ST7 April 2013 Question 2 inconsistency

[Polz87]

In the solution to part (ii) the investment income on free reserves during 2014 is assumed to be

1000 * 2.5% (1 + g/2) where g is the rate of growth in written premium.

This appears to assume that the free assets also grow at rate g, which holds true given the assumption that the solvency ratio stays the same as 2013.

But in parts ( iii) and (iv) where the solvency ratio isn't staying the same the formula above no longer holds true for the investment income on the free assets but yet appears to still be used in the calculations in the solutions.

For instance in part (iii) the free assets at the end of the 2014 are meant to be 1101.3
( which you can arrive at by using a simultaneous equation like in part (i)) yet the formula in the ASET solutions

1000 + 1000*0.025*(1+25%/2)+60x1.25

gives 1103.1.

Similarly for 2015

1103.1. + 1103.1*0.025(1+25%/2) + 75*1.25

gives 1228 not 1224

Can you explain this ?

 

[Darren Michaels]

In the solution to part (ii) the investment income on free reserves during 2014 is assumed to be

1000 * 2.5% (1 + g/2) where g is the rate of growth in written premium.

This appears to assume that the free assets also grow at rate g, which holds true given the assumption that the solvency ratio stays the same as 2013.

But in parts ( iii) and (iv) where the solvency ratio isn't staying the same the formula above no longer holds true for the investment income on the free assets but yet appears to still be used in the calculations in the solutions.

For instance in part (iii) the free assets at the end of the 2014 are meant to be 1101.3
( which you can arrive at by using a simultaneous equation like in part (i)) yet the formula in the ASET solutions

1000 + 1000*0.025*(1+25%/2)+60x1.25

gives 1103.1.

Similarly for 2015

1103.1. + 1103.1*0.025(1+25%/2) + 75*1.25

gives 1228 not 1224

Can you explain this ?

In parts (iii) and (iv) you are correct that we cannot assume that the solvency margin stays constant, but we can still use the fact that the free reserves will increase over the year by the insurance profit plus any investment income earned on the free reserves. The latter being 2.5% of the average of the free reserves over the year.

So if F is the free reserves at the end of 2014 we know that

F=1000+60(1+g)+((F+1000)/2)*2.5%

substituting g =25% gives F=1101.3.