Q. Suppose an insurer writes business which, over time, generates a
ratio of investable liabilities to annual earned premium of 1.3 and
produces an underwriting profit margin of -1% of earned premium. If
the insurer obtains an 8% investment return on total assets, what is
the minimum premium-to-surplus ratio required to provide at least a 20%
return on stockholder's equity?
A. TRR = (IA/S)(IRR) + (P/S)(UPM)
.20 = [(1.3P/S + 1)(.08) + (P/S)(-.01)
.20 = .08 + [P/S][(.8)(1.3) - .01]
P/S = 1.28
Specifically, I do not understand the "+ 1" in the second line of the
model solution. Can anyone explain where this comes from? Or is this
a mistake in the model answer? I got an answer of P/S = 2.12. Does
anyone agree with this?