Not really a study per se, but a long time ago I did a comparison of total gun ownership to the murder rate, based on U.N. data, and more guns correlated to a lower murder rate on average.
"20 out of the 25 (80%) of countries with the lowest homicide rates in the world had a higher gun ownership rate higher than the world average. Of these, 15 had a gun ownership rate higher than 15 per person (60%), and 7 (28%) have a firearm ownership rate of 30 per 100. For country's with the highest homicide rates, 8 out of 25 (32%) had higher gun ownership rate than the world average. Only 2 out of 25 (8%) had a rate at or above 15.0, and zero had a rate higher than 30.0. Essentially, 80% of countries had more than the world average for gun ownership, and 60% had significantly more than the world average, compared to 32% and 8% for high homicides."
