I'm happy that the PVIF rises and the free surplus falls as a result of strengthening the reserving basis. However, I'm unsure as to why if r>i, the EV will fall, I would have thought it was other way around using the diagram in the notes? Could anyone explain, perhaps with a numerical example would be best? Many Thanks
Let's consider a very simple insurer. It has assets of 250, reserves of 180 and a cashflow to pay of 185 in one year's time. It assumes an investment return i=5% and has a risk discount rate of r=10%. The net assets are then: 250 - 180 = 70 Its PVIF is then: (180(1.05) - 185) / 1.1 = 4 / 1.1 = 3.636 So EV = 70 + 3.636 = 73.636 Now if the insurer strengthens its reserves to 200. The net assets are then: 250 - 200 = 50 (so they've gone down) Its PVIF is then: (200(1.05) - 185) / 1.1 = 25 / 1.1 = 22.727 (its gone up) So EV = 50 + 22.727 = 72.727 So the EV has gone down. What has happened is that reserves were increased by 20. These reserves rolled up with 5% interest and were then released. They were then discounted back at 10%. 20 x 1.05 / 1.1 < 20, so the EV has fallen. I hope this helps. Mark
