But here's the problem: If a fire or a windstorm destroyed a large part of your house, causing $150,000 damage, your new insurance company would not foot the entire bill. Depending on jurisdictional laws, each company would probably pay half -- $75,000 apiece. You can certainly see why both companies would want something for the risk taken on your behalf.
Here's what happens in real life with your type of situation, assuming there have been no losses. Most insurance companies are not under any obligation to issue a full refund, simply because they would have had to pay a claim, had there been one. However, most insurance companies will be benevolent and refund premiums back to the date that your new coverage started if you furnish proof and if the backdating isn't more than three or four weeks.
Understand that insurance companies can refuse to back date a cancellation request retroactively and often will say "no" if your request is more than four weeks old.
If a request to back date and refund the premium paid on an old policy is ever turned down, look into whether the refusal came from the insurance company or if it was done by an insurance agent, who didn't check with the company.
In such situations, you could ask your new agent to intercede for you. He or she can have you sign a cancellation request, attach proof of your new coverage retroactive date and send both directly to your old insurance company, bypassing the old agent.
If that doesn't work, then live with this relatively small expense, knowing full well that your old home insurance company would have had to pay at least 50 percent of any loss during the time when both policies were in force.