Robbin: IRR, ROE, & PVI/PVE

Question 1

return from 2 perspectives

Answer 1

1. return provided to equity investor who provides capital to insurer
2. return earned by insurer

Question 2

2 hypothetical companies & assumption

Answer 2

1. single policy company: insurer that writes an individual policy
2. book of business: insurer that writes an annual policy that is scaled version of single policy
   - each insurer is assumed to be liquidated when last loss & expense payment on final policy is made

Question 3

3 models to measure return of insurance policy

Answer 3

1. internal rate of return on equity flows, IRR
2. growth model CY return on equity, ROE
3. present value of income over present value of equity, PVI/PVE

Question 4

internal rate of return on equity flows, IRR

Answer 4

return earned by equity investor in single policy company

Question 5

growth model CY return on equity, ROE

Answer 5

ROE that will be earned by the book of business insurer if it grows at a constant rate

Question 6

present value of income over present value of equity, PVI/PVE

Answer 6

this is based on the PV of projected income and equity of single policy company model

Question 7

models determine the price of policy by aiming to

Answer 7

generate a return greater than hurdle rate

Question 8

paper assumes only difference between 2 accounting frameworks is

Answer 8

that SAP incurred expenses are incurred according to a fixed pattern whereas in GAAP the expenses are incurred as premium is earned

Question 9

investable assets

Answer 9

UEPR + XRSV + LRSV + S - RECV

Question 10

IRR on Equity Flows - Objective of model

Answer 10

method selects an underwriting profit provision to achieve a target rate of return on the equity flows

Question 11

equity flows could arise due to

Answer 11

Stock purchase/repurchase

Dividend payment

Question 12

for insurers, the initial equity flow

Answer 12

will always be negative

• an equity flow to insurer is required to find initial surplus need, S0
• equity is required to contribute to initial acquisition costs (under SAP accounting, the acquisition costs are incurred upfront)

Question 13

IRR can have be multiple roots but issue would not arise when calculating IRR on anticipated equity flows because

Answer 13

the equity flows only change signs once

Initial equity flow is to insurer

Next few equity flows can be to equityholder or insurer

Final equity flows are all to equityholder (due to earnings of investment income and takedown of surplus)

Question 14

one issue with the IRR on Equity Flows method is that it makes assumption

Answer 14

that cash flows are reinvested at IRR which may differ from market rate

Question 15

IRR on Equity flows – equation summary

Answer 15

Step1: derive Income

Income = (GAAP UW income + investment income)*(1-tax)

GAAP UW Income = SAP UW Income + SAP IE – GAAP IE

Invested Assets = SAP reserves + surplus - receivables

Invested Income = invested assets*interest rate

Step2: derive Equity

DAC = SAP IE – GAAP IE (as of each period of time)

GAAP Equity = SAP Surplus + DAC

Step3: derive IRR

Equity flow = income – change in GAAP equity

Question 16

PVI/PVE Measure - Objective of model

Answer 16

PVI/ PVE method aims to determine an Underwriting Profit Provision which the ratio of PV of Income to PV of equity = a target rate of return

-single policy generates income over several years and has equity requirements that last over a year

Question 17

PVI/PVE is based on

Answer 17

PV of income over PV of equity

discounts income to end of 1st year in order to produce definition of return that is consistent with usual definition of ROE

Question 18

PIV/PVE – equation summary

Answer 18

Step1: derive income

Same as IRR

Step2: derive equity

Same as IRR

Step3: Calculate PVI/PVE

PVI is discounted to time 1

PVE is discounted to time 0

PVI/PVE

Question 19

growth model assumes

Answer 19

insurer is growing at fixed rate g

Question 20

growth company end of period balances for a period are not equal to beginning period balances from the following period because

Answer 20

a new policy is added at the beginning of the following period

Question 21

if insurer has been growing for n periods:

Answer 21

it will hit equilibrium growth phase = income statement and balance sheet accounts will be increasing @ growth rate

Question 22

growth can be considered to be self-sustaining

Answer 22

as equityholders will not need to supply any more capital once this growth rate is reached

-thought here is that income generated is just that which is necessary to support growth at that rate

Question 23

profit provisions and indicated premiums are chosen to produce a return =

Answer 23

selected target return

Question 24

models discussed in paper produce indicated premiums that are sensitive to changes in certain key inputs

Answer 24

sensitivity to changes in surplus = higher surplus loading factors are shown to produce higher required profit provisions

sensitivity to changes in interest rates = raising interest rate reduces required profit provision

-makes sense because higher investment income would mean less UW income as required to hit a target

sensitivity to changes in loss payout = increasing duration reduces the required profit provision