2-step trending

[atkinsmt]

Was it necessary to show the step-1 trending? I just showed step-2 and applied to (the latest average WP) x (earned exposures in the hist. period).

[Vorian Atreides]

Most likely . . .

Step 1 trend factor = latest avg WP / hist avg EP (approx 1.077)

Step 2 trend factor = (1+r)^(trend period) where trend period is from the avg written date of that latest avg WP to the avg earn date of the forecast period (from 7/1/09 to 1/1/12 or 2.5 years; so 1.05^2.5 = 1.130)

Net trend factor (1.077*1.130 = 1.217) is applied to the aggregate historical EP.

[FourKicks]

Step 2 trend factor = (1+r)^(trend period) where trend period is from the avg written date of that latest avg WP to the avg earn date of the forecast period (from 7/1/09 to 1/1/12 or 2.5 years; so 1.05^2.5 = 1.130)

are you sure about that? isn't the 'trend to' date the average written date during the period the rates will be in effect (pg. 85, W&M)?

[Need Vacation]

are you sure about that? isn't the 'trend to' date the average written date during the period the rates will be in effect (pg. 85, W&M)?

I was thinking about too, but then again its the earned premium that we're trending, so I wrote that as one of my assumptions that because of that I'm using "avg earned date".

[FourKicks]

I was thinking about too, but then again its the earned premium that we're trending, so I wrote that as one of my assumptions that because of that I'm using "avg earned date".

they trend the earned premium in W&M too, but they still trend to the average written date of the forecast period. i might be missing something...

[Vorian Atreides]

The overall trend needs to go from the same type of avg date to the same type of avg date. The "middle point" in the 2-step doesn't have to be one or the other but should be based on that latest data point used for the first step.

And it doesn't make sense to trend from an avg written date for earned data.

[gaddy]

I'm pretty sure step 2 should have trended from 7/1/09 to 7/1/11 since you ended step 2 with avg. written premium (on the average written date). I, however, did what VA did on the actual exam.

[FourKicks]

And it doesn't make sense to trend from an avg written date for earned data.

i agree it doesn't seem to make sense...but look at pgs 84-86 of W&M, that's exactly what they do; they trend to average written date and then apply it to earned premium.

[DrActuary]

I am not sure if I got this correct:

The first step to trending is between Onlevel WP (2009) to Onlevel EP (respective year). I think I got a 1.4 for 2008 and a 1.109 for 2009

The second step to trending is a 1.05 ^ trend years (trend years is from 7/1/2009 to 7/1/2011) trend years of 2 years.

since we are asked to calculate the CY 2008 EP at prospective levels, I got the OLEP x 1.4 x 1.05^2


This should be roughly around 752,000 +change

[gaddy]

I am not sure if I got this correct:

The first step to trending is between Onlevel WP (2009) to Onlevel EP (respective year). I think I got a 1.4 for 2008 and a 1.109 for 2009

The second step to trending is a 1.05 ^ trend years (trend years is from 7/1/2009 to 7/1/2011) trend years of 2 years.

since we are asked to calculate the CY 2008 EP at prospective levels, I got the OLEP x 1.4 x 1.05^2


This should be roughly around 752,000 +change

In step one, you have to compare average WP (2009) to average EP (2008). This leads to VA's step one answer.

[Vorian Atreides]

The nice thing about the step one trend is that there is no need to worry about trend dates.

[Wmorrissey]

Doesn't the trend period w/ two step depend on whether the premium trend was developed from written or earned? If you put 2.5 years, I think the assumption is that the premium trend was based on the earned premium, with the 2.0 years the assumption is that the trend was based on written. They did not put what the trend was based on, but the book seems to rely on the written premium for trending, so that was my assumption.

[DrActuary]

how much do you think the examiner would cut or give for this problem?

[gaddy]

I imagine your exposure error is not huge - you did the right thing, just not taking the average. Pure speculation, but that seems like a .25 to .5 size error. Considerable debate on the trend date, but the fact that that may be the only other problem one makes, I think that also would be a .25 to .5 error.

[atkinsmt]

But, do you think we needed to explicitly show the step-1 trend? It's not needed. If you take the latest ave WP, and multiply by the historical Earned Exp and the step-2 trend, you get the same answer as when you apply the step-1 and step-2 trends to the total EP for the historical period.

[booyah81]

Most likely . . .

Step 1 trend factor = latest avg WP / hist avg EP (approx 1.077)

Step 2 trend factor = (1+r)^(trend period) where trend period is from the avg written date of that latest avg WP to the avg earn date of the forecast period (from 7/1/09 to 1/1/12 or 2.5 years; so 1.05^2.5 = 1.130)

Net trend factor (1.077*1.130 = 1.217) is applied to the aggregate historical EP.

THat's what I got, except with the forecast period trend date being the average written date, but I guess it slipped my mind that it was EP. Oh well.

[Vorian Atreides]

EP\ \times\ \frac{\;\frac{WP}{WE}\;}{\frac{EP}{EE}}\ =\ EP\ \times\ \frac{WP}{WE}\ \times\ \frac{EE}{EP}\ =\ \frac{WP}{WE}\ \times\ EE

Where
WP = aggregate WP
WE = Written Exposures
EP = aggregate EP
EE = Earned Exposures

However, while they don't explicit ask for the step one trend, it is part of the two-step trending process.

[Vorian Atreides]

how much do you think the examiner would cut or give for this problem?

Here's my guess as to the point break down for the problem (based on complexity of work involved):

Step 1 trend: 1 point (1/2 point for calculating avg earned prem and avg written prem; 1/2 point for correctly applying the correct info to obtain the step 1 trend factor)

Step 2 trend: 3/4 point (1/2 point for correct trend length; 1/4 for correct trend factor)

Final answer: 1/4 point

[Vorian Atreides]

THat's what I got, except with the forecast period trend date being the average written date, but I guess it slipped my mind that it was EP. Oh well.
If you used the avg written date in the forecast period, you'll likely get full credit since that's what's in the text.

I did draw out a diagram showing the overall trend period I was working from. Hopefully that'll mitigate the loss of points for not doing it according to W&M.

[chicken_po_boy]

i agree it doesn't seem to make sense...but look at pgs 84-86 of W&M, that's exactly what they do; they trend to average written date and then apply it to earned premium.

This is what I did too.

For Step 1, I agree with VA's method.

[rj_rattigan]

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