This study investigates the performance of Bitcoin as a diversifier under different constraining portfolio optimization frameworks. The study employs different constraining optimization frameworks that seek to maximize risk-adjusted returns (Sharpe ratio) of the portfolio by optimizing allocations to each asset class (asset allocation). The performance attributes are evaluated by comparing the portfolios both with and without Bitcoin under frameworks ranging from equal-weighted, risk-parity, and semi-constrained to unconstrained. This study suggests that Bitcoin, due to its exotic nature, unwavering appeal, and unknown set of drivers, could act as a diversifier in normal market conditions, and it might also have some borderline hedge to safe haven properties. The results further suggest that while Bitcoin may be a potential diversifier for a risk-seeking investor, the risk-averse investor must exercise caution by limiting their exposure to Bitcoin in their portfolios, as unnecessary exposure may increase the probability of losses in extreme market conditions.