InvYld

genevieve

Hi,

I have been doing the problems and usually the Inv Income used in the denominator and numerator are the same.

Here is the formula in the wiki:

InvYld = 2 x ( Net.InvInc + OCI ) / ( Invested Assets [start of yr] + Invested Assets [end of yr] - Net.InvInc )

I am wondering if that formula is correct. I think we should not include OCI in the numerator if it is not in the denominator. In the problem that it refers to, OCI = 0.

Gene

Francois

This is the ADJUSTED investment income.
You also need to substract the OCI from the denominator.
Note that this MSA ratio does not have the Pooled funds Investments like our new Investment yield

exam6_pass

Hi,
for "invested assets" above -> do you know what's included?
based on Questions it looks like it includes: Bonds, shares, debentures, real estate, cash
(doesn't include items like receivables) ? Anything else i've missed?

thanks

graham

From page 20.10 of the sample quarterly statement (asset side of the balance sheet), investments include:

Investments:

* Short Term Investments
* Bonds and Debentures
* Mortgage Loans
* Preferred Shares
* Common Shares
* Investment Properties
* Other Loans and Invested Assets

Cash is listed on a line separately above the investments, and receivables are listed separately below the section on investments.

This should be consistent with the solutions to the exam problems. If not, please let me know.

exam6_pass

in 2019 spring Q21, looks like cash is also included?

graham

Ok, I see what's going on now. There is an error in the examiner's report solution to 2017.Fall Q13a.i that I didn't notice before. In that problem they specifically included cash as part of investment income but this is not correct. There was a similar problem in 2019.Spring Q21 and it appears the CAS corrected themselves in that solution. Cash should be part of the calculation, but it should be listed separately from investment income.

This is the formula they're using from the CCIR annual statement instructions and does indeed list cash as a separate component from investment income:

They get the correct answer in both cases but the formula looks different. I will edit the wiki article to reflect this. Thank you for bringing it to my attention.

exam6_pass

hi, Do you know what formula are they using in 2019fall Q16 to calculate inv yield?
I used the formula above and got different answer..

graham

If you're referring to the 5% investment yield, I'm not sure you can calculate that from the given information. You would need the value of V at year-end 2017, but they only give you year-end 2018. Am I interpreting your question correctly?

exam6_pass

sorry, so my question is I think they used "INV yield" to calculate NII (net inv income),
do you know how did they do that? what formula was used.

graham

Now that I'm looking at this question again, it looks like something isn't quite right. It looks like they are mixing 2018 and 2019.

• They are calculating underwriting income, losses, and expenses for 2018.
• But for investment income, it looks like they're doing the calculation for 2019, starting with the year-end 2018 values in the "with catastrophic event" column. They are taking the year-end value of bonds and cash (700000+100000) then subtracting the reinsurance premium and reinstatement charge (0.05+0.02)*450000. Then they multiply the the result by the investment yield of 5%.

All of this implies the treaty was purchased on Jan 1, 2019 which doesn't make sense. The catastrophe has already happened in 2018. (They also say the reinsurance premium is paid at inception but they don't say when that is.)

I wrote to the CAS exam committee about it. I'll let you know if I get an answer. Please let me know if you think I misread the question myself.

exam6_pass

hi Graham, thanks -
One follow up question - this is how I calculated the NII (net inv income):

5% = 2*NII (Invested assets curr yr+ Invested Assets prior yr - NII)
-> invested assets curr yr = 700 K + 100K = 800K
-> invested assets prior yr = 0 (not given)
-> NII = 19512

for your comment below:
"then subtracting the reinsurance premium and reinstatement charge" -> how is this part of the inv yield formula?
where did the "2" from 2*NII go ?

thanks

graham

Ok, you made the assumption that invested assets from the prior year was 0 because it wasn't given but I'm not sure that's a valid assumption. I checked the statement of the problem because sometimes they say something like: "This insurer began operations on Jan 1, 2018". (If that were true, you could assume investment income for the prior year is 0.) If you wanted to know the investments from the prior year, you could use the formula for investment yield and work backwards. If you do that then investments from the prior year works out to 806,925.

Anyway, I think I see now where you're having trouble. There are different ways of calculating investment income. You tried using the above formula but it won't work because you are missing the prior year investments. But there is another way to do it. If you're given the investment yield, you can calculate investment income directly just by multiplying your investments by the yield. That's what was done in the examiner's report.

• they had 700K + 100K = 800K of investments
• but because they bought reinsurance, they had to then had to subtract the reinsurance premium and reinstatement charge from the amount they had to invest
• reins prem + reinstatement charge = (0.05 +0.02) x 450,000
• so they had 800K - (0.05 +0.02) x 450,000 = 768,500 to invest
• then multiply this by the given 5% yield: 768,500 x 5% = 38,425

I still don't think the problem entirely makes sense but that's their reasoning for the investment income piece.

exam6_pass

ahh - makes sense. Haven't seen that formula before - thanks for the explanation!

KiwiBO

hi @graham , in the investment yield formula, can i know is the logic of substracting the inv income from the denominator?

graham

Hi @KiwiBO,

This formula is only an approximation to the true investment yield. To calculate the exact value, you would have to examine each investment separately and calculate some sort of weighted average across all your investments.

But we're not going to do all that so here's an example of an extremely simple way to approximate investment yield that uses Vb as the basis:

• Suppose you start the year with $100 cash so Vb=100.
• Suppose you invest in a bond that earns 5% interest.
• At the end of the year, you would have $105 so I=5.
• The investment yield would be I/Vb = 5/100 = 5%.

But that's a bit too simple. We can get a slightly better approximation using the formula further up in this thread:

The formula uses (Vb+Ve-I) as the basis. The reason this formula is better is that it takes into account premiums (and other non-investment income) the insurer may receive during the year. For example:

• Suppose that in addition to starting with $100 cash, they received $10 per month in earned premium and invested it as they received it.
• Theoretically, they would then earn an additional 12 months of interest of the first $10 received in January.
• Then they would earn 11 months of interest on the next $10 received in February and so on, but that calculation gets complicated quickly.

So instead, the formula basically takes an average of the beginning and ending cash balance as the basis for calculating investment yield:

• (Vb + Ve) / 2

But they don't want this basis to include investment income they received during the year. They want the basis to be just the non-investment cash they receive from premiums during the year (and investment income from prior years). If they didn't subtract I from the denominator, their investment yield would appear lower than it really is, especially if the investments did really well in that year. So the short way of answering your question is:

• Subtracting I from the denominator provides a better approximation to the true investment yield.

(Note that these investment earnings would be rolled into Vb for the next year.)

KiwiBO

@graham Thanks for the step-by-step explanation. This makes a lot of sense to me.

Part of where I came from is the inconsistency to the definition of RoE = 2*net income / (E_b+E_e). Isn't the net income need to be taken out for a similar consideration?

graham

Oh, I see. One thing to remember is that these are not mathematical definitions or theorems so in that sense there is no right or wrong. Instead, you can think of them as "useful" or "not useful" in providing information about the company.

Here are my comments about ROE:

• I think you do have a valid point because if net income is allowed to flow into equity during the year, this would change the denominator. The difference versus the investment yield formula however is that for investment yield it is the same term "I" in both the numerator and denominator. In contrast, the ROE formula has "NI" in the numerator but "equity" in the denominator, so what would you subtract? I guess you could subtract the portion of net income that was allowed to flow into equity during the year but then you would need more detailed information on how the company treats net income in its accounting procedures and that could get messy very quickly.
• Note also the the MSA Ratios reading defines ROE differently anyway. It's the (after-tax) net income divided by beginning equity.

So, there is no definitive answer as to why the formulas are the way they are. You have to look at several different metrics and consider all the information carefully to really understand the financial state of a company.

KiwiBO

Got it. Thanks again: ) @graham

AndrewL

Hi @graham,

Sorry for the inconvenience but I do not see any difference between the solution S2017Q13 and S2019Q21.
In both, we calculate

Invested Assets = Cash + (Bonds & Debentures) + (Common Shares) + (Real Estate)

Please let me know what I am missing here.

Thanks,
Andrew

Edit: After reading this post, https://www.battleactsmain.ca/vanillaforum/discussion/868/invested-asset#latest, I think I now get it.

From my understanding, V is not equal to invested assets.
Is there a specific term to call V?

Staff-T1

I'd maybe call it investable assets (?) Since cash is investible but is not really being invested currently