In zero-shot cross-lingual transfer, a supervised NLP task trained on a corpus in one language is directly applicable to another language without any additional training. A source of cross-lingual transfer can be as straightforward as lexical overlap between languages (e.g., use of the same scripts, shared subwords) that naturally forces text embeddings to occupy a similar representation space. Recently introduced cross-lingual language model (XLM) pretraining brings out neural parameter sharing in Transformer-style networks as the most important factor for the transfer. In this paper, we aim to validate the hypothetically strong cross-lingual transfer properties induced by XLM pretraining. Particularly, we take XLM-RoBERTa (XLM-R) in our experiments that extend semantic textual similarity (STS), SQuAD and KorQuAD for machine reading comprehension, sentiment analysis, and alignment of sentence embeddings under various cross-lingual settings. Our results indicate that the presence of cross-lingual transfer is most pronounced in STS, sentiment analysis the next, and MRC the last. That is, the complexity of a downstream task softens the degree of crosslingual transfer. All of our results are empirically observed and measured, and we make our code and data publicly available.