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Franchise value (F) definition


economic value of future renewals to the firm


Total economic value (TEV, aka market value or market capitalization)


TEV = current economic value (C) + franchise value (F)


Objective of Asset Liability Management (ALM)


measure & manage the degree to which the economic value of an insurer is adversely exposed to changes in interest rates


Franchise value and ALM and accounting rules


franchise value is not recognized in ALM or accounting rules


Goal of firm's according to Panning


minimize exposure to interest rate risk while limiting exposure to accounting rules that can adversely impact solvency/ratings


Simplified assumptions of the Panning model (original version, 6)


1. all premiums are collected & expenses paid on 1/1
2. true value of losses & LAE is known and paid on 12/31
3. constant surplus, expenses, and expected losses in each year
4. no taxes
5. flat term structure of interest rates
6. all calculations are as of 1/1 immediately after business is written


UW income


UW income = premium - loss - expense


Investment income


investment income = (surplus + premium - expense) * risk-free rate


Premiums required to achieve target return on surplus


premium = [(surplus * (target ROS - risk-free rate) + loss) / (1 + risk-free rate)] + expense


Current economic value (C) definition and formula


balance sheet value on 1/1

C = surplus + premium - expense - loss discounted to time 0


Franchise value formula (fixed version) & assumptions (3)


F = (premium - expense - loss discounted to time 0) * (d / (1 - d))

where d = client retention / (1 + risk-free rate)

assumes constant:
1. client retention
2. interest rates
3. target return on surplus


Market value to book value ratio


market value to book value = total economic value / current economic value


Relationship between client retention (cr), franchise value (F), and market value to book value ratio (3)


As client retention increases:
1. franchise value increases
2. market value to book value ratio increases
3. franchise value as a % of TEV increases


Target return on surplus (k) assumptions (2)


1. k = a (constant target return on surplus) - original version
2. k = a + by = target returns are a function of the risk premium (a) and the risk-free rate (y) >> setting b<>0 allows premium to vary with interest rates


Franchise value formula with varying interest rates


F = [client retention * surplus * (a + (b - 1) * risk-free rate] / [(1 + risk-free rate) * (1 + risk-free rate - client retention)]


Dollar duration


Dollar duration = PV * D


Duration of franchise value (D(F))


D(F) = [(a - b + 1) / ((1 + y) * (a + by - y))] + (1 / (1 + y - cr))

D = dF/dy
y = risk-free rate
cr = client retention


Duration of total economic value (D(TEV))


D(TEV) = (D(C) * C + D(F) * F) / (C + F)

= weighted average duration of franchise value and current economic value


Reason that the duration of franchise value (D(F)) is greater than the duration of losses and expenses


because premium CFs are sensitive to interest rates


Impacts of an increase in interest rates with fixed k (2) and how to mitigate


1. PV(premium) decreases (unavoidable)
2. Dollar value of future premiums decreases (minimize by using a pricing strategy that allows interest rates to vary, k = a + by)


Reason that firms want to reduce duration of invested assets


to minimize exposure to interest rate risk


Ways firms can reduce the duration of invested assets (2)


1. changing the composition of the investment portfolio
2. purchasing derivative security's that modify the asset portfolio


Problems with reducing the duration of invested assets (2)


1. with larger franchise value, it is more difficult to manage interest rate risk by reducing duration
2. regulators and rating agencies will not be able to see the benefits (b/c they only see accounting numbers), which may lead them to believe the firm is in distress


Panning's recommended pricing strategy


optimize a and b parameters in k = a + by to retain a given target return and reduce duration (D(TEV)) to acceptable levels


Limitation of Panning's recommended pricing strategy


desired combination of target return on surplus and target duration of TEV can only be maintained for a narrow range of interest rates (b/c price-interest rate relationship is non-linear)

*standard ALM has the same limitation


Advantage of Panning's recommended pricing strategy


dynamic pricing policy is invisible to external audiences, so it avoids potential regulator or rating agency risks from reducing duration


Implications of Panning's model on ALM (3)


1. franchise value is real
2. franchise value is exposed to interest rates due to discounting of future CFs
3. despite importance, franchise value tends to be invisible and unmanaged


Duration of current economic value, D(C) and simplifying assumption


D(C) = [D(Assets) * PV(Assets) - D(Liab) * PV(Liab)] / C

where PV(Assets) = S + P - E
PV(Liab) = L / (1 + y)

simplifying assumption: D(C) = 1


Relationship between duration and interest rate risk


higher duration of TEV = higher interest rate risk