Cell Range Expansion (CRE) is a promising technique for the enhancement of traffic offload to pico cells. CRE is realized by adjusting the trigger timing of handover (HO) toward/from pico cells. However, inappropriate setting of trigger timing results in HO failures or Ping-Pong HOs. Both the HO failures and the Ping-Pong HOs degrade the continuity of user data services. Therefore, when CRE is applied, both the HO failures and the Ping-Pong HOs should be kept suppressed in order to guarantee the continuity of services for users. However, in the conventional studies, the application of CRE is discussed without consideration of HO performance. This paper clarifies the application range of CRE from the perspective of HO performance by taking the HO failure rates and the Ping-Pong HO rates as HO performance measures. As an example, we reveal that there is an appropriate CRE bias values which keep both the HO failure rate and Ping-Pong HO rate less than 1%. Such an appropriate CRE bias value range is smaller than the one without consideration of HO performance, which is reported in the conventional studies. The authors also observed that Ping-Pong HO occurs due to the short staying time of users at pico cells in high velocity environment. The rate of such Ping-Pong HOs becomes more than about 1% when the user velocity is more than 60km/h. Therefore, it is more difficult in high velocity environment than that in low velocity environment to find appropriate CRE bias values.