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


  • 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


  • 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…


things i can add:

-stratified sampling has no theoretical support

-monte carlo advantages:

–better incorporates taxes

–shows shortfall risk

-monte carlo disadvantages:

–since inputs are distributions of the variables, there is a bias or error associated with the inputs

Hope I’m not wrong on any, lol, feel free to make comments!

Schweser did a good work on SS08. UBL allows no contraints and it does not have a reverse engineering process.

MC simulation is a dynamic approach and accept various input assumptions. ALM is a static approach and can work with MC simulation.

Monte carlo sim is appropriate when :

[1] terminal wealth is path dependent->analytical solution framweork inappropriate

[2] we need to easily incoporate tax-cashflow-transaction costs in the simulation process.

It’s correctly understood

MCS - used in aseet allocation, VAR calculations,in determining TVM at retirement in real terms …where else?

Unconstrained BL = you CAN short and have negative weights - the first post here says otherwise

Does UBL needs to run MVO? Thanks.


P No - 270, Vol 3

We call this unconstrained Black–Litterman model, or UBL model, because the procedure does not allow non-negativity constraints on the asset-class weights.

Words here are confusing…But yes i realized unconstrained every where meant negative weights are allowed but should equal to 1


Is there any practical difference between the two other than the lack of short sale constraint? I do not recall much difference other than that.

Neutral (starting point)

for UBL------> asset classes weight implicit in global b/m----views are incorporated in weights

For BL-----> its market neutral return (unadjusted) implicit in global b/m…views are incorporated in returns----view adjusted market return

So you are saying they are the same but investor views are reflected by adjusting weights in UBL (e.g. overweighting areas you expect to outperfom) but returns are adjusted in BL (simply increase the return if you tink it will outperform rather than overweighting)


Which one has the short sale restriction - UBL or BL?


Just think “unconstrained” means no constraints on short sales.

Reading this thread is more likely to confuse you than just reading the EOC review in Schweser

Yeah, & also about shorting which is allowed in UBL

Feel free to correct if any mismatch, pls!