diversified (since global bencmark weight are starting point), overcomes estimation error problem in conventional MVO

**Black-Litterman**

- Equilibrium market returns as
**Neutral starting point** - To have equlibrium mkt return, first need to define Equilibrium mkt weights & covariance - these weight (considered optimal) are taken same as in UBL - from a diversified global B/m - back solve return - I guess this is why it is also called as
**REVERSE OPTIMISATION**) *Weights are given no special insight. Use same weight as in global bencmark.*- On these market equilibrium returns have
**views & confidence levels of investors**&**ADJUST** - They call it then _
**View - adjusted market equilibrium returns**_ - Run mean variance optimization get Efficient Frontiers & portfolio

**Advantages :**

Considers current market condition & investors expectations (improvement over historical return based MVO) - collaborating market equilibrium returns (i guess present mkt scenario) with investors views helps to dampen the extreme views investor may hold which could have dominated optimation

- Well diversified (same as UBL - anchored to global B/m weights)
- Overcomes estimation error problem in conventional MVO

**REF**

- Run optimation many times - hovering around the point estimates return & covariance. (I think they use Monte carlo simulation here?)
- Each simulation trial generates set of return & variances - simulated efficient portfolios
- Intergrate many simulated efficient portfolios into one become
**REF**(here integrating into one leads to averaging of each input)

**Advantages:** Stable, diversified than traditional MVO, **Disadvantage -** no therotical support

Please share your inputs if you have understood these processes differently…

thnx!