Your belongings are not covered by property insurance obtained by the owner. Loss of your valuables even in the event of a disaster or accident that may happen, are not covered for replacement or repair.
Renters Insurance is not as expensive as you think. Most premiums are $100-300 a year depending on the policy and agency. Shop around and find the coverage that works best for you.
You can easily add on renters insurance to a current policy like auto insurance. Sometimes bundling coverage gives better discounts.
Check out some more information on these sites below about the importance of renters insurance: