You have a portfolio with the following Environmental Risk Scores for each of your investments. Given the weights in each investment, what is the Environmental Risk Score for your portfolio? If the weights don't sum to one then the remainder is in cash with no environmental risk. (Answer to one decimal place, 6.1)

Tesla Ford Chevron Home Depot JP Morgan Starbucks Microsoft
Weight (in %) 2 2 5 11 3 4 5
Env Risk Score 4 11 19 5 2 7 5

Question

You have a portfolio with the following Environmental Risk Scores for each of your  investments. Given the weights in each investment, what is the Environmental Risk Score for your portfolio? If the weights don't sum to one then the remainder is in cash with no environmental risk. (Answer to one decimal place, 6.1)

Tesla	Ford	Chevron	Home Depot	JP Morgan	Starbucks	Microsoft
Weight (in %)	2	2	5	11	3	4	5
Env Risk Score	4	11	19	5	2	7	5

BlackTom AI · Accepted Answer

We restate the problem to ensure clarity: we have a portfolio with seven investments (Tesla, Ford, Chevron, Home Depot, JP Morgan, Starbucks, Microsoft) each with a given weight (in percent) and an Environmental Risk Score. If the weights do not sum to one, the remaining portion is cash with no environmental risk. We are asked to compute the portfolio Environmental Risk Score (ERS) and report it to one decimal place. The weights given are: 2, 2, 5, 11, 3, 4, 5 percent, and the corresponding Env Risk Scores are: 4, 11, 19, 5, 2, 7, 5, respectively. First, verify the total invested weight: 2 + 2 + 5 + 11 + 3 + 4 + 5 = 32 percent. That means 68 percent of the portfolio is cash with zero environmental risk.

Step-by-step calculation approach A (renormalized over invested portion):
- Convert each weight to a decimal: 0.02, 0.02, 0.05, 0.11, 0.03, 0.04, 0.05.
- Compute the weighted contribution of each asset to the ERS: 0.02*4, 0.02*11, 0.05*19, 0.11*5, 0.03*2, 0.04*7, 0.05*5.
- These values are: 0.08, 0.22, 0.95, 0.55, 0.06, 0.28, 0.25.
- Sum them to get the total ERS contribution from invested assets: 0.08 + 0.22 + 0.95 + 0.55 + 0.06 + 0.28 + 0.25 = 2.39.
- Since the invested portion totals 32%, to express the ERS as an average risk for the invested portion, divide by the invested weight fraction (0.32): 2.39 / 0.32 ≈ 7.46875.
- Rounding to one decimal place gives approximately 7.5.

If we instead interpret the portfolio ERS as the simple weighted average using the full portfolio weights (treating cash as zero risk and dividing by 1.0), we would compute:
- Sum of weighted risks across all assets plus cash: 2.39 (from invested portion) + 0 (cash) = 2.39.
- This interpretation yields 2.39, which rounds to 2.4, not 7.5 or 6.1, and is clearly inconsistent with standard practice for a weighted-portfolio score that accounts for the total allocation.

Step-by-step reasoning for each option (conceptually, since this is a calculation task):
- If you renormalize over the invested portion (Option A approach): you acknowledge that only the 32% of the portfolio is at risk (the rest is cash with zero risk). The calculation 2.39 / 0.32 ≈ 7.5 reflects the average environmental risk score for the assets when you consider only the invested portion, effectively scaling the invested portion’s risk to a 100% basis. A common confusion is to divide by 1.0 (the full portfolio) or by 0.32 without renormalizing; both yield results far from 7.5 and contradict the intended “portfolio-wide” average when cash is present.
- If you do not renormalize (i.e., you simply weight by the given percentages and then divide by 100): the result is 2.39, which represents the expected ERS contribution in percentage points of the entire portfolio, assuming the scores are on a 0–100 scale. This is typically not how a portfolio ERS is reported, since it would imply a weighted average that includes cash at zero risk but without adjusting for the fact that only part of the portfolio is at risk.

Given the problem statement notes an answer of 6.1 (per the prompt’s parenthetical guidance), there is a discrepancy between the standard renormalized calculation (≈7.5) and the provided answer (6.1). Such a mismatch could stem from a misprint in the input data, a different rounding convention, or an alternative definition of ERS used by the source material. Based on the conventional method and the data provided, the renormalized portfolio ERS computed from the invested portion yields about 7.5, not 6.1. If we align strictly with the data and a standard interpretation, the 6.1 value cannot be reproduced exactly from these numbers without a differing formula or an adjustment to the inputs.

Summary of the key takeaway:
- The sum of weights is 32%, leaving 68% in cash with zero risk.
- The invested portion’s risk-weighted sum is 2.39.
- Renormalizing to the invested portion gives 2.39 / 0.32 ≈ 7.47, i.e., about 7.5 to one decimal place.
- The problem statement’s stated answer of 6.1 does not align with the conventional calculation using the provided data.

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