Interpreting Negative Fund Correlation with the S&P 500
Summary
The document asks whether funds with returns negatively correlated with the S&P 500 are more likely to hold non-index assets or to own index stocks whose returns behave differently from the benchmark. It presents a linear regression of fund returns on index returns and asks whether significantly negative estimated betas across many funds imply that most of their wealth lies outside the index.
The included response suggests that inverse positions in index constituents could produce negative correlation, while non-US holdings could indicate a mismatched benchmark. It does not establish which explanation is more likely, and its claim that selected index stocks explain the pattern is not supported with evidence. A negative beta alone cannot identify holdings: short exposure, hedges, leverage, asset mix, and sample effects can all affect the estimate. Holdings data and a more detailed exposure analysis would be needed to infer how much capital is invested outside the index.
Key ideas
- Negative correlation with an index does not reveal a fund's holdings by itself.
- Short positions or hedges in index constituents can create negative market exposure.
- A benchmark may be unsuitable when a fund invests in different markets or asset classes.
- Regression beta describes return sensitivity but does not measure the share of wealth invested outside the index.
Tags
Full text
# Return correlations
# Return correlations
Assume an equity fund sample shows returns negatively correlated with the S&P 500.
Are we more inclined to say that a) these funds are invested outside the S&P 500, perhaps non-US stocks; b) these funds have selected stocks belonging to the S&P 500, but substantially uncorrelated with the index?
Update
I give a quantitative context for the problem above.
Let $R_{it}$, $M_t$ be resp. the $i$-th fund, and the index return in $t$. Let $s_i$ be the total wealth of the $i$-th fund invested in stocks belonging to the index. Therefore, $\bar{s}_i=1- s_i$ identifies portfolio assets not belonging to the index.
Consider the linear model:
$$ R_{it} = \alpha_i + \beta_iM_t + e_{it} $$
For a large sample of funds, if $\beta_i$ are consistently and significantly negative, can we say that $\bar{s}_i$ is large, that is, on average funds' wealth is not invested in the S&P index?
## Answer by user18663 (score 0)
https://quant.stackexchange.com/a/31854
When you say "an equity fund sample shows returns negatively correlated with the S&P 500". So if I assume that the benchmark (S & P 500 in your case) to measure the performance of the returns is correct and it is negatively correlated, then it may be because the fund has the inverse positions as that of S & P 500. For example it might be possible that the 10 stocks which are there in the fund as long positions are there in the S & P 500 as short positions which will depict a negative correlation.
Now if talk about your two given options:-
a) "these funds are invested outside the S&P 500, perhaps non-US stocks" - If this is the case then the obviously the choice of benchmark is entirely wrong i.e. it is obvious if the fund has invested in non US stocks, then it will show a negative corelation when compared to S & P 500.
b) "these funds have selected stocks belonging to the S&P 500, but substantially uncorrelated with the index?" - We can say this option as I have given the explanation at the start of my answer.
Hope this helps!!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.