Investment Income from Insurance Operations (Archive)

Explanation of (2016.Fall #14a)

The given information covers what you need to calculate Investment Income from Insurance Operations and the excess (deficiency) ratio for calendar year (CY) 2015, which is actually part (b)

AY (Accident Year)	net APV @12/31/14	net APV @12/31/15	Paid in CY 2015
2012	2,500	2,000	600
2013	4,500	3,800	650
2014	5,000	4,000	1,200
2015		5,300

	12/31/14	12/31/15
Unearned Premium Reserve (UPR)	4,000	4,500
Premium Deficiency Provision (PDR)	500	100
Unearned Commissions (UEComm)	1,000	1,200
Policy Holder Receivables (PH Recvs)	0	200

The formula or concept behind this type of question is that the investment income attributable to insurance operations equals:

• (yield rate) x (the 'money' the company has lying around)

This money includes APV(UCAE & IBNR) (unpaid claims & adjustment expenses) and other items. The idea is to invest this money in the interim, before it is actually paid to the claimant. Great idea! Recall that APV = Actuarial Present Value and includes discounting for the time value of money as well as PfADs.

Both the source text and the examiner's report provide a complicated-looking formula for this. Basically, you have to calculate 2-yr averages of all the relevant quantities then add/subtract them as appropriate. Liabilities are added; assets are subtracted. (But note that not all balance sheet assets and liabilities are included in this calculation.)

Formula: Investment Income from Operations (source text)

Anyway, here's a tip:

• I find it easier to keep track of what I'm doing if I always organize the given information into a table as shown below:

For example, the UPR for CY2014 and CY2015 is given as 4,000 and 4,500, so the 2-yr average is 4,250. Since UPR is a liability, we put it in the + items column. Easy!

+ items	avg(CY-1, CY)	- items	avg(CY-1, CY)
APV:	13,550	DPAE:	0
UPR:	4,250	receivables: installment premiums	0
UEComm:	1,100	receivables: policy holder + agents & brokers	100
PDR:	300
TOTAL	19,200	–	100	= 19,100

→ The values for UEComm, PDR, and receivables for policy holders + agents & brokers) are all easy - just take the average of the columns in the 2nd table of the question.

→ On the last line of the table, take the sum of the + items and subtract the sum of the -items to get to the total money to be invested, 19,100

The final step is to multiply this by the given yield rate of 5% to get investment income from insurance operations = 955.

→ The only hard part (of course, there has to be a HARD part) is the APV of 13,550.

• If we make the assumption that this company started operations in 2012, then we calculate APV for CY2014 and CY2015 as follows:

CY2014: SUM(APV at Dec14) over all accident years = 2,500 + 4,500 + 5,000 = 12,000

CY2015: SUM(APV at Dec15) over all accident years = 2,000 + 3,800 + 4,000 + 5,300 = 15,100

• Then the 2-yr average is simply 13,550.

The next mini BattleQuiz covers the above problem and others on calculating investment income from balance sheet amounts. They all have the same format. (Difficulty level is medium.)

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