Cummins Capital Flashcards
(11 cards)
RAROC
EVA
EVAOC
Risk Adjusted Return On Capital
* RAROC = Net Income / C
* net income is after taxes and capital expenses
* if RAROC ≥ LOB’s cost of capital then writing the LOB is consistent with firm value maximization
Economic Value Added (EVA)
* EVA = Net Income - cost of capital * C
* if EVA ≥ 0 then writing the LOB is consistent with firm value maximization
Economic Value Added on Capital (EVAOC)
* EVAOC = Net Income / C - cost of capital
* if EVAOC ≥ 0 then writing the LOB is consistent with firm value maximization
Friction Costs
What is it? Examples
Since capital is invested in marketable securities, they are subject to certain friction costs that will reduce the return on this capital
* Agency & Informational Costs - management may behave opportunisically and not invest in a way that would that’d maximize shareholder value
* Double Taxation - investing in securities via insurance companies has lower after tax returns than purchasing the securities directly
* Regulations - various regulations ma force insurer to hold inefficient investment portfolios
Capital Asset Pricing Model (CAPM)
Expected ROE, cost of equity capital
rE = rf + βe * (rM - rf)
* βe = Cov(rE, rM)/Var(rM) = firm’s equity beta coefficient
* (rM - rf) = expected market risk premium
Net Income = I = rA * A + r1P1 + r2P2
* A = assets | P = Premium
Net Income / E = rE = rA * [ (E + L1 + L2) / E ] + r1P1/E + r2P2/E
* A = E + L1 + L2 | Assets = Liabilites + Equity
rE = expected ROE | rf = risk-free rate | rM = expected market return
βE, βA, β1, k1, s1
What is it? Formula
βE = βA(1 + k1 + k2) + β1s1 + β2s2 = firm’s equity beta coefficient = Cov(rE, rM)/Var(rM)
- βA = firm’s asset beta coefficient
- β1 = insurance risk beta for coefficient LOB 1
- k1 = Li / E = liability leverage ratio for LOB 1
- s1 = Pi / E = premium leverage ratio for LOB 1
Required UW Return for LOB
r1 = -k1 * rf + β1(rM - rf)
* for LOB 1
* each LOB pays interest for use of policy holder funds (-ki * rF)
* each LOB receives a rate of return based on the systematic risk of the LOB βi(rM - rf)
Under CAPM, we do not allocate capital by LOB. We charge each LOB for at least the CAPM cost of capital
CAPM Approach Problems
- CAPM only reflects the systematic UW risk (UW risk correlated with the market portfolio), but does not reflect other risks such as extreme events/tail risks
- βi is hard to estimate
- Rate of return are impacted by other economic factors, not just β, which are ignored by the model
VaR Approach
P(X1 > E[X1] + C1) = P(X2 > E[X2] + C2) = ε
* Solve for C1 and C2
* ε = exceedance probability S(x)
Another way:
P(X1 / E[X1] > 1 + C1 / E[X1]) = P(X2 / E[X2] > 1 + C2 / E[X2]) = ε
Higher risk LOBs require more capital relative to expected losses
VaR Approach Problems
- Firm may not have enough capital to ensure all LOBs meet the specific exceedence probability. Can raise the probability level or raise more capital
- Stand-alone exceedence probabilities do not reflect diversification across LOBs
- VaR approach does not reflect the amount by which losses might exceed the exceedence probability level
Insolvency Put Option / EPD
Value of policyholder claim, Advantage / Disadvantage
Value of Policyholder claim = L * exp(-rt) - P()
where P() is the value of insolvency put option or EPD
Advantages:
* Preferable to using VaR because it considers the EV of the amount that can be lost rather than just looking at the exceedance probability
* it is consistent with the theory around pricing risky debt contracts
Disadvantages
* Does not reflect diversification across LOBs - similar to VaR approach
Merton Parole / Marginal Method
- Incorporates diversification: sum of standalone LOB capital requirements exceed the total capital requirement
- Sum of marginal capital is < total firm requirement –> lead to unallocated capital –> leads to higher EVA and RAROC
Myers-Read Method
Surplus to liability ratio in LOB i, Pros/Cons
si = s - [∂p/∂σ] / [∂p/∂s] * [ (σiL - σL^2) - (σiV - σLV) ] / σ
* s = surplus to liability ratio of the firm
* σ = firm’s overall volatility parameter
* p = P/sum(Li) = firm’s insolvency put option per dollar of total liabilities
Advantages
* M-R method allocates the full capital of the firm, unlike the M-P method
* M-R is a microallocation method, this aligns more closely with normal operations of a firm. Firms typically make small changes to an existing book (pricing/underwriting change)
Disadvantages:
* M-P method might be preferable when a firm is adding entire business to the firm
