FIN-10:Risk and Return Actuarial Considerations
CAS Seminar on Ratemaking
Las Vegas, Ne
March 11-13, 2001
Moderator/Panelist
Robert F. Wolf
William M. Mercer/MMC Enterprise Risk
Panelists
Russ Bingham
Hartford Financial Services
Agenda

Overview

Net Present Value & Internal Rate of
Return Models - Characteristics and
Considerations

Complete Rate of Return Model

Compare and Contrast

Questions and Answers

FIN-11: Parameter Estimation/ Current
Research
Marginal Balance Sheet
Impact
Useful to Look at a hypothetical
Balance Sheet where all elements
are at market values, not statutory
accounting values.
Let K = Policyholder Supplied Funds.
Let S = Shareholder Supplied Funds
Assets
Liabilities
K
K+S
Capital
S
Marginal Balance Sheet
Impact
Let RA = Return on Assets
supplied by both policyholders
and shareholders.
Costs
RL
Returns
RA
RL = Cost of Debt. Borrowing
From Policyholders. Borrowing PHSF
K+S
K
RE = Cost of Capital. Using SHSF
S
Costs
RE
Marginal Balance Sheet
Impact
This relationship develops
into the generally accepted
view that an insurance company
is a levered trust.
Costs
RL
Returns
RA
K+S
K
Levered Trust
(K+S)RA = KRL + SRE
S
Costs
RE
Mission
Determine Fair
Premium
Marginal Balance Sheet
Impact
Product Market
Supply = F(cost of capital)
Policyholders supply funds (premiums) in return for compensation
for adverse financial outcomes from fortuitous contingent events.
PHSF Flow = Premiums in return for expenses and losses.
K
Financial Market
Stockholder Invests S to Back Policyholder
Supplied Funds (K)
In Return,
Equityholders Demand a Return (Re)
on Stockholder Supplied Funds (S) (Dividends or future
appreciation of enterprise value)
SRe
S
Derivation of Equilibrium
Underwriting Profit
….So Equityholders want SRE
Insurance Company Can Provide
Equityholders a Portion of Their Return
by Investing S in portfolio of securities.
...Have to return the remainder
S (RE-RA)
from Insurance Operations (i.e. Returns
on Policyholder Supplied Funds)
Why is RE> RA?
….because equityholder are taking the risk.
They can achieve RA by investing in the
same portfolio of securities on their own.
Fair Rate of Return
Solve for RL such that Stockholder
demand in returns in excess of investment
returns equates to the economic return on
Policyholder Supplied Funds
SHSF
S (RE-RA)
=
PHSF
K(RA-RL)
Cost of Debt Capital ===>
Profit Load

……If we solve for RL,
= RA - (S/K)(RE- RA)
RL

RL should serve as Risk Adjusted
Discount Rate for Loss Reserves

Risk Adjusted Rate < RA

Let Ru = Underwriting Profit Margin

RU = - K RL/Premium

Insurance Company Earns Positive
Economic Returns on Underwriting if RA
> RL (Ru> - (K/Premium) RA )
Fair Rate of Return
Solve for RU such that Stockholder
demand in returns in excess of investment
returns equates to the economic return on
Policyholder Supplied Funds
SHSF
(S/Prem) (RE-RA)
=
PHSF
(K/Prem) RA+RU
Solving for Return on Equity
…….We get the usual leverage formula:
RE = (1 + K/S)RA + (Prem/S)RU
Investment
Leverage
Underwriting
Leverage
Parameters
RE, RA, K, S
What Should You Use for Each?
P = D (1+Growth)/(1+ Cost of Capital) + D(1+Growth)2/(1+ Cost of Capital)2+...
= D(1+Growth)/(Cost of Capital - Growth)
Considerations: Parameters

Cost of Capital (RE)
– Dividend Growth
Model
– CAPM
– Cost of Holding
Capital




RBC
Best’s
Undiscounted
Reserves
Policyholder
Supplied Funds (K)
– Business as Usual

Investment Income
(RA)– New Money Yields
– Imbedded Yields
– Risk Free Rate

How Much Capital
(S)
– Allocated v.
Apportioned
– Marginal
Discounted Cash Flow Models
Two General Types
Net Present Value
Internal Rate of Return
Net Present Value Models

More Emphasis on Policyholder and
Insurance Company Flows (Myers/Cohn)

Select IRR = Cost of Capital

NPV = CF1 / (1+IRR) + CF2/(1+IRR)2+ ...

If NPV > 0, Good Deal

If NPV < 0, Bad Deal

Set Premiums P, such that NPV = 0

Solve for Ru : P = L(1+G) + F
1- V-Ru
Internal Rate of Return

Policyholder Supplied Funds important only
to extent it effects Shareholders and the
Insurance Company Flows

0 = CF1 / (1+IRR) + CF2/(1+IRR)2+ ...

Solve for IRR

If IRR > Cost of Capital then Good Deal

If IRR < Cost of Capital, then Bad Deal

Set Premiums P, such that IRR = Cost of
Capital
Discounted Cash Flows
Examples
Certain and Uncertain CFs
DCF Model - Cashflows are
Certain
Frame 1: Cash Flows are Risk Free
Assumptions
surplus to premium
loss ratio
expense ratio
risk free rate
Time
Surplus
0
1
2
50.00
-57.50
Cash Flows
Time
CFs
0
-50.00
1
57.50
Sum
7.50
0.5
75.0%
25.0%
6.0%
Premium Expenses
100.00
Premiums
100
capital
50
CFs are at end of period.
Loss Paid at end of year
Losses
Investm
Income
-25.00
-75.00
NPV
-50.00
54.25
4.25
Profit Load =
7.50
Investible
Funds
125.00
0.00
0.0%
All Cash
Flows are
Risk Free.
Hence all
cashflows
are discounted
at the risk
free rate
Solve for LR such that NPV=0
Frame 2 : Cash Flows are Risk Free
Assumptions
surplus to premium
loss ratio
expense ratio
risk free rate
Time
Surplus
0
1
2
50.00
-53.00
Cash Flows
Time
CFs
0
-50.00
1
53.00
Sum
3.00
0.5
79.5%
25.0%
6.0%
Premium Expenses
100.00
Premiums
capital
Losses
Investm
Income
-25.00
-79.50
NPV
-50.00
50.00
0.00
Profit Load =
7.50
100
50
Investible
Funds
125.00
0.00
-4.5%
Indifference between a certain loss ratio of 79.5%
and an uncertain LR of 75.0%
Risky Cashflows
Frame 3 : Cash Flows are Risky
Assumptions
surplus to premium
loss ratio
expense ratio
risk free rate
Certainty Equiv LR
Time
Surplus
0
1
2
50.00
-53.00
Cash Flows
Time
CFs
0
-50.00
1
53.00
0.5
75.0%
25.0%
6.0%
79.5%
Premium Expenses
100.00
Premiums
capital
Losses
Investm
Income
-25.00
-79.50
NPV
-50.00
50.00
Profit Load =
7.50
100
50
Investible
Funds
125.00
0.00
0.0%
By Definition, Inv Income Certainty Equivalent is risk-free rate
Sum
3.00
0.00
Another Hypothetical Example

Assumptions
– Premiums of $100
Paid 80%
@Inception, 20% a
year later
– Losses are paid at
the end of each of
the next three years
in proportions of
30%,20%, 10%
– Expense Ratio is
20% of premium,
75%of which is paid
@inceptions, 25% a
year later.
– Investment Yield is
10.0%
– No Federal Income
Taxes
– Reserve/Surplus
Ratio is 2.5
Discount Cash Flows Discounted at the Rate of
the Cost of Capital
Frame 4 : NPV Example
Premiums
Losses
Expenses
Cost of Capital
Reserves/Surplus
Inv Yield
100.00
85.00
20.00
15.0%
2.5
10.0%
Time
With a -5.0%
profit load,
NPV >0,
therefore we
should write
these policies
0
1
2
3
Assumptions
80.00
20.00
42.50
25.50
15.00
5.00
Premium
80.00
20.00
100.00
Losses
0.00
42.50
25.50
17.00
85.00
Profit Margin
Loss Ratio
Expense Ratio
IRR
17.00
Surplus
Expenses
Flow
15.00
40.00
5.00
-28.50
-16.15
-9.18
20.00
-13.83
Inv Inc
10.50
5.95
2.38
18.83
Balance Sheet Items
Time
0
1
2
3
Inv
Assets
105.00
59.50
23.80
0.00
Other
Assets
35.00
0.00
0.00
0.00
LRsv
0.00
42.50
17.00
0.00
UEPR
100.00
0.00
0.00
0.00
Reqd
Addl
Surplus
Surplus
40.00
0.00
17.00
0.00
6.80
0.00
0.00
0.00
-5.0%
85.0%
20.0%
15.0%
CF
NPV
-40.00
-40.00
28.50
24.78
16.15
12.21
9.18
6.04
13.83
3.03
Solve for Premium such that
NPV=0
Frame 5 : NPV Example
Premiums
Losses
Expenses
Cost of Capital
Reserves/Surplus
Inv Yield
95.88
85.00
19.18
15.0%
2.5
10.0%
Time
One can write
at an 88.7%LR
to cover cost of
capital
Assumptions
76.70
19.18
42.50
25.50
14.38
4.79
Premium
0
76.70
1
19.18
2
3
95.88
Losses
0.00
42.50
25.50
17.00
85.00
Profit Margin
Loss Ratio
Expense Ratio
IRR
17.00
Surplus
Expenses
Flow
14.38
38.35
4.79
-23.12
-16.15
-9.18
19.18
-10.10
Inv Inc
10.07
5.95
2.38
18.40
Balance Sheet Items
Time
0
1
2
3
Inv
Assets
100.67
59.50
23.80
0.00
Other
Assets
33.56
0.00
0.00
0.00
LRsv
0.00
42.50
17.00
0.00
UEPR
95.88
0.00
0.00
0.00
Reqd
Addl
Surplus
Surplus
38.35
0.00
17.00
0.00
6.80
0.00
0.00
0.00
-8.7%
88.7%
20.0%
15.0%
CF
NPV
-38.35
-38.35
23.12
20.11
16.15
12.21
9.18
6.04
10.10
0.00
A -8.7%
profit load
is floor
benchmark
Set Discounted Cash Flows to
0 and Solve for IRR
Frame 6 : IRR Example
Premiums
Losses
Expenses
Cost of Capital
Reserves/Surplus
Inv Yield
100.00
85.00
20.00
15.0%
2.5
10.0%
With a -5.0% Time
profit load,
the IRR =
20.5%
therefore we
should write
these policies
Time
as it
exceeds cost of
capital of
15.0%
Assumptions
80.00
20.00
42.50
25.50
15.00
5.00
Premium
0
80.00
1
20.00
2
3
100.00
17.00
Losses Expenses
0.00
15.00
42.50
5.00
25.50
17.00
85.00
Profit Margin
Loss Ratio
Expense Ratio
IRR
20.00
Surplus
Flow
40.00
-28.50
-16.15
-9.18
-13.83
Inv Inc
10.50
5.95
2.38
18.83
Balance Sheet Items
0
1
2
3
Inv
Assets
105.00
59.50
23.80
0.00
Other
Assets
35.00
0.00
0.00
0.00
LRsv
0.00
42.50
17.00
0.00
Reqd
Addl
UEPR
Surplus
Surplus
100.00
40.00
0.00
0.00
17.00
0.00
0.00
6.80
0.00
0.00
0.00
0.00
-5.0%
85.0%
20.0%
20.5%
CF
NPV
-40.00
-40.00
28.50
23.64
16.15
11.12
9.18
5.24
13.83
0.00
Solve for Premium such that
IRR=Cost of Capital
Frame 7 : IRR Example
Premiums
Losses
Expenses
Cost of Capital
Reserves/Surplus
Inv Yield
95.88
85.00
19.18
15.0%
2.5
10.0%
Time
One can write
at an 88.7%LR
to cover cost of
capital.
Assumptions
76.70
19.18
42.50
25.50
14.38
4.79
Premium
0
76.70
1
19.18
2
3
95.88
Losses Expenses
0.00
14.38
42.50
4.79
25.50
17.00
85.00
Profit Margin
Loss Ratio
Expense Ratio
IRR
17.00
19.18
Surplus
Flow
38.35
-23.12
-16.15
-9.18
-10.10
Inv Inc
10.07
5.95
2.38
18.40
Balance Sheet Items
Time
0
1
2
3
Inv
Assets
100.67
59.50
23.80
0.00
Other
Assets
33.56
0.00
0.00
0.00
LRsv
0.00
42.50
17.00
0.00
UEPR
95.88
0.00
0.00
0.00
Reqd
Addl
Surplus
Surplus
38.35
0.00
17.00
0.00
6.80
0.00
0.00
0.00
-8.7%
88.7%
20.0%
15.0%
CF
NPV
-38.35
-38.35
23.12
20.11
16.15
12.21
9.18
6.04
10.10
23.12
16.15
9.18
0.00
Again,
-8.7%
profit load
is floor
benchmark
Assumption Variations

If Premium Payment
Patterns are Revised
From 80/20 Payouts
to 45/45/10, then
IRR moves from
20.5% to 13.2%. If
revised from 80/20
to 100/0, the IRR
moves from 20.5%
to 23.8%

If Loss Payments
Revised From
50/30/20 to
20/30/50, the IRR
moves from 20.5%
to 23.4%. If revised
to 90/10, then the
IRR moves to 15.2%
Assumption Variations

If Less Surplus is
Required, say
reserves/surplus
ratio = 3, then IRR
moved from from
20.5% to 22.5%
– More Leverage

If More Surplus is
Required, say
Reserves/Surplus
Ratio = 2, then IRR
moves from 20.5%
to 18.5%
– Less Leverage
Myers-Cohn (a Particular NPV
Application) Assumptions

Insurance Company Invests Efficiently - Ru
Should Not Compensate for Inefficient
Insurer Investment Portfolios

Equityholders (SH) are Efficient Investors
- Ru Should not Compensate for Inefficient
Equityholders


S: Surplus Can be Imputed to a Policy
Underwriting Models Should Only Reflect
Systematic Risk (i.e. Risk That is
Undiversifiable)
Myers-Cohn (a Particular NPV
Application) Assumptions

….also directly considers the double
taxation issue for shareholders and
considers is a cost born by Policyholders
Myers-Cohn Equation
Net Present Value of Policy
=
Present Value of Collected Premium
The Present Value of Loss and Loss Adjustment Expense
Present Value of Other Expenses
Present Value of Tax on Underwriting Profit
Present Value of Tax on Investment Income on Policyholder and
Stockholder Supplied Funds
…….One Approach to estimate risk adjusted rate uses
Capital Asset Pricing Model
Capital Asset Pricing Model
Expected
Return
Expected
Return
20.1
Rf= 6.0

1.0
Risk
Premium
R*= 15.4
1.5
R* = rf + * (market risk premium)
 = Risk
Capital Asset Pricing Model
Quick Review



Investors are Risk Averse
Only Care About Mean and Variance of
Portfolios
E(Ri) = Rf + Bi (E(Rm) - Rf )
 Ri = Rate of Return on Asset i
 Rf
= Risk Free Rate
 Rm = Rate of Return on Market Portfolio
 Bi = Cov (Ri.Rm)/Var (Rm)
Estimation of Underwriting
Betas
Be = (1+K/S)Ba +(1/S)Bu
.
One Way to do it. See Derivation in Appendix.
Observations on Equilibrium
E(Ru) = -KRf + Bu(E(Rm)-Rf )

Derivation in Appendix

Similar to Certainty-Equivalent Formula

Does Not Depend on Investment Income

Does Not Depend on any Return on Equity
Target

Does Not Depend on Premium to Surplus
Leverage

Risk Premium (E(Rm)-Rf) Fairly Stable
Estimating Underwriting Betas
directly has some issues…...

Line of Business Considerations

State Betas Difficult to Estimate

Few Pure Property/Casualty Insurers
Publicly Traded

Prior Underwriting Profits Based Upon
Prior Methodologies - Nonapplicable
NPV v. IRR
Personal Bias - I like NPV better.
 Bad Experiences with IRR

– Case Study: Captive Feasibility and Tax
Deductibility
Case Study

Client is self-insured
– Deducts Losses when Losses are paid.
– If accident year has 10 year pay-out, tax
deductions are amortized over ten years

If pay a premium to insurer, tax is
deducted upon payment of premium
(implicitly deducting for future paid
losses in year one).
Case Study

Client can Form a Captive Insurance
Company
– If special conditions are met, premium paid
to Captive may be deducted.

Feasibility - Is this Worthwhile?
$100 Million of Tax Deductions Taken as Losses are Paid
If you form a Captive, and certain conditions are met…..
…then you can take your deductions as premiums
NPV Perspective
Cost of Capital
15.0%
Captive Tax Deductions - current
CF
0
1
2
3
4
5
6
7
8
9
10
Max Investment =
NPV
CF
20
20
10
10
10
10
5
5
5
5
17.4
15.1
6.6
5.7
5.0
4.3
1.9
1.6
1.4
1.2
100.0
60.3
0
1
2
3
4
5
6
7
8
9
10
26.7
Cash Flow Difference
NPV
CF
-20.0
100.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-20.0
87.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
80.0
67.0
0
1
2
3
4
5
6
7
8
9
10
NPV
-20.0
80.0
-20.0
-10.0
-10.0
-10.0
-10.0
-5.0
-5.0
-5.0
-5.0
-20.0
69.6
-15.1
-6.6
-5.7
-5.0
-4.3
-1.9
-1.6
-1.4
-1.2
-20.0
6.7
If your investment in the Captive is no more than $26.7 Million,
then form the captive.
At $26.7 Million, the NPV=0.
NPV Approach

Net Present Value
35
25
15

5
25
20
15
10
NPV
5
0
-5
-10
Marginal Cost of
Captive
As longs as marginal
Cost of the Captive
is less than $26.7
Million... …
It’s a good deal.
…..Now Let’s do it the IRR Way
$100 Million of Tax Deductions Taken as Losses are Paid
IRR Perspective
IRR
9.3%
Captive Tax Deductions - current
CF
0
1
2
3
4
5
6
7
8
9
10
Set NPV to 0
Captive Tax Deductions - current
NPV
CF
20
20
10
10
10
10
5
5
5
5
18.3
16.7
7.7
7.0
6.4
5.9
2.7
2.5
2.2
2.1
100.0
71.5
0
1
2
3
4
5
6
7
8
9
10
Cash Flow Difference
NPV
CF
-20.0
100.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-20.0
91.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
80.0
71.5
0
1
2
3
4
5
6
7
8
9
10
NPV
-20.0
80.0
-20.0
-10.0
-10.0
-10.0
-10.0
-5.0
-5.0
-5.0
-5.0
-20.0
73.2
-16.7
-7.7
-7.0
-6.4
-5.9
-2.7
-2.5
-2.2
-2.1
-20.0
0.0
If you invest $20.0 Million in captive, your accelerated tax deductions
imply IRR of 9.3% which is < cost of capital of 15.0%
…….therefore bad deal?
IRR Approach

Internal Rate of
Return

35
25
15

5
35.0%
30.0%
25.0%
IRR 20.0%
15.0%
10.0%
5.0%
0.0%
Marginal Cost
of Captive
The Greater the
Cost of the Captive
the Better the IRR?
…the better the
Deal?
…what’s going on?
IRR- Practical Pitfalls
Variation of the Classic IRR Pitfall “Oil
Pump” Case
 …and I fell right into it.
 Moral of the Story, if you can’t explain it
intuitively, it’s probably wrong.
 NPV never served me wrong yet.
 ….Use NPV.

IRR - Practical Pitfalls
Consider two Choices - Cost of Capital =12.5%
Investment A
Time 0 -100.0 Million
Borrowing B
Time 0 100.0 Million
Time 1 + 50.0Million
Time 2 +75.0 Million
Time 1 -50.0Million
Time 2 -75.0 Million
IRR(A) = 15.1%
Good deal because 15.1%>12.5%
IRR(B) = 15.1%
Bad Deal Because as Borrower,
because you want
IRR<Cost of Capital
IRR Pitfalls

Property/Casualty Cash Flows may have
>1 sign reversal
–
–
–
–

deposit premiums + audit premiums
retrospective premium adjustments
Agents Balances
Are you borrowing/investing?
Reinvestment Rate Assumption
IRR v NPV
Consider two Investments
Investment A
Time 0 -12.0 Million
Investment B
Time 0 -12.0 Million
Time 1 + 10.0Million
Time 2 +6.5 Million
Time 1 + 5.0Million
Time 2 +12.5 Million
Using NPV, Investment B is better as long as discount rate <20.0%,
otherwise Investment A is Better.
Because NPV(A) < NPV(B) if IRR<20.0%
Why?
NPV(B)<NPV(A) if IRR>20.0%
IRR v. NPV
Again Consider Two Investments
Investment A
Time 0 -12.0 Million
Investment B
Time 0 -12.0 Million
Time 1 + 10.0Million
Time 2 +6.5 Million
Time 1 + 5.0Million
Time 2 +12.5 Million
Now Using IRR, IRR(A) = 26.3% while IRR(B) = 25.0%
…Implies
…..Investment A better than Investment B
True…..only if Cashflows in A are reinvested at a rate 26.3%
Conclusion
Moral of the Story, if you can’t explain it
intuitively, it’s probably wrong.
 NPV never served me wrong yet.
 ….Use NPV.
 IRR approach = NPV Approach if you
define the problem correctly
 ……and that is Russ’s story

Appendix 1
One Way to derive BU
Three Betas

BA = Cov (RA.Rm)/Var (Rm)

BE = Cov (RE.Rm)/Var (Rm)

BU = Cov (RU.Rm)/Var (Rm)
One Approach: Use Ba and Be and
back into Bu
Equity Beta



E(Re) = Rf +
Be(E(Rm) - Rf )
Estimated via
Regressing
historical Re with
Market
Equityholders
Require a Rate of
Return Based
upon Their
Systematic Risk


Unsystematic Risk
Can be Diversified
Away
Still Need to
Determine
–
–
–
E(Ra)?
1/S ?
K?
Asset Portfolio Beta

E(Ra) = Rf + Ba(E(Rm) - Rf )

Only Systematic Risk is Contemplated as
Identified by BA.

Unsystematic Risk Can Be Diversified
Away

BA = Estimated via Wtd average of
elements in Portfolio
Decomposition of Betas
Be = Cov ( Re,Rm)/Var (Rm)
Re = (1 + K/S)Ra + (1/S)Ru
Therefore,
Be = (1+K/S)Ba +(1/S)Bu
Derivation of Underwriting Profit
E(Re) = Rf + Be (E(Rm) - Rf )
= (1 + K/S)E( Ra )+ (1/S)E(Ru)
E( Ra ) = Rf + Ba(E(Rm) - Rf )
Be = (1+K/S)Ba +(1/S)Bu
Therefore,
E(Ru) = -KRf + Bu(E(Rm)-Rf )
Appendix 2
Example of Myers/Cohn Approach
Myers- Cohn
Example Given
Given







Expected Loss and Loss Adjustment Expense
= $10,000 , Paid in Equally at the end of
Period 1 and Period 2, Respectively
Tax Rate on Investment Income = 25.0%
Tax Rate on underwriting Profit = 35.0%
Risk Free Rate = 8.0%
Reserve Discount Rate = 5.0%
Premium/Surplus Ratio = 2.00
No Other Expenses
Myers-Cohn
Example
Premium Cash Flows

Premium Cash Flows

Premium is Paid at Time 0

Present Value of Premium Flow = P
Myers-Cohn Example
Paid Loss Cash Flows

Present Value of Loss and Loss Adjustment
Expenses

5000/ (1.05) + 5000/ (1.05)2 = 9297.052
Myers-Cohn Example
Tax on Investment Earnings Cash Flows
Present Value of Taxes on Investment Income at Time
0:
(P + .5P)(.08)(.25) / (1.08) = .028P
Present Value of Taxes on Investment Income at Time
1:
(P - .5P + .5P(.5))(.08)(.25)) / (1.08)2 = .013P
Present Value of Taxes on Investment Income at Time
2:
(P - 1P + .5P(0))(.08)(.25)) / (1.08)3= 0
Myers-Cohn Example
Tax on Investment Earnings Cash Flows
Present Value of Taxes Paid on Investment
Income = .028P +.013P = .041P
Myers-Cohn Example
Tax on Underwriting Profit Cash Flows
Present Value of Tax on Accrued
Underwriting Profit
P(.5)(.35) / 1.08 + P(.5)(.35)/1.082 (5000)(.35)/1.05 - (5000)(.35)/1.052 =
.312P - 3253.968
Myers-Cohn Example
Computation of Underwriting Profit

P = 9297.052 + .041P + .312P - 3253.968

P = 6043.08 + .353P

P = 9340.155

P = L / (1-Ru) = 10000/ (1-Ru)

9340.155 = 10000/ (1- Ru)

Ru = - .071