Best's Capital Adequacy Ratio

Best's Capital Adequacy Ratio (BCAR) is A.M. Best's measure of an insurer's balance-sheet strength: the capital it has, set against the net required capital (NRC) that its investment, credit and underwriting risks call for once a covariance adjustment allows that those risks are unlikely to peak together. BCAR is not on the Fall 2026 syllabus — the outline assigns only pp. 1–7 and Appendix A of Feldblum, excluding formulae, and BCAR sits in Section 5 (p. 15) — but twelve 2013–2019 questions draw on it, and the outline's financial-health task still names the key financial measures used by rating agencies.

$\begin{aligned} \text{NRC} &= \sqrt{S} + B_7 \\ S &= B_1^2 + B_2^2 + B_3^2 + (0.5B_4)^2 \\ &\quad + (0.5B_4 + B_5)^2 + B_6^2 \end{aligned}$

$\text{BCAR} = \frac{\text{Adjusted surplus}}{\text{NRC}}$

The components: $B_1$ fixed-income securities, $B_2$ equity securities, $B_3$ interest rate, $B_4$ credit, $B_5$ loss and LAE reserves, $B_6$ net premiums written and $B_7$ business (off-balance-sheet) risk — grouped as investment, credit and underwriting risk, the three categories the 2015–2017 answers name. BCAR feeds balance-sheet strength, which the 2015 answer lists with operating performance and business profile as the components of a Best's rating.
Calibration (Feldblum): BCAR keeps the RBC structure of independent categories with a covariance adjustment, adds interest-rate risk and risks hard to read from the statements (asbestos and pollution, catastrophe), and calibrates every charge to a $1\%$ expected policyholder deficit — the capital $Z$ at which aggregate excess-of-loss cover above $Z$ has a pure premium of $1\%$ of reserves. On industry figures a $120$ basis point rate rise gives that $1\%$ , so each portfolio is stressed by $120$ bp.
The covariance (square-root) adjustment recognises that the components are unlikely to develop at the same time. It shrinks small categories most: with equal volatility, equities one-tenth the size of reserves have one-tenth their marginal effect (Feldblum). Feldblum prints the root as a plain sum of $B_1^2$ to $B_6^2$ ; the published answers, like A.M. Best's own criteria, add half the credit charge to the reserve charge before squaring. $B_7$ stays outside the root because A.M. Best expects capital for it without a diversification benefit.
The later form. A.M. Best's current criteria — and the Fall 2019 answer — add catastrophe risk $B_8^2$ inside the root and state BCAR as a score, $(\text{AC} - \text{NRC}) / \text{AC} \times 100$ , positive when available capital (AC) exceeds NRC; scores are read at several VaR confidence levels. The 2013 and 2014 answers use the ratio above, and the 2013 answer reads a BCAR over $100\%$ as secure. Common 2019 errors were writing $0.5B_4^2$ for $(0.5B_4)^2$ and not multiplying by $100$ .
The natural catastrophe stress test takes a first event off surplus, raises recoverables and reserves by $40\%$ of the ceded and net losses, and deducts a second event (worked below). Its purpose is to show how sensitive balance-sheet strength is to a catastrophe — A.M. Best does not require an insurer to survive two major events. How far the stressed BCAR may fall — the tolerance — depends on financial flexibility (able and willing to replace capital at once), historical volatility of balance sheet and results, and exposure to frequency (several events in a season).
Compared with the MCT. BCAR charges significantly for future premium, because A.M. Best expects the balance sheet to support next year's planned business as well as the current book (2018 answer); the MCT's unexpired-coverage margin applies its factors to the greater of net unexpired coverage and $30\%$ of net premiums received in the past year. Both reduce capital for diversification, but the MCT's diversification credit uses one $50\%$ correlation between asset risk (credit plus market) and insurance risk, where BCAR takes a square root over all its components. Against DCAT (renamed FCT in 2020), BCAR's catastrophe test shares the multiple events but uses a different severity threshold (2015 answer).

Net Required Capital and BCAR An insurer reports ($000s): $B_1 = 6{,}000$ , $B_2 = 14{,}000$ , $B_3 = 2{,}500$ , $B_5 = 52{,}000$ , $B_6 = 24{,}000$ , $B_7 = 100$ , and adjusted surplus of $80{,}000$ . For credit risk: agents' balances of $3{,}000$ carry a $5\%$ factor; reinsurer X (rated A+) owes recoverables of $40{,}000$ plus a ceded reserve deficiency of $1{,}000$ , with a $2\%$ capital factor; reinsurer Y (rated A-) owes $15{,}000$ plus $1{,}500$ , with a $6\%$ factor. The reinsurance dependence factor is $1.20$ , with a minimum dependence charge of $1\%$ of adjusted recoverables.

(a) Calculate BCAR as the 2013 sample answer does. (b) If the insurer also had a catastrophe charge $B_8 = 20{,}000$ , what score would the later form give, taking available capital as $80{,}000$ ?
Answer (a) Credit risk. Recoverables are charged on the amount including the ceded deficiency:
 $\begin{align*} \text{Recoverables charge} &= 41{,}000(0.02) + 16{,}500(0.06) \\ &= 820 + 990 \\ &= 1{,}810 \\ \text{Dependence} &= \max\big(1{,}810(0.20),\ 0.01(57{,}500)\big) \\ &= \max(362,\ 575) \\ &= 575 \\ B_4 &= 150 + 1{,}810 + 575 \\ &= 2{,}535 \end{align*}$ 
Net required capital, with half of $B_4$ standing alone and half added to the reserve charge:
 $\begin{align*} S &= 6{,}000^2 + 14{,}000^2 + 2{,}500^2 + 1{,}267.5^2 \\ &\quad + 53{,}267.5^2 + 24{,}000^2 \\ &= 3{,}653{,}283{,}113 \\ \text{NRC} &= \sqrt{S} + 100 \\ &= 60{,}442 + 100 \\ &= 60{,}542 \\ \text{BCAR} &= \frac{80{,}000}{60{,}542} \\ &= 132\% \end{align*}$ 
Above $100\%$ , so secure on the 2013 reading. The components sum to $101{,}135$ , so the covariance adjustment removes about $40\%$ of gross required capital — and almost all of what is left is reserve and premium risk.

(b) Later form. $B_8^2$ joins the root:
 $\begin{align*} \text{NRC} &= \sqrt{S + 20{,}000^2} + 100 \\ &= 63{,}765 \\ \text{BCAR} &= \frac{80{,}000 - 63{,}765}{80{,}000} \times 100 \\ &= 20.3 \end{align*}$ 
Adding a $20{,}000$ charge raises NRC by only about $3{,}200$ : inside the root a charge much smaller than the reserve charge adds little. The positive score says available capital exceeds NRC, by $20\%$ of available capital.

The Natural Catastrophe Stress Test The insurer above (adjusted surplus $80{,}000$ , in $000s) has earthquake as its main catastrophe exposure and a $25\%$ tax rate. For the first event, its gross pre-tax PML is $150{,}000$ and its net pre-tax PML $30{,}000$ (after retention, coinsurance and reinstatement premium). Its 1-in-100 year net pre-tax earthquake PML is $16{,}000$ . With the higher recoverables and reserves, net required capital rises to $64{,}000$ .

Apply the stress test as the 2013 and 2016 sample answers describe it, and discuss whether A.M. Best would tolerate the result for a subsidiary of an international group with ten years of stable combined ratios.
Answer The adjustments:
 $\begin{align*} \text{1. First event off surplus} &= 30{,}000(1 - 0.25) \\ &= 22{,}500 \\ \text{2. Recoverables up} &= 0.40(150{,}000 - 30{,}000) \\ &= 48{,}000 \\ \text{3. Reserves up} &= 0.40(30{,}000) \\ &= 12{,}000 \\ \text{4. Second event off surplus} &= 16{,}000(1 - 0.25) \\ &= 12{,}000 \end{align*}$ 
The second event is the 1-in-100 year loss because earthquake is the main exposure; where hurricanes dominate, the answers take the second event equal to the first. Steps 2 and 3 are why NRC rises — larger recoverables raise the credit charge, larger reserves the reserve charge.
 $\begin{align*} \text{Stressed surplus} &= 80{,}000 - 22{,}500 - 12{,}000 \\ &= 45{,}500 \\ \text{Stressed BCAR} &= \frac{45{,}500}{64{,}000} \\ &= 71\% \end{align*}$ 
Tolerance. A fall from $132\%$ to $71\%$ is large, but all three factors favour this insurer: a parent group gives financial flexibility to replace capital quickly; stable results mean low historical volatility; and an earthquake is not a peril that recurs within a season the way hail, tornado or hurricane can. A regional mutual with volatile results and hail exposure, stressed to the same figure, would get less tolerance. A.M. Best's current criteria keep steps 1–3, on the 1-in-100 year all-perils PML, and in place of a second-event deduction adjust the $B_8$ catastrophe charge for the reinsurance left after the first event.