In　this　paper　we　theoretically　investigate　the　statistical　properties　of　three　popular　bid　ask　spread　estimators,　i.e.,　the　covariance　estimator　of　Roll　(1984),　the　High-Low　(HL)　estimator　based　on　daily　high　and　low　prices　developed　by　Corwin　and　Schultz　(2012)　and　the　Close-High-Low　(CHL)　estimator　recently　proposed　by　Abdi　and　Ranaldo　(2017).　The　biases　and　mean　squared　errors　(MSE)　of　these　three　estimators　have　been　derived　and　compared　with　each　other　asymptotically,　which　reveals　explicitly　the　superior　performance　of　HL　and　CHL　estimators　over　Roll＇s　estimator.　Moreover,　if　the　volatility　is　relatively　small　compared　to　the　spread,　the　performance　of　the　CHL　estimator　is　superior　to　the　HL　method.　Then　the　subsequent　simulation　studies　and　bootstrap　analysis　on　empirical　examples　also　verify　the　theoretical　results.　The　comparison　method　discussed　here　is　different　from　the　existing　literature,　which　usually　resorts　to　the　correlation　between　the　bid-ask　spread　estimators　with　a　benchmark　calculated　from　high-frequency　data　as　they　compare　the　performance　of　different　estimators.　(C)　2019　Elsevier　B.V.　All　rights　reserved.