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Just a bunch of formulas - covers the calculation & interpretation of key financial metrics. Examples are ROE (Return on Equity) and U/W Leverage. These ratios are used to assess the financial health of an insurer and can be used in conjunction with other assessment tools like DCAT (Dynamic Capital Adequacy Testing) and ORSA (Own Risk Solvency Assessment). This paper is generally updated every year, and there are usually no material changes. I will point them out if there are. (There were no material changes for the Fall 2018 update.)   Forum

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  • Overall Diversification Score = ( LOB diversification score ) x ( geographic diversification score )
  • LOB diversification score = 8 (on a scale of 1-10)
  • geographic diversification score = 8 (on a scale of 1-10)


  1. overall diversification score
  2. maximum possible diversification score


Based on past exams, the main things you need to know (in rough order of importance) are:

  • calculation of ROE, ROR, ROA, net U/W leverage, investment yield
  • evaluating financial health of an insurer according to the acceptable range for each MSA ratio
  • (other MSA ratios such as diversification score are asked less often)
  • shortcomings of MSA ratios (insurer characteristics not captured in the MSA ratios)
reference part (a) part (b) part (c) part (d)
E (2018.Spring #21) ROE, ROR, leverage:
- calculate
financial health:
- evaluate
E (2017.Fall #25) ROE:
- calculate
other MSA ratios:
- your choice
financial health:
- evaluate
E (2017.Spring #13) ROE, ROR, leverage:
- calculate
financial health:
- evaluate
UCAE recoverable:
- calculate
E (2016.Fall #22) ROE, ROR, leverage:
- calculate
financial health:
- evaluate
E (2016.Spring #23) ROE, ROR, ROA:
- calculate
financial health:
- evaluate
E (2015.Fall #22) equity:
- calculate (CCIR.ARinstr)
ROE, leverage, COR:
- calculate
financial health:
- evaluate
E (2015.Spring #26) non-liquid assets:
- calculate
financial health:
- evaluate
- compare
E (2014.Fall #23) ROE, ROR, ROA:
- calculate
financial health:
- evaluate
E (2013.Fall #23) MSA shortcomings:
- items not captured
investment yield:
- calculate
diversification score:
- explain
E (2012.Fall #21) financial health:
- evaluate
- calculate
claims/(total liabs):
- calculate

In Plain English!


MSA stands for Market Security Analysis. They are a Canadian-owned analytics firm focused on the Canadian insurance industry. In case you're curious, their website is located here

There are 4 broad questions from this reading that you may be asked: (In practice, however, most of these ratios do not appear on the exam.)

  • What are the names of the MSA ratios?
  • What are the acceptable ranges?
  • What are the formulas for each ratio?
  • What do they mean?

Note that a company can fail some of these ratios in a given year and still be considered healthy. This happens frequently. A more comprehensive analysis looks at trends in these ratios over several years.

Note also that there are important aspects of a company that these simple numerical tests simply cannot measure. (This is covered briefly in mini BattleQuiz 3) My favourite intangible but crucial aspect of a company is its prospects for growth and innovation. How can innovation be measured by a formula???!!!! Innovative companies have a constellation of practices to encourage curiosity, engagement, and creativity. When you get to Feldblum's paper on rating agencies Feld.RtAgs, he discusses something called interactive ratings. An interactive rating is a comprehensive analysis of a company to asses its ability to pay claims, a narrow goal. But that's the kind of in-depth analysis you would have to do if you wanted to assess a company's prospects for innovation. I hope when you guys are big-shot FCAS members, you'll give some thought to developing that sort of culture at wherever you work! Have fun with it!

All About the Ratios

Let's organize the information into 2 tables: (The highlighted ratios are those that have been asked on prior exams.)

  • Regulatory Early Warning Ratios (9 ratios)
Name of Ratio Acceptable Range Formula Meaning
MCT (Minimum Capital Test) > 150% CapAv / minCapReq measure of capital adequacy
ROE (Return on Equity) > 5.4% ( NI.preTax - TotTax ) / Eq sustainability of earnings (need a few years of ROE values)
ROR (Return on Revenue) > 6.2% ( U/W.Inc - CapGains + InvInc + IncFrmSubs ) / GWP income relative to revenue-generating capacity
ROA (Return on Assets, after tax) > 2.6% ( NI.preTax - TotTax ) / (2-yr avg of assets) efficiency measure for income-generation
Ins RO.NEP (Ins Return on Net EP) > 4.0% ( U/W.Inc - CapGains + InvInc(from U/W.Inc ) / NEP core earning capacity
-------- -------- -------- --------
Liab / LiqAss < 105% Liabilities / ( Liquid Assets ) liquidity measure
Net.LsRsvs / Eq < 200% ( Net.Loss.Reserves ) / Eq high ratio could mean financial distress
1yrDevlpt / Eq > -10% ( 1 yr development ) / Eq adverse development could mean under-reserving
Net.Levg (Net Leverage) < 500% ( Net.Liabilities + NWP ) / Eq stability measure (high ratio means excessive writing)
  • Supplementary Ratios (9 ratios)
Name of Ratio Acceptable Range Formula Meaning
AdjInvYld (Adjusted Investment Yield) n/a see below measures income and capital gains relative to assets
chg(NWP) % (% change in NWP) n/a NWP(yr = x) / NWP(yr = x-1) growth measure - high value may indicate capital strain
chg(GWP) % (% change in GWP) n/a GWP(yr = x) / GWP(yr = x-1) growth measure - high value may indicate capital strain
chg(Eq) (change in equity) n/a EQ(yr = x) / EQ(yr = x-1) lower value indicates lower ability to support growth
-------- -------- -------- --------
AOCI / Eq n/a AOCI relates to unrealized gains/losses
ReIns.Recovs / Eq n/a high value indicates dependence on ReInsRs
Net.U/W.Levg < 300% NWP / Eq higher ratio indicates capital strain
2-yr COR (Combined Operating Ratio) < 100% see CCIR A/R instructions higher ratio indicates U/W loss
Overall Diversification > 65 ( LOB diversity score ) x ( geographic diversity score ) each factor is 1-10. How InsR tracks Can market performance
  • AdjInvYld = 2 x ( Net.InvInc + OCI ) / ( Invested Assets [start of yr] + Invested Assets [end of yr] - Net.InvInc - OCI )

The first mini BattleQuiz provides easy versions of the basic MSA ratio calculations and 1 old exam problem to get you started. Master these before moving on.

Note that in the mini BattleQuiz below, some of the BattleCards are actually old exam questions. Click E in the left-hand column to open a PDF with the full exam question and answer.

mini BattleQuiz 1 You must be logged in or this will not work.

Explanation of 2017.Spring #13ab (Investment Yield, ROE)

Normally the problems on the MSA ratios are not too hard, but they threw in a twist on this one. I don't want to reproduce the given info here, so click (2017.Spring #13) for examiner's report. The answer is explained well, but I want to make a few comments.

Part (a).i

You're asked to calculate InvYld (investment yield). Your first step is to write out the formula given above (which you memorized, right??!!)

  • The twist is that they don't directly give you the values you need in the formula. You have to have a general understanding of the B/S beyond what's in this reading. In particular, you have to know two additional formulas:
Invested Assets = Cash + (Bonds & Debentures) + (Common Shares) + (Real Estate)
Net.InvInc = InvInc + (Realized Gains/Losses) - (Inv.Expenses)

If you know these additional formulas, it's easy. If you don't, you can take an educated guess and do the best you can.

Part (a).ii

You're asked to calculate ROE (Return on Equity). The first step is obviously to write out the formula ROE = ( NI.preTax - Tot.Tax ) / Eq

  • You're directly given Tot.Tax = 2,500 and Eq = 30,000, but you have to know how to calculate NI.preTax:
NI.preTax = ( NEP - net.UCAE - TotAcq - GenExps ) + net.InvInc
Note the net.InvInc came from part (a), but you must also recall that
NEP = NWP - chg(UEP)
  • So, NEP = 44,000 - (-1,200) = 45,200 (because they give you chg(UEP) as a decrease, so you have to reverse the sign, which is confusing.)
  • NI.preTax = 6,700
  • (NI.preTax - Tot.Tax) = 4,200, which is the numerator in the ROE formula. (Note the error in examiner's report in the calculation of Net Income. The answer is correct, but they forgot to subtract the tax of 2,500 in their intermediate step.)
Finally, ROE = 4,200 / 30,000 = 14.5%

Comparison to ROE Problems on Prior Exams

Let's compare the 2017.Spring ROE problem to these past ROE exam problems, which I think were easier:

E (2016.Fall #22a.i)
E (2016.Spring #23a.i)
E (2015.Fall #22a & #22b.i)

You're asked to calculate the same thing, ROE, but you're given slightly different data.

  • In 2017.Spring, you're given equity, but must calculate NI as an intermediate step.
  • In those past problems, it's reversed: you're given NI, but must calculate equity as an intermediate step.

But calculating equity is usually easier.

  • There are basically three ways to calculate equity. See Calculating Equity for the various formulas for equity. (See also the examiner's reports for solutions to these 3 problems.)

Learn these two versions of the ROE problem!!

mini BattleQuiz 2 You must be logged in or this will not work.

More Practice

Non-numerical questions:

mini BattleQuiz 3 You must be logged in or this will not work.

Older exam questions:
  • Be sure to check the this forum post which highlights an inconsistency between the CAS solutions to:
E (2017.Spring #13c)
E (2012.Fall #21c)
  • User comments:
    • ineedcoffee (don't we all!) asked a very good question regarding calculating ROR and when realized gains have to be subtracted from investment income.
    • jefor139 noted an issue with the answer in the examiner's report to E (2012.Fall #21b).

mini BattleQuiz 4 You must be logged in or this will not work.



  • The rows highlighted in the table.


  • Know the meaning of the ratios highlighted in the tables.
  • Understand the two versions of the ROE problem explained in the previous section.


  • Be able to calculate the highlighted ratios
  • Practice on the old exam problems

Final Comments:

  • If you're uneasy about ignoring the non-highlighted items, you can come back to them later in your study. (There was 0.5 pt question in (2013.Fall #23c) about interpreting the diversification score.)
  • These MSA questions are normally an easy question because they are repetitive and you can get:
    • 1/4 of the points just by writing down the formula
    • 1/4 of the points just by writing down the acceptable range
    • 1/4 of the points just knowing the meaning of the ratio
  • Then just crank out the calculation as quickly as you can. If you get it wrong, the point deduction will be low.
  • Note that (2015.Spring #26a) was what I think of as a math contest type of problem. It was interesting, but I think there is a low probability of another question like this appearing on the exam. (It also looked time-consuming). If you do see another problem like this, you should at least write out all the formulas you think might be appropriate. Get that partial credit!!!!

Full BattleQuiz You must be logged in or this will not work.



  1. overall diversification score = 8 x 8 = 64
  2. maximum possible diversification score = 10 x 10 = 100