Why can't Hong Kong set it's own monetary policy?
The answer is very simple...
The essence of monetary policy is interest rates. If a government or central bank effectively set the interest rates for an economy, it can set its own monetary policy.
Hong Kong does not have this luxury. Suppose interest rates in Hong Kong were higher than that in the US. Investors will transfer wealth from the US to Hong Kong (buying HKD with their USD) in order to profit from the price difference. The result of increased demand for Hong Kong currency will increase the supply of money in Hong Kong. An increased supply of money lowers the Hong Kong interest rate, as the financial system soaks up the excess liquidity. This process continues until the interest rate difference is too small for investors to profit from moving currency between the two economies.
Any remaining differences in interest rates should be explainable by one of two things:
1) Transaction costs. The steps outlined above are not cost-free; thus arbitrage will not fully remove interest rate differentials
2) Fixed exchange rate credibility. If investors believe that the fixed exchange rate regime may be changed, then the equilibrium interest rate differential will reflect expected exchange rate gains or losses and also the risk to investors of being exposed to exchange rate volatility.