
33 Cal.Rptr.3d 98 (2005)
131 Cal.App.4th 1572
Melissa McKINLEY, Plaintiff and Appellant,
v.
XL SPECIALTY INSURANCE COMPANY, Defendant and Respondent.
No. C047068.
Court of Appeal, Third District.
July 21, 2005.
*99 Reid, Axelrod, McCormack, Griffis & Ruane and Peter Axelrod, San Rafael, CA, for Plaintiff and Appellant.
Kern and Wooley, Peter T. Kirchen, Darrell M. Padgette and Ronald J. Skocypec, Los Angeles, CA, for Defendant and Respondent.
DAVIS, Acting P.J.
In this bad faith action arising from an insurance subrogation claim, plaintiff Melissa McKinley (McKinley) appeals the trial court's judgment that she was not covered under the insurance policy at issue. The trial court determined that since McKinley was not an insured under the policy for the damage in question, the insurer, defendant XL Specialty Insurance Company (XL Specialty or XL), did not act in bad faith by bringing an unsuccessful subrogation action against her by way of arbitration. We agree and shall affirm.

BACKGROUND
On July 9, 2001, McKinley, a licensed pilot, rented a plane from Todd Aero for the purpose of receiving advanced flight instruction. McKinley signed a written rental agreement the same day and proceeded to fly the plane with her instructor pilot, Kathrynne McPherson, who was an approved pilot under the requirements of the policy. Regarding the issue of financial responsibility, the rental agreement states: "The Pilot renting the aircraft assumes full financial responsibility for any loss, theft, casualty or damage caused to the aircraft or components thereof while being rented by Pilot."
*100 While the flight went smoothly, the same could not be said for the landing. The plane suffered a "gear-up landing," damaging its hull.
XL Specialty paid Todd Aero (and/or the registered owner of the plane) approximately $41,000 for this damage under "Coverage F" (Physical Damage Coverages) of the insurance policy. XL then brought a subrogation action in Todd Aero's name against McKinley. The trial court ordered the matter to arbitration, where McKinley ultimately was found not liable for the plane damage.
McKinley then filed the present action. She claims she is an insured under the XL Specialty policy. She alleges essentially that XL Specialty acted in bad faith: XL should have defended and indemnified her regarding Todd Aero's damage claim rather than have sued her in subrogation for it. As a threshold matter, the trial court found that McKinley was not covered under the XL Specialty policy for the damage to the Todd Aero aircraft; therefore, XL could sue her in subrogation and she could not maintain an action for bad faith against XL for having done so.

DISCUSSION
The issue in this appeal is whether McKinley is an insured under the XL Specialty policy for the damage to the Todd Aero aircraft; if so, XL Specialty should have defended and indemnified McKinley for this damage rather than have sued her in subrogation for it. McKinley bases her bad faith action on her status as an insured under the XL policy; she does not argue that XL acted in bad faith by believing that she had something to do with the damage to the plane. We independently interpret the XL Specialty policy and conclude McKinley was not insured under the policy for this damage. (See Cooper Companies v. Transcontinental Ins. Co. (1995) 31 Cal.App.4th 1094, 1100, 37 Cal.Rptr.2d 508.)
An insurer has no right of subrogation against its own insured with respect to a loss or liability for which the insured is covered under the policy. Thus it follows that "[i]f the policy does not cover the insured for a particular loss or liability, ... it would neither undermine the insured's coverage nor be inequitable to impose the loss or liability on the insured if the insured caused or was otherwise responsible for the loss or liability." (Truck Ins. Exchange v. County of Los Angeles (2002) 95 Cal.App.4th 13, 21, 115 Cal.Rptr.2d 179.)
The XL Specialty policy consists of the following relevant provisions. The basic insuring agreement of the policy states:
"Insurance Company [XL Specialty] ... agrees with the Named Insured identified in the Declarations Page herein [Robert Todd dba Todd Aero] as follows:
"Insuring Agreements
"I. Liability Coverages [¶] ... [¶]
"Coverage B  Property Damage Liability  To pay on behalf of the Insured all sums which the Insured shall become legally obligated to pay as damages because of property damage[.][¶] ... [¶]
"III. Physical Damage Coverages
Coverage F  All Risk Basis  To pay for any physical damage to or loss of the aircraft, including disappearance of the aircraft."
Additionally, the XL Specialty policy has a "Student and Renter Pilot Liability Endorsement" (Endorsement No. 3). Endorsement No. 3 states in pertinent part: "In consideration of an Additional Premium ..., Liability Coverages provided herein are extended to include as `Insured' any person operating the aircraft under *101 the terms of any rental agreement or training program which provides any remuneration to the Named Insured for the use of such aircraft.... [¶][U]nder this Endorsement, the Company's Limit of Liability shall read only as follows:
"Liability Coverage: [¶] ... [¶]
"B. Property Damage $100,000.00 each occurrence[.]"
XL Specialty paid the damage claim to Todd Aero (and/or the registered owner of the plane) under "Coverage F," which, as noted, covers any physical damage to the aircraft under an all-risk basis. As the rental business owner and "Named Insured" of the aircraft, Todd Aero's claim for damage under the policy is a first-party property damage claim (to pay for physical damages to its own aircraft), and not a third-party liability claim (to pay for property damage to a third party's property caused by the aircraft). "First-party coverage refers to types of insurance under which the insurer contracts to pay benefits directly to the insured, as distinguished from liability or third-party coverage under which the insurer contracts to indemnify the insured against liability to third parties. First-party coverage includes life insurance, health and accident insurance, disability insurance, title insurance, property damage insurance, fire insurance, medical payments coverage and other types of policies providing for payments directly to the insured." (Shernoff et al., Insurance Bad Faith Litigation (2004) § 5.01, p. 5-2, fn. 4, italics added.)
In addition to the physical damage coverage provided by the XL Specialty policy under Coverage F (which applies only to the named insured, Todd Aero, or the registered owner, and not to McKinley), the XL policy includes provisions for liability coverage, including Coverage B for Property Damage Liability. As pertinent in this respect, Endorsement No. 3 has been added to the XL policy. Endorsement No. 3 extends the XL policy's Coverage B for Property Damage Liability to a renter pilot, such as McKinley, in the amount of $100,000.00 for each occurrence.
McKinley argues that Endorsement No. 3 covers her for purposes of damage to the rented airplane. However, Endorsement No. 3 refers only to "Liability Coverages," which do not include damage to the airplane itself. (Emphasis added.) As noted, liability coverage is third-party coverage under which XL contracts to indemnify the insured against liability to third parties. The damage to the aircraft here did not involve damage to a third party's property, but rather damage to the insured's (i.e., first party, Todd Aero's) property. If an equipment rental company has an insurance policy that provides third-party liability/property damage coverage to an equipment renter, the renter cannot transform that policy into one providing first-party physical damage coverage; otherwise, the renter could wreck the rented equipment and claim coverage for that damage under the liability/property damage coverage. Thus, Endorsement No. 3-Liability Coverage B cannot be invoked to cover McKinley for damage to the aircraft itself.
The definitions of the terms "property damage" and "physical damage" in the XL Specialty policy further support this interpretation. "Property Damage" is defined as: "(a) physical injury to or destruction of tangible property which occurs during the policy period, including loss of use thereof at any time resulting therefrom, or (b) loss of use of tangible property which has not been physically injured or destroyed, provided such loss of use is caused by a covered occurrence." "Physical Damage" is defined as: "direct and accidental physical loss of or damage to the aircraft, hereinafter called loss, but does not include loss of use or any residual depreciation in *102 value, if any, after repairs have been made." There is no mention or reference to damage to the airplane itself in the definition of "property damage." In general, the term "property damage" in the XL policy is tied to liability coverage. Specifically, Liability Coverage B (Property Damage Liability) in the XL policy includes no mention of damage to the plane itself. Any reference to damage done to the aircraft is contained in the policy's definition of "physical damage" and in Coverage F (Physical Damage Coverage), which has its own separate insuring agreement heading; this further highlights the distinction between Liability Coverages and Physical Damage Coverages in the XL policy.
Exclusion 7, to which the parties refer, is also consistent with this distinction between first-party coverage for physical damage to the airplane itself (coverage that applies only to the named insured, i.e., Todd Aero, and/or the registered owner of the plane) and third-party liability coverage for property damage to a third party's property that is caused by the airplane (coverage that applies to the named insured, Todd Aero, and/or the registered owner, and to McKinley as a renter-insured under Endorsement No. 3). Exclusion 7 states as pertinent: "This policy does not apply: [¶] ... [¶] 7. Under Coverages B and D [Property Damage Liability] to property damage to property owned, occupied, rented or used by, or in the care, custody or control of the Insured ...."
Nor does McKinley hold a position akin to Todd Aero in the insurance equation in relationship to the plane's owner. Todd Aero is the named insured and owner of the rental business, and is generally insured under the policy. McKinley rented the aircraft on one occasion, and was specifically insured for third-party property damage liability during that rental episode. Todd Aero is a first party under the XL policy; XL cannot pay off the plane's owner and then seek that payment from Todd Aero. Todd Aero took out the insurance to avoid this. The insurance context here is similar to a common insurance situation such as first-party insurance on a leased car, where the lessor actually owns the car and the lessee takes out an insurance policy. If the car is damaged, the lessor's interest in the car is protected by the insurance, and the insurer does not sue the lessee, the named insured.
In addition, the rental agreement that McKinley signed includes a clause regarding the purchase of outside insurance by the renter. It states: "Insurance: The aircraft insurance protection provided by Todd Aero is available for inspection at Todd Aero upon request. Although Todd Aero provides insurance for the aircraft, it is strongly encouraged that the Pilot take out renter's insurance." More to the point, the rental agreement, as noted, also states: "The Pilot renting the aircraft assumes full financial responsibility for any loss, theft, casualty or damage caused to the aircraft or components thereof while being rented by Pilot." While the rental agreement is not dispositive, the purpose of these clauses is clearto encourage renters to obtain outside insurance in case of a situation such as this; McKinley apparently purchased outside insurance here. The XL Specialty policy on Liability Coverage B/Property Damage, including Endorsement No. 3, applies only to third-party liability situations and does not include any coverage for first-party physical damage to the aircraft itself.
In the end, an insurer who has paid a claim for damage to rented equipment cannot be said to have acted in bad faith in seeking subrogation from a renter reasonably believed to have caused that damage.


*103 DISPOSITION
The judgment is affirmed.
We concur: NICHOLSON and RAYE, JJ.
