Having a difficult time in understanding the unconstrained black-litterman model.
I keep reading the following definition:
“The BL approach reverse-engineers that the expected returns implicit in a diversified market portfolio…”
What do they mean by ‘implicit’ and ‘market portfolio’? How are co-variances able to ‘reverse engineer’ returns that differ from the expected return? Is market portfolio every single asset class, every stock etc? Somewhere else they start with the MSCI world index and adjust the weights based on their preferences, can this model be applied to other asset classes or specific indexes?
I shall attempt to clarify: Listing down all the important terms first
RO(Reverse Osmosis…er… Reverse Optimization)
_ Historical _ Variance, Covariance
Market optimal Asset Wt. (based on step 2)
Manager’s view at every step (Bayesian correction for the error term)
Consider 2,3 as the inputs to an Optimizer . The Optimizer will throw you the _ implicit historic _ E®. Add step 4 to it for each such return. Of course managers without views will have the bayesian correction as 0.
Compare this with the then prevailing _ actual historic _ return. Define your strategy. Holding securities that are underpriced and selling off those that are overpriced.
Extend the above logic in a protfolio scenario.
Extend the potfolio to a _ diversified market portfolio. _
UBL and BL have no difference in operations except for the obvious, short selling being allowed in the latter.
Hope, I have been able to drive the point through.
Consider 2,3 as the inputs to an Optimizer . The Optimizer will throw you the _ implicit historic _ E®."
These are the steps that throw me off. How does Hhstorical variance and covariances produce a E® that differs from the historical returns? I keep thinking that variance and co-variance of returns are dervived off of historical returns so back-solving for return using variance and co-variances just land you at historical returns? I
The step-by-step process by Abal/Frank looks correct. However I would recommend getting any prep provider with a video on this topic rather than following the step-by-step process above. First time I read about black-litterman model, it was blackout! I found a video by Arif extremely helpful.
No need to share the video. The expln. is much simpler :
OP- The point you overlooked is the _ Bayesian correction… _ and that is what is amiss
In a way, the BL or UBL challenges the strong form EMH. In addition it allows to incorporate the manager’s views
Suppose we are talking about 2005 and the historical returns from January 1 2005 onwards. Your starting point is the historical variance and covariance and the optimal weight there of.
We are talking about 3 stocks A. B,C with weights(market optimal) Wa, Wb, Wc.
June 01 2005, the co. A reports a major failure in its reserach on which it was banking for the next 10 years projection, but also reports super growth in sales in North American market.
The market reduces the reqd. rate for the stock’s super performance and adds a premium for the research failure and thus you see a higher P/E which seems justified. As a portfolio manager , you abide with the action and agree to the revised M-Cap for A and the market optimal weight (June 2005)there of. In BL world now there is no change as far as A is concerned.
July 2006, Stock B is unde the SEC scanner for a suspected accounting fraud but for some reasons the portfolio manager believes that this piece of new information has not been updated and the market has fairly remained neutral and not punished B or has not punished B adequately. As a portfolio manager you have a view about B and now you _ incorporate this new piece of information in your B stock’s assesment _ and thus the Bayesian correction takes place. With revised weight Wb (underweight that is) you now calculate the E(rb) and subsequently E(r,portfolio).
You carry this practice over and now at December 2014 you have a BL optimised portfolio return _ that is different than the market observed return. _
You Bayesian correction was responsible fo the deviation and in a way you also challenged the Strong Form EMH.
Okay. You use the co-variances/variances of returns to determine the market portfolio of returns. THEN you adjust the market weights based on the manager’s expectations of said returns? Is this right?
So you then back into the implied returns using the manager adjusted weights (over/underweight) to solve for returns implied by variances/co-variances of the market?
The steps are confusing because it says to calculate implied returns when really it’s just the unadjusted market returns. THEN you calculate implied returns from the adjusted market weights.
