Ferrari - Relationship of UW, Investment, Leverage, and Exposure to Total Return on Owners’ Equity

Question 1

Investors are interested in

Answer 1

ROE

Question 2

Society is interested in

Answer 2

ROE

Question 3

Regulators/actuaries are interested in

Answer 3

ROS

Question 4

in most industries, leverage results from

Answer 4

taking out loans

Question 5

for an insurer, leverage arises from

Answer 5

from its reserves since these are essentially loans from the PH

Question 6

investment income I/A can be thought of as

Answer 6

main source of return to insurer

Question 7

just like other industries, return is modified by

Answer 7

amount of leverage R/S

Question 8

leverage can either cause returns to

Answer 8

increase or decrease

direction depends on relationship between I/A and U/R:

Question 9

direction depends on relationship between I/A and U/R:

Answer 9

() = (I/A + U/R)

1. if insurer has UW profits, (+U/R), term in () Is positive (assuming positive investment income) so it makes sense for insurer to keep writing business
2. if U/R is negative, but absolute value is less than I/A, term in () is still positive, implying that is still profitable to keep writing business
3. if U/R is negative and causes term in () to become negative, it makes sense for insurer to stop writing business since writing business will reduce ROE

Question 10

term U/R (in case of UW losses) can be thought of as

Answer 10

interest cost incurred by firm to use the reserves which were contributed by the PHs

Interest: Underwriting returns, U/R = U/P * P/S * S/R

**The reserves are similar to loans from the insureds to the insurer (and are therefore non-equity capital). The underwriting losses are the interest on these loans.

The Underwriting Loss can be thought of as the cost of borrowing money from the policyholder. These losses are uncertain, and therefore variable.

Question 11

interest on a normal loan

Answer 11

is known in advance of the loan

The underwriting loss is not known until many years in the future.

Question 12

With debt loans

Answer 12

analysts know that higher amounts of loads will result in higher interest rates. However, higher amounts of reserves for insurers, due to higher amounts of written premium, may not necessarily result in higher discount rates, due to the reduction in risk from diversification.

Question 13

The Impact of Insurance Leverage

Answer 13

• for companies in all industries, increased leverage results in increased volatility of results
• insurers share this property, increased insurance leverage results in increased variability in returns
• greater level of risk associated with an increased leverage

Question 14

Optimum Capital Structure

Answer 14

is the mix of owners’ equity and liabilities which maximized value of the firm

Question 15

2 factors which affect the value of the firm

Answer 15

Expected earnings stream

Rate at which this stream is discounted by the market (discount rate)

Question 16

mix of owners’ equity and liabilities affect

Answer 16

both of these factors -> so impacts value of the firm

Question 17

↑ R/S →

2 relationships

Answer 17

↑ R/S → ↑ Earnings stream → ↑ Firm Value

↑ R/S → ↑ Volatility → ↑ Discount Rate → ↓ Firm Value

Question 18

can be seen that writing more business and therefore growing reserves has

Answer 18

both a positive and negative impact on the value of the company

-key is to find amount of reserves at which value of company reaches a peak (optimal capital structure)

Question 19

in order to assist in the calculation of optimum capital structure, actuary should determine:

Answer 19

1. expected relationship between I/A and U/R and resulting impact on expected earnings stream of writing more business
2. increase in probability of unfavorable results due to higher volatility and resulting impact on insurer value due to higher discount rates applied by market

Question 20

accounting for debt in optimal capital structure for non-insurer is simpler than accounting for __ in calculation for insurer

& reasons

Answer 20

reserves

1. with debt, valuation analysts know that an increased level increases risk and therefore results in demands by creditors for higher interest rates
2. relationship is not straight forward for insurers; earlier conclusion that increasing reserves results in higher volatility to insurer is derived from holding everything else constant; in reality, higher level of reserves implies a higher amount of premium written; possible that this higher level of premium will increase the diversification of risk and have a negative impact on variability of results

Question 21

when determining optimal capital structure, one factor have to account for

Answer 21

is volatility of investment earnings stream

Question 22

if investment earnings stream is very volatile

Answer 22

insurers reduce the leverage from reserves in order to prevent total risk from getting too large

Question 23

there are multiple uses of the determination of optimal cash structure

Answer 23

1. if public believes that the company is not insuring enough people, it may be able to justify this by demonstrating the optimal capital structure calls for a relatively low reserve/surplus ratio
2. it can be seen if an overly aggressive investment portfolio is driving the low ratio of reserves: surplus from the optimal cash structure analysis
3. if the optimal structure requires a higher reserve: surplus ratio than average company, this may suggest that the industry is overcapitalized

Question 24

some people may conclude from ROE equation that premium volume must be expanded as long as I/A remains above U/R

Answer 24

• conclusion ignores additional risk that arises from writing more premium
• Ferrari’s conclusions are derived by focusing on certain variables in the equation and holding everything else constant
• in reality, variables do interact with eachother

Question 25

incorporating these __ into formulae would result in more accuracy

Answer 25

interrelationships

Question 26

3 such interactions include

Answer 26

1. ↑P/S → ↓I/A

Driven by:

• higher portion of surplus from current business and is therefore in the form of either cash or agent’s balances; this can not be invested
• higher ratio of P/S results in more risk to owners’ equity; to compensate, insurers will need to follow more conservative investment policies
  2. ↑U/P → ↑P/S
• higher underwriting profit means that insurers can write more business

**A growth in P/S may cause U/P to decrease, as the underwriting standards may need to be loosened for the insurer to grow.

3. ↑U/P → ↑I/A
   - similar, higher UW profit means that insure can engage in more aggressive investments

Question 27

Ferrari did mention 1 relationship in his paper:

Answer 27

U/P would decrease from higher P/S due to UW standards being loosened in order for the company to grow

-Balcarek argues that this relationship is not strong as insurer can avoid this decrease in U/P by ensuring that current UW standards are maintained while growing the business

Question 28

two reasons why the investment gain on assets may increase and two reasons why it may decrease if premiums increase

Answer 28

Increase: -more money to invest from the additional premiums -due to the increased diversification, the company can undertake more aggressive investments

Decrease: -Higher portion of the assets are uninvestable (agents’ balances) -The increase in leverage may call for more conservative investments

Question 29

insurance leverage ratio

Answer 29

This looks at the relationship between the money “borrowed” from the policyholders (reserves) and the owner’s investment in the company (surplus)​

R/S

S = surplus + equity in UEPR

R = admitted assets – S

Question 30

Insurance Exposure

Answer 30

P/S

Looks at dollars of premium written that are backed by each dollar of surplus

Question 31

Use of return measures

Answer 31

i. Investors: To determine which company to invest in

ROE. Prefer companies that generate a higher return from a given equity investment.

ii. Regulators: To make sure rates are not excessive, inadequate, unfairly discriminatory

ROS. Want insurers to earn a reasonable markup relative to sales

iii. Society: To determine which companies are best using resources

ROA. Prefers that companies use the assets efficiently

Question 32

An insurer’s reserves are a form of

Answer 32

non-equity financing and provide a form of leverage for the insurer

Question 33

Non equity financing increases

Answer 33

volatility of the insurers earnings

This will result in:

1. a larger discount rate when valuing the insurer
2. possible increased earnings

The two effects will offset to some degree depending on the amount of leverage.