Is the
return on opening surplus calculation under Analysis of surplus the same as the
return on net assets calculation under Embedded value.
AoS : Formula
The course notes seem to describe the AoS's calculation as:
Opening surplus (A - L) * actual return + Opening L (backing assets) * (actual return - expected return)
AoS : numerical example
For e.g. using the AoS's example from the course notes, where A(0) = 2200, L(0)= 2000, a = 1% e = 0.5%,
The opening surplus = A(0) - L(0) = 200
The
return on opening surplus is calculated as
- (2200 - 2000) * (0.01) + 2000 * (0.01 - 0.005)
- = 200 * 0.01 + 2000 * (0.005)
- = 2 + 10 = 12
The closing surplus is calculated as :
- A(1) = A(0) * (1+a) = 2200 * 1.04 = 2222 less
- L(1) = L(0) * (1+e) = 2000 * 1.005 = 2010
- S(1) = A(1) - L(1) = 2222 - 2010 = 212
The surplus arising is calculated as:
- S(1) - S(0) = 212 - 200 = 12
- This ties in with the return on opening surplus calculation above (assumed to be the only source for the surplus arising)
EV: formula
The EV calculation for "
return on net assets" should reflect the "actual return earned on the starting net assets" and is split into:
- expected return and
- excess of actual return over expected return
Would its formula therefore be:
expected return * (assets backing opening liabilities) + (actual return - expected return) * (net assets)?
EV: numerical example
Using my EV formula above each numbered point would be calculated as:
- 0.005 * L(0) = 0.005 * 2000 = 10
- (0.01 - 0.005) * {A(0) - L(0)} = 0.005 * 200 = 1
This adds to 10 + 1 = 1 which is not equal to the calculation from the AoS of 12.
My questions are:
1. Is my AoS's formula of
"return on opening surplus" correct?
2. Is my EV's formula of "
return on net assets" correct for each component (1) and (2)?
3. Should question 1 and 2 be equal to each other?
Thanks in advance
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