# 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?

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.