Hey guys,
In the study text, the following sentence appears with regard to reverse-optimization to improve the quality of the ‘Expected Returns’ input of MVO:
“Instead of starting with expected returns (and other inputs) and deriving optimal portfolio weights from the global market portfolio and derive expected returns consistent with those weights.”
This does not make sense to me, because my understanding is that the ‘Expected Returns’ input in an MVO is expected return of each investable asset class, and not the expected return of the whole portfolio.
In reverse optimization, you start with the expected return on the global market portfolio (with known weights for each asset in that portfolio) and somehow solve for expected return for each asset.
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Yes, using the observable wights and betas of the individual assets that conform that portfolio and the total return of the portfolio.
For example, we can do reverse optimization of the S&P 500 index and find out the implicit expected returns of each stock that lay inside the index using the weights (observable data) and betas (observable data) of each stock. Also, we will need the total return and risk of the whole portfolio (observable data).
This is just like solving the equation for individual expected returns instead for the whole portofolio return and risk (which MVO does).
Remember in L2 when we could imply the growth rate the market is expecting for a singular stock just by solving “g” from:
Price = Dividend x (1+g) / (discount rate - g) … (Gordon Model)
As long as we can observe the market price, distributed dividends and the appropiate discount rate, we can solve the equation for “g” and see what growth rate the market is assuming for this particular stock. An investment decision rule could be that if “g” is quite high for the stock type, then this stock could be presumably overpriced and viceversa.
In reverse MVO, we want to discover the expected returns of each asset inside the portfolio analysed and check if it is reasonable or not. Also, we can find overpriced or underpriced singular assets and create an active portfolio taking advantage from those “fundamental” deviations. It’s a nice tool.