# MSA Ratios

September 16, 2018 This is more a test of WHAT is included in each of the equations, then understanding the equations themselves.  Many times the examiners have forced the candidates to solve for ONE of the items in the equation so they can calculate secondary ratios (eg. use RoR to calculate I. Ret).

## P&C Return

Please be familiar with the return prior to learning the following ratios.  The quarterly return will show all the pieces that make up concepts like “investment operations” or “underwriting operations” etc.  Completing the following calculations requires and understanding of what each part of the equation means.

## Definitions

E = Equity, NI = Net Income, A = Assets, L = Liabilities, $NI_{-tax}$ = Net Income no taxes, G = gains, NP = Net Premium, CP = Ceded Premium, GP = Gross Premium, W = Written, E = Earned, Unpaid = Net Loss Reserves (Net Unpaid Claim Liabilities).

Net Liabilities = L – Reinsurance Liabilities (unearned premium, unpaid claims)

Summary

 Short Name Range Equation measure RoE Return on Equity 5.4% $\frac{NI}{E}$ or $\frac{2\times NI}{E_b+E_e}$ sustainability of earnings RoR Return on Revenue (excl. gains) 6.2% $\frac{UW + II + Subs}{GWP}$ income to revenue generation capacity RoA Return on Assets 2.6% $\frac{2 \times NI}{A_b+A_e}$ efficiency to generate revenue from asset base I.Ret Insurance Return on NPE (excl. gains) 4.0% $\frac{UW + II}{NPE}$ core earning capacity L.LA Liabilities as % of Liquid Assets 105% $\frac{L}{A - \mbox{non-liquid assets}}$ liquidity Unpaid.E Unpaid claims to Equity 200% $\frac{Net.Unpaid}{E}$ given the uncertainty of unpaid claims 1-YR DEV One Year Development to Equity -10% $\frac{margin}{E}$ Adverse (negative) implies under-estimates Net.LEV Net Leverage 500% $\frac{NPW+Net.L}{E}$ Excessive premium writing will erode financial stability UW.LEV U/W Leverage 300% $\frac{NPW}{E}$ Capital strain and vulnerability Adj.Y Adjusted Yield (all assets) N/A $\frac{2\cdot (NII+OCI)}{A_b+A_e-(NII+OCI)}$ Measures income and capital gains relative to deployed assets i Yield (invested assets) N/A $\frac{2\cdot (NII)}{A_b+A_e-(NII)}$ Measures income relative to deployed assets

Net Liabilities = Total Liabilities – Unpaid Claims And Adjustment Expenses Recoverable – Unearned Premiums Recoverable

or Liabilities Net of Reinsurance.

## RoE – Returns on Equity

Net Income (20.30 Line 89) / Equity (20.20 Line 49)

This is a very standard measure most companies use.  There’s not much to say here.

## RoR – Returns on Revenue (20.30)

Return = UW Income (20.30 Line 29) + Investment Income (Line 32) – Realized Gains (Line 33)  + Income from Subsidiaries (Line 41)

Revenue = GWP = Ceded (Line 01)+ Assumed (Line 02)

An interesting perspective: a pure insurance company wholesaler (NWP = \$0) would just make net commissions and the RoR would be net commission / GWP

## RoA – Return on Assets

Uses same income as RoE:

Net Income (20.30 Line 89) / Assets (20.10 Line 49)

Note: Assets = Average Assets (Column 01  + Column 03) / 2

## I.Ret – Insurance Return

Like RoR, just no Income from Subsidiaries and used net earned premiums.  Considering NPE is typically less than GWP it’s surprising to see a lower tolerance (4.0%)

Return = UW Income (20.30 Line 29) + Investment Income (Line 32) – Realized Gains (Line 33)

Income = Net Premiums Earned (20.30 Line 06)

Worth reminding you at this point that

NPE (Line 06) = NPW (Line 04) + Decrease (increase) in Net Unearned (Line 05)

Basically, premiums written throughout the year is either: EARNED or UNEARNED (stored) at year end.  When UNEARNED (stored) premiums are consumed (decrease) they are transferred to income as earned premiums

So, $\Delta WP = \Delta \mbox{unearn} + \Delta \mbox{earn}$ $\Delta \mbox{earn} = \Delta WP - \Delta \mbox{unearn}$ $\mbox{earn} = WP - \Delta \mbox{unearn}$

## Leverage

Insurers should not write more premiums than they have equity to support.   This is similar to a mortgage: your house shouldn’t be more than 5x your deposit (20% down).

### Underwriting (5x) $\frac{NPW+Net.L}{E}$

#### Observations:

• Net Liabilities = Liabilities – [Asset] Reinsurance Assets ( 20.10 Line 30, 31)
• Equity (20.20 Line 49)= Assets (20.10 Line 89) – Liabilities
• Assets = Non-reinsurance Assets + reinsurance Assets (binary equation)
• – Equity = – ([Non-reinsurance Assets + reinsurance Assets] – Liabilities )
• – Equity = Liabilities (20.20 Line 29) – reinsurance Assets – Non-reinsurance Assets
• Equity = Non-reinsurance Assets – Net Liabilities

### Net Leverage (3x) $\frac{NPW}{E}$

### Reserve Leverage (2x) $\frac{Net.Unpaid}{E}$

## Obvious equations:

1. Liabilities as % of Liquid Assets (105%)
2. One year development over Equity (-10%)