Hi Question: A Lloyd’s syndicate is expanding the volume of binding authority business written in its US property account. During 2014, 30% of the £15m US property premium income was written through binding authorities. During 2015, this increased to 50% of the £18m US property premium income. All binding authorities incept on the 1 July annually. (iii) Calculate, showing all your workings, the unearned premium reserve for the US property business as at 31 December 2015, stating any assumptions made. Can someone please explain why the business written through the binding authority incepts evenly throughout the year whereas the non binder business incepts only on 1 July?
We don’t assume the non-binder business incepts on 1 July. The examiners provide various alternative calculations, some based on more approximate assumptions than others. I would assume business incepts uniformly, so my calculation would be this: For 2014, non-binder premium written = £15m * 70% = £10.5m For 2015 non-binder premium written = £18m * 8 50% = £9m By 31 December 2015, all of the business written in 2014 will be fully earned and therefore no unearned premium reserve is required. The business written during 2015 incepted on average on 1 July 2015 and therefore will be 50% earned by 31 December 2015. Hence, the unearned premium reserve required = £9m * 50% = £4.5m.
Hi Rishita First of all, we should calculate the premium written from the binding authority for each year. This is equal to 4.5 (=15 * 30%) in 2014 and 9 (=50% * 18) in 2015. With respect to the business written in 2014 through the binding authority, policies incept between 1 July 2014 and 30 June 2015, so the last policy will expire on 30 June 2016. Similarly for business written in 2015, policies incept between 1 July 2015 and 30 June 2016, so the last policy will expire on 30 June 2017. {We are implicitly assuming that policies are annual.} To calculate the UPR, we will further assume that policies incept uniformly over the year. Hence, for business written between 1 July 2014 and 30 June 2015, 50% will attach in 2014 (end of September) and 50% in 2015 (end of March). Policies attaching in 2014 will be fully earned as at the valuation date of December 2015 and policies attaching in 2015 will only be 75% earned (from end of March to end of December). The UPR for the 50% of the 2014 policies that attached in 2015 as at Dec 2015 will be equal to = 50% * 4.5 * 25% = 0.5625 In the same fashion, the UPR in respect of the 2015 policies will be equal to 75% of the business attaching in 2015 and 100% of the business attaching in 2016, hence = 50% * 75% * 9 + 50% * 9= 7.875 The total UPR in respect of the binder business as at December 2015 = 7.875 + 0.5625 = 8.4375 The total UPR in respect of the non-binder business as at December 2015 (from Katherine's workings above)=4.5 Total UPR in respect of whole of business = 12.9375 I hope this helps, have a great festive period!
