Restrict clipping of DataFrame.corr only when cov=False

pandas/_libs/algos.pyx

@@ -391,10 +391,11 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
                     # clip `covxy / divisor` to ensure coeff is within bounds
                     if divisor != 0:
                         val = covxy / divisor
-                        if val > 1.0:
-                            val = 1.0
-                        elif val < -1.0:
-                            val = -1.0
+                        if not cov:
+                            if val > 1.0:
+                                val = 1.0
+                            elif val < -1.0:
+                                val = -1.0
                         result[xi, yi] = result[yi, xi] = val
                     else:
                         result[xi, yi] = result[yi, xi] = NaN

pandas/tests/frame/methods/test_cov_corr.py

@@ -497,3 +497,13 @@ def test_corr_within_bounds(self):
         corr_matrix = df2.corr()
         assert corr_matrix.min().min() >= -1.0
         assert corr_matrix.max().max() <= 1.0
+
+    def test_cov_with_missing_values(self):
+        df = DataFrame({"A": [1, 2, None, 4], "B": [2, 4, None, 9]})
+        expected = DataFrame(
+            {"A": [2.333333, 5.500000], "B": [5.5, 13.0]}, index=["A", "B"]
+        )
+        result1 = df.cov()
+        result2 = df.dropna().cov()
+        tm.assert_frame_equal(result1, expected)
+        tm.assert_frame_equal(result2, expected)