Many loans come with a maximum LVR of 95%, which means you cannot borrow more than 95% of the value of your home. What this also means is that if you wish to refinance you must have at least 5% equity in your home.
To put yourself in the best position to refinance, you should have at least 20% equity in your home.
Applying for a refinanced home loan with no equity is difficult unless you can get someone to go guarantor. Find out more about how you can refinance your home loan with little or no equity.
Remember that lenders look at your equity as a means to assess risk. The more equity you have, the lower risk you present to the lender.