Panning

Question 1

Untaxed Net Income

Answer 1

kS = UW Income + Investment Income
* k = target return on surplus
* UW Income = P - L - E
* Investment Income = y * (S + P - E)

Solve for P = [S(k-y) + L] / (1+y) + E

Premium collected and expenses paid at beginning of year
Losses paid at end of the year

k = target return on surplus | y = rf = risk free rate

Question 2

Target Return on Surplus, k

Answer 2

k = a + by
* where y = spot interest rate corresponding to the maturity of the firm’s liabilities

Question 3

Current Economic Value / Franchise Value

Answer 3

C = S + P - E - L/(1+y)
* Value on current assets on Jan 1st
* Premium and expenses are paid at beginning of year
* Losses at 12/31

Franchise Value = Cash flows from future renewals
F = [ P - E - L / (1+y) ] * d / (1-d)
* where d = cr / (1+y)
* cr = current retention

(1 + d + d^2 + d^3 … d^n) = 1/(1-d)
(d + d^2 + d^3 … d^n) = d/(1-d)

Total Economic Value = C + F

y = risk free

Question 4

XXX

Duration of Franchise Value, D
Dollar Duration

Answer 4

D = (a-b+1) / (1+y)(a+by-y) + 1 / (1+y-cr)
Dollar Duration = PV * D

Question 5

Duration of Assets (Surplus), Liabilities, Current Economic Value, Total Economic Value

Answer 5

Assets (Surplus) - 1 year
Liabilities - 1 year
Current Economic Value - 1 year (derived from assets and liabilities)
Total Economic Value = wtd average[franchise value, current econ value]

Question 6

How to Reduce Duration

Answer 6

Change composition of investment portfolio
* At most can reduce to D = 0
* The greater the franchise value, the more difficult it is manage interest rate risk by reducing the duration of investment portfolio (i.e. franchise value make up a larger portion of total econ value)
* Regulator and rating agencies would be confused as to why they are changing investments, they may think the firm is increasing risk

Change pricing strategy that alters the sensitivity of firm’s total econ value to changes in interest rates
* Target return on surplus, k = a + by
* Adjust a, b so that D = (a-b+1) / (1+y)(a+by-y) + 1 / (1+y-cr) is lower
* Changing pricing policy is invisible to regulators and rating agencies
* Limitation: can only be maintained for a narrow range of interest rates