Calculating ESG Scores for Long-Short Portfolios

# ESG score for shorted stocks and for long-short portfolio


# ESG score for shorted stocks and for long-short portfolio












I was wondering how to compute an extra-financial score of a portfolio like, for instance, the ESG score. This score can is typical bounded between 0 and 10 (or 100) (see for example IVA methodology of MSCI. How would one get the score of a portfolio from its constituents? What is the score of a shorted stock?

More generally I am interested in the construction of portfolios with a minimum score but that is trivial after the above question is solved.

## Answer by mperlow (score 2)

https://quant.stackexchange.com/a/42777

It will be inherently tied to your business goals.

For example, if shorting a "bad ESG" stock is a goal of the portfolio, then the taking a weighted average, i.e. sum(position_size * IVA), where position sizes are allowed to be negative, will work as intended. This will allow the opt. engine to attempt to short as many "bad esg" stocks and long "good esg" stocks as possible within the additional constraints that you provide.

This can be thought of similar to calculating the beta of a portfolio. Beta of a portfolio can be calculated by taking the weighted sum, i.e. sum(position_size * beta), and they all add up nice and linearly. Beta of a portfolio can for sure flex to negative (i.e. short 100% S&P 500 ETF (SPY) has a market beta of -1).

## Answer by Borun Chowdhury (score 1)

https://quant.stackexchange.com/a/42785

As the answer by mperlow states the score may be simply the weighted average of scores where the weights are the portfolio weights. This is indeed the method used by MorningStar with an extra effect added based on other consideration. At zeroth order this answer would do.

This in hindsight is obvious and was what I thought of in the beginning but it was a bit confusing in that the contribution of a bad stock (with say a score of 2) seemed to reduced the score of the portfolio

$$ s_{portfolio} = \dots - w_B s_B \dots $$

but this is an illusion because the scores are bounded in $[0,10]$. If we think of the scores as the deviation from the mean $\tilde s_i = s_i \to s_i - 5$ then its clear that the effect of shorting a bad stock is actually to increase the score of the portfolio

$$ \begin{eqnarray} \tilde s_{portfolio}-5 &=& s_{portfolio}-5 \\ &=& \dots - w_B \tilde s_B \dots \\ &=& \dots - w_B (s_B-5) \dots \end{eqnarray} $$

This doesn't change anything (because of the linear nature of the problem) but does suggest that using scores that are deviations from the mean may be a bit more intuitive. Note also that the score of the portfolio is not bound to be in the same interval as that of the individual companies but that is not a surprise given that we are leveraging.