Robin - Analysis of Surplus and Rate of Return

Question 1

What is policyholder-supplied funds?

Answer 1

It is conceptually viewed as the accumulated balance of paid premiums less the sum of loss and expense payments. The relative amount of PHSF by line is related to the time lag between the receipt of premiums and the payout of losses and expenses.

The investment income offset due to policyholder-supplied funds could be estimated by projecting underwriting cash flows prospectively or by looking at calendar year data.

When taking a calendar year approach, one must estimate what portion of the total investment income is generated by policyholder-supplied funds. The remaining portion is earned on stockholder-supplied funds, and some argue it therefore should not be credited to the policyholders.

Question 2

What is stockholder-supplied funds?

Answer 2

Include the insurance company’s surplus plus amounts needed to offset the portion of the loss and expense reserve not covered by premiums.

Question 3

What are the five types of underwriting profit?

Answer 3

1. Underwriting profit provisions included in manual rates and in rate filings to change manual rates
2. Corporate target underwriting profit provisions which insurance company management may request as information when deciding how much to charge.
3. Breakeven underwriting profit provisions: defined to generate an expected return to stockholders equal to the rate of return on risk-free investments.
4. Charged underwriting profit provision: may differ from the provision in the manual rate as well as from the target and the breakeven provisions. The charged rate is obtained by applying experience and schedule rating modifications and other adjustments to the manual rate.
5. Actual underwriting profits may differ from the provision charged because the provision for losses and expenses will seldom be exactly accurate and actual catastrophe losses rarely match catastrophe provision in one year.

Question 4

What are the seven method discussed in this paper?

Answer 4

1. CY Investment Offset Procedure
   traditional profit load is reduced by subtracting an investment figure derived from CY data
2. PV offset procedure
   an offset to traditional profit load. Here the offset reflects the difference in the PV of the loss payment patters of the LOB under review and some short-tailed reference line.
3. CY return method
   dose not use traditional profit load
   provision is set so as to achieve a selected target return, where return is calculated with investment income figures derived from CY data
4. PV of Income over PY of Equity
   a PV return is defined as the ratio of PV of accounting income over the annualized PV of equity. The UW profit is adjusted until the PV return = a target return.
5. PV return on Cash Flow
   UW profit provision is set so that the PV of UW cash flows and investment income on investible equity less income tax payments is equal to the PV of the changes in equity.
   UW CFs, Investment income, and tax payments are discounted using the rate of return on investments, while the changes in equity are discounted at the target rate of return
6. Risk-Adjusted Discounted CF method
   does not use the traditional profit load nor target return
   The premium is calculated so that the PV of premium payments will = the PV of paid loss, expense, and income taxes. Since the loss payments are not know with certainty, they are discounted at a new money risk-adjusted rate which is lower than the new money risk-free rate.
7. Internal Rate of Return on Equity Flows
   estimate flows of money between hypothetical stockholder and a hypothetical company. These equity flows are related to the projected stream of total income and the assumed surplus requirements. The profit provision is found by adjusting the premium until the yield on the equity flow = target rate of retrun

Question 5

What is the underwriting profit provision in the premium formula

Answer 5

L: Loss
c: Loss proportional expense ratio
FX: Fixed Expense
VR: Variable Expense Ratio
CR: Combined Ratio
U: Underwriting Profit Provision

Premium, P = (1+c)L + FX + PVR + PU
=> P = [(1+c)L + FX]/[1-(VR+U)]

The combined ratio is the ratio of losses and expenses to premium:
CR = VR + [(1+c)L+FX]/P

The combined ratio is related to the underwriting profit profit provision as follows:
U = 1 - CR

Question 6

Method1: CY Investment income offset procedure - Key Advantage and disadvantage

Answer 6

Advantages:
1. Practical. Figures come from documents already filed with statutory authorities.

2. CY investment portfolio yields tend to be relatively stable, especially if capital gains are excluded
3. Calculation is fairly short and the logic behind it is not too difficult

Disadvantages:

1. Lack of an underlying general economic theory to support the calculation.
2. Possibility of distortion when there is rapid growth or decline in loss volume or when there are significant changes in loss reserve adequacy.

In stable growth scenarios with stable patterns of reserving, it seems appropriate.

Question 7

Method1: CY Investment income offset procedure - CY results are an inherently retrospective summary of contributions from current and prior PYs, their applicability in prospective ratemaking could be challenged. Describe two justifications for using CY results.

Answer 7

Prior growth history and loss experience of the line could distort the answers. => Unless the line has experienced rapid growth or decline, the figures will tend to balance out over several years.

Certain adjustments can be made to partly correct the problem. e.g. the portion of investment income offset due to loss reserve can be stated relative to incurred loss and then be put at level consistent with the permissible loss ratio in the rates.

Question 8

Method1: Describe a particular CY investment offset procedure

Answer 8

1. find the ratio of pre-tax investment income relative to average invested assets. Then apply appropriate tax rates to the various classes of investment income to calculate the after-tax portfolio yield.

One issue: how to treat capital gain, both realized and unrealized?

• not included
• include only realized capital gains, using multi-year rolling average to enhance stablity
• reflect all capital gains, with some averaging over several years to avoid excessive volatility

2. estimate policyholder-supplied funds
   Estimation is done indirectly by looking at the UEP reserve and loss reserve. These liabilities are offset by assets, some are investible, some were supplied by the policyholder.

W.r.t UEP reserve, the 1st step is to obtain the ratio of average direct UEP to direct EP from annual statement. Then this ratio is reduced to account for prepaid expenses and premium balances owed to the company. Prepaid expenses include all or part of commissions, premium tax, other acquisition expenses and company overhead. => point here: company has already paid out the expenses, so the premium paid to cover them are not generating investment income.

W.r.t the loss reserve, 1st compute the ratio of CY loss reserve to CY incurred losses. (may use a multi-year average for more stable results). The reserves to incurred loss factor is then multiplied by the permissible loss ratio. => ratio of reserves to premiums.

Question 9

Method1: What is the equation for policyholder-supplied funds and final underwriting profit provision?

Answer 9

Add picture (pg 19-20/86)

Question 10

Method2: What is the underwriting profit provision

Answer 10

add picture (pg 22)
U = U0 - DELPVLR

Question 11

Method2: How to select interest rat for discounting losses?

Answer 11

1. In keeping with the prospective nature of ratemaking, new money yields are theoretically preferable
2. Portfolio yields are more stable and more easily verifiable. Their use also eliminate concern that the company is using different yields in its rate filing and financial statements.
3. One can use after-tax interest rate to partially account for income taxes

Question 12

Method3: CY ROE method - how to calculate ROE, and underwriting profit target

Answer 12

ROE = INC/EQ = (U*P + II - FIT)/EQ

U: underwriting profit provision
P: Premium
II: Investment Income
FIT: Federal Income Tax

add picture (pg 26)
INC = (1-tu) * U * P + II(AFIT)

II(AFIT) = i(AFIT) * (PHSF * P + S)

Then:
U = ……

Question 13

Method3: What are the issues for using a CY return method?

Answer 13

1. subject to biases due to rapid growth or changing reserve adequacy
2. question of how to select and defend a target return
3. whether one should use GAAP equity or statutory surplus
4. How to pick an appropriate leverage ratio (premium-to-surplus ratio). Should it balance against a company’s actual surplus or should a target leverage ratio be assumed? Should the leverage ratios vary by line?

Question 14

Method3: What are the positive features for using a CY return method?

Answer 14

1. Figures used in the calculation are published, making verification relatively simple.
2. Key attraction: it produces a ROE which is comparable to GAAP ROE

Question 15

Method4: PVI/PVE Model

Answer 15

Underwriting profit provision is set so PVI/PVE achieve a target present value return

r = PV(INC)/PV(EQ)

Question 16

Method4: PVI/PVE Model - How to select discount rate?

Answer 16

Rate used in discounting income is often selected to be the pre-tax, risk-free, new money yield on taxable investments. Usually, same rate is used to discount the equity.

Rationale for using pre-tax yield:
Income taxes are explicitly included in the income. The target return is set a few points above the pre-tax, risk-free rate on taxables.

If the rate is risk-free, there is no need to worry about investment default risk. Another justification for using the risk-free rate is that the resulting underwriting profit provision will not depend on the particular investment strategy of a company.

One could conceive of using different rates in discounting income and equity: could discount equity using the target rate of return.

Question 17

Method4: PVI/PVE Model - advantage

Answer 17

Advantages:
1. based on a measure of return that is both comparable to GAAP ROE and a generalization of the standard definition of the rate of interest.

It does require selection of rates for calculating investment income and taking PVs, and one must choose a target return. One may encounter some debate on the choice of these parameters:
- a regulator may lean toward a relatively low target return and a relatively small amount of surplus

Question 18

Method5 - PV CF return model

Answer 18

Underwriting profit provision is set so that PV of total CF = PV of the changes in equity

An investment rate of return is used to calculate PV of total CF while a target rate of return is used in computing the PV of changes in equity.

Total CF = sum of UW CF + II on investible equity - Income taxes

UW CF consists paid premium - paid losses & expenses

The basic relation may be expressed as:
PV(ΔEQ;r) = PV(TCF;i)

Equation for total CF: TCF = UWCF + INVIEQ - FIT
where UWCF = underwriting CF
INVIEQ = Investment Income on Investible Equity
FIT = Federal Income Tax

        Investible Equity is referring to the portion of equity which can be associated with investible assets. This consists of roughly the statutory surplus.

Question 19

Method5 - PV CF return model: biggest criticism

Answer 19

it is not exactly clear what sort of profit is being measured. PV of total CF can not be easily reconciled with GAAP accounting since timing of UW CF is not generally equaly to the timing of GAAP underwriting income.

Question 20

Method 6: risk-adjusted discounted cash flow model: This method calculates a “fair” premium directly, what is fair premium?

Answer 20

Fair premium is the sum of the risk-adjusted present value of UW CFs + an amount to cover the PV of income taxes.

Question 21

Method 6: risk-adjusted discounted cash flow model: What is the risk adjustment?

Answer 21

The risk adjustment is accomplished by discounting flows at a risk-adjusted rate that is usually less than the risk-free rate.

Question 22

Method 6: risk-adjusted discounted cash flow model: What is the basic equation?

Answer 22

Add picture - pg40

Question 23

Method 6: risk-adjusted discounted cash flow model: What is the risk-adjusted rate formula?

Answer 23

Add picture - pg41 (CAPM formula)

Question 24

Method 6: risk-adjusted discounted cash flow model: How to apply the CAPM concept to liabilities?

Answer 24

With liability such as loss reserve, there is no open market with publicly disclosed prices to provide empirical validation for the theory.

Anecdotal evidence suggests that the price for loss portfolio transfers is usually greater than the PV of the loss transferred when PVs are computed at the risk-free rate. => beta for liabilities is negative.

An indirect approach: Beta for stocks of the companies - beta for the investment portfolios held by the companies

Trouble is that this method has not been able to distinguish betas by line of business.

Question 25

Method 6: risk-adjusted discounted cash flow model: Advantages

Answer 25

1. Intuitive and directly grounded in modern financial theory
2. Defining a fair premium without resort to a total rate of return measure => sidesteps the question of what is the right target of return
3. no return relative to equity, the selection of a surplus requirement is not as critical

Question 26

Method 7: Internal Rate of Return on Equity Flow Model

Basic formula for IRR

Answer 26

pg 44

Question 27

Method 7: Internal Rate of Return on Equity Flow Model: Formula for equity flow

Answer 27

pg 46

Question 28

Method 7: Internal Rate of Return on Equity Flow Model:What is the critical distinction between the surplus and stockholder investment in the company?

Answer 28

From equity flow perspective, what is most important is what the stockholders will put into the company and what they will get back. Statutory and GAAP accounting rules and requirements are important because they can affect the equity flow.

Statutory Surplus requirements and the conservative bias of Statutory accounting rules then to increase the amount of money required from stockholders, and delay or decrease the flow of funds to them.

GAAP can also impact the flow of equity, because in a few cases, GAAP is more conservative than Statutory accounting. One example is the accrual of GAAP policyholder dividend reserve liability not recognized under statutory accounting.

Question 29

Method 7: Internal Rate of Return on Equity Flow Model:Advantages

Answer 29

1. it calculates a return to stockholders that is directly analogous to the interest rate on a loan. It is clear what return is being measured.
2. it reflects the rule of accounting insofar as they impact flow of funds to stockholders. i.e. the cost of conservatism in statutory accounting is included.

Question 30

Method 7: Internal Rate of Return on Equity Flow Model: Disadvantages

Answer 30

1. Need to select a target return and a surplus requirement. This forces one to address the issues of how to “price” the elements of risk in terms of increasing the required surplus, increasing the target return, or both.