# Why did Tower Group fail?

## Statistical analysis of Tower Group A.M. Best Schedule P (2011) data clearly indicates a woeful level of under-reserving

Statistical analysis of Tower Group's year end 2011 A.M. Best Schedule P data reveals alarming reserve health indicators and woeful reserve inadequacy.

In short:

- Inflation (social and economic) of paid losses exceeded earned premium growth by 11% per year for the last five years (2006~2011);
- To reach Tower Group's reserves held and loss ratios - assumed future calendar year trend must be
;*-16% per year*for all future calendar years - Tower Group's projected calendar year liability stream is far too low (by approximately $1B) as at year end 2011;

- Tower Group's survival ratio (1.33) is well below the industry average (2.41)

- (no wonder it isn't surviving); - We demonstrate that the traditional actuarial techniques including Mack (volume weighted average link ratios), applied to Paids and Incurreds lack predictive power, do not quantify and measure inflation, and provide completely false indications.
- According to our analyses further significant reserve strengthening (or upgrades) are very likely.
- To reach Tower Group's reserves for its biggest line, Commercial Multi-Peril - the assumed future calendar year trend must be
**-22% per year for all future years**.

Was too much reliance placed on traditional actuarial techniques for long-tail liability losses which were long past their use-by date? Did the company maintain stable loss ratios because it was using Bornheutter Ferguson?

There would have been **no adverse paid loss experience**, had the company identified the model that reflected the salient risk characteristics of the business.

The **effective forecast assumptions** employed by Tower Group were in **complete contradiction** of past trends (and volatility).

**Significant reserve strengthening was entirely predictable.**

### The ensuing sequence of events was just a matter of time.

- August 2013: Tower Group announced the necessity of reviewing the estimation of its loss reserves and warned of loss reserve hits of $60 million to $110 million.
- October 2013: A.M. Best downgrades Tower Group's rating to B++.
- November 2013: as a result of a comprehensive review, loss reserves were increased by $326.7 million in addition to other restatement adjustments.
- December 2013: Tower Group stock falls further 10% of its workforce are cut.
- February 2014: adverse loss reserve charges were revised from the range $75 million - $105 million to be recorded as $143 million.

Note in January 2014 Tower announced it entered into a Merger agreement with ACP Re - a Bermuda based reinsurance company.

We are concerned reserve upgrades will be required for many years into the future unless the reserving methodology applied to Tower Group's portfolios is seriously revised.

Here's why.

### Inflation (social and economic) of paid losses exceeded earned premium growth by 11% per year for the last five years (2006~2011)

The ideal place to begin our investigation is to describe the trends in entire Tower Group data – that is, all lines combined. We perform this analysis after normalising for earned premium on the paid loss development array.

The model for the aggregate of the long tail liabilities is displayed above. We observe:

- The development decay is relatively fast;
- Accident years are stable after adjusting for earned premium;
- Calendar year trends show a 10.98% increase every year since 2006; and
- Volatility increases out in the tail of the development (like one would expect).

It is the third point that is the most critical. As we have already normalised by earned premium, this means that **paid losses are increasing faster than earned premium by nearly 11% every year**.

Ouch!

### To reach Tower Group's reserves held and loss ratios - assumed future calendar year trends must be *-16% per year *for all future calendar years

*-16% per year*for all future calendar years

In order to reach the reserves held figure submitted by Tower Group for the data at year end 2011 ($921M), we have to apply the following future calendar year trend assumption (the vertical green line separates the past (left) from the future (right)).

That's right.

The calendar year trend (future inflation: social plus economic) is assumed to be:**-16% per year**. Not only that, the calendar year trend must be *more negative* than any previously observed historical calendar year trend over the last ten years.

Were the 11% calendar year trend to continue, under the Tower Group scenario losses would then be increasing faster than premiums by **27% per year**!

### Accordingly Tower Group's projected calendar year liability stream is far too low

The forecasted liability stream for the -16% trend scenario looks something like the table (below left) below.

For each observed cell (prior to calendar 2011), we have the pair of **observed **and **model mean** values.

For each future forecast cell (post calendar year 2011) we have the projected distribution** mean** and distribution **standard deviation**.

Aggregate** means** are also calculated for the future calendar period (bottom rows) and accident year aggregates (rightmost columns) along with their distribution **standard deviations**. Calendar year summaries of **observed** versus **fitted** are in the column on the left.

In the paid loss data, the losses are increasing across the accident years (blue dashed line) in development years zero and one. However, in the projected data (post 2011) for the development years six and seven (red dashed line), the mean losses are projected to decrease over the same accident years.

Let's compare the projected Tower Group reserve mean with the distributions obtained if the calendar year trend of 10.98%+_ continues.

Note the Tower Group mean (dotted line) is well below the forecast distributions assuming the 10.98%+_ trend continues (boxplots with connected means). That the Tower Group reserve mean trend is outside the 1% percentile of this forecast for all calendar years is a further indication of the gravity of the Tower Group reserve deficiencies and that **reserve strengthening was inevitable**.

Now we compare the resulting cumulative losses by calendar year between the two forecasts.

If the paid losses actually followed the 10.98% trend line then we would expect average "adverse development" of $293M by 2013.

This **adverse development** is **not** a result of unexpected losses arising from the data, **but rather unexpected losses compared to the projected forecast**. That is, adverse development arises as a result of poor methodology not truly unusual losses.

Did Tower Group know that in the past there was 10.98% trend and that the future trend required to obtain their ultimates and loss ratios by accident year and total is -16%?

**We suspect not.**

We show that the ultimates held by Tower Group at year end 2011 match closely with the forecast scenario designed to reach Tower Group's reserve held.

What about the Case Reserve Estimates (CREs)?

Uh oh.

Let's enlarge that lower display.

Case Reserve Estimates are increasing over 2002~2007 and decreasing thereafter (calendar year 2009~2010 shows an increase, but is balanced by the decrease in level in the same accident year) by 8.8% per year.

These calendar year trends are in the opposite direction to the losses!!

### What about Tower Group's loss ratios?

For the Tower Group scenario, the loss ratios look good. In fact there is no evidence from the numbers that losses are growing faster than earned premium.

The projected reserve losses look plausible compared to the Case Reserve Estimates as the Case Reserve Estimates are also too low!

Incurred But Not Reported (INBR) is 37.2% of reserves held.

How does this compare to the Industry? The industry IBNR is 48.7% for the same proportion of business volume.

Perhaps this is part of the problem. If the actuarial department was using a method such as Bornheutter-Ferguson to estimates the losses based on earned premium, then they would not see the growth in losses since the method calibrates the expected losses to the earned premium.

Unfortunately for Tower Group, the loss ratios are more likely to look like this (where the 11%+_ trend continues).

Note the huge increases in loss ratios in accident years 2008~2011 - right where Tower Group had so-called ‘adverse development’.

Let's look at the survival ratio.

### Tower Group survival ratio is substantially lower than the industry average

Perhaps, an obvious metric to check is how long the reserves can last for given payments like those in the last calendar year. That is, total held reserves divided by the total losses in the last calendar year.

For writers of P&C Insurance, especially long-tail lines like Worker’s Compensation, the multiplier should be much higher than 1.

Tower Group’s survival ratio for the whole company is **only** 1.33. This means that Tower Group could only survive one more year of losses at the same level of those observed in 2011. Perhaps Tower Group writes shorter long tail lines – let’s check against the industry.

For the industry we find, for *the same allocation of business* (based on total earned premium), the industry survival ratio is 2.41. This means, on average the industry would be **reserving 80% more** than Tower Group for the same business volume.

How could anyone justify such a low level of held reserves?

## Traditional Actuarial Techniques

### Link Ratios applied to the Paid Losses have no predictive power and do not capture or quantify the calendar year trends.

Incremental Paid Losses in development period 2 and 3 are not correlated to the previous cumulatives (periods 1 and 2 respectively)

Therefore link ratio methods (including Mack) have no predictive power.

Choosing link ratios by judgement **cannot overcome lack of correlations**.

The Mack method (equivalently volume weighted averages) estimates a trend lower than that in the data. So does the arithmetic average link ratio.

The seesaw pattern in the last calendar years is due to calendar year 2010 being better than expected.

### Link Ratios applied to the Incurred Losses have no predictive power and do not capture or quantify the calendar year trends.

Incremental Incurred Losses in development period 2 and 3 are not correlated to the previous cumulatives (periods 1 and 2 respectively). Therefore they have no predictive power.

As with the paid losses, the Mack method estimates a trend lower than that in the data.

Interestingly the Mack method yields a mean reserve estimate of 1.059 Billion which is not much higher than reserves held of $922 Million.

## Summary

With well established statistical tools available to verify the reasonableness of future forecast assumptions, this result is inexcusable. Earlier intervention and monitoring would not have jeopardised the company.

- Tower Group's projected calendar year liability stream is far too low (by approximately $ 1B) as at year end 2011;
- Inflation (social and economic) of paid losses exceeded earned premium growth by 11% per year for the last five years (2006~2011);
- To reach Tower Group's reserves held and loss ratios - assumed future calendar year trends must be
;*-16% per year*for all future calendar years - Tower Group’s survival ratio (1.33) is well below the industry average (2.41) - (no wonder it isn't surviving); and
- According to our analyses, further significant reserve strengthening (or upgrades) are very likely.
- Standard actuarial techniques have no predictive power for the Tower Group’s long tail LOBs, nor do they quantify the calendar year inflationary trends. They therefore give false indications.

This is why Tower Group arrived at the situation it did in 2013.

Whatever methods were used to estimate the total loss reserves were woefully inadequate and put shareholder’s funds at risk.

Poor decisions were made by management on what reserves should be allocated and the premiums to charge on new/renewal business.

Just like HIH, Tower Group should serve as a warning to insurance (and reinsurance) companies.

Is your insurance (reinsurance) company using the right reserving methodology or are you also at risk of adverse development arising from defective loss reserve estimates?

Are you insuring a company that has misrepresented its risk exposure?

If you would like further information on Insureware's analysis of Tower Group, including of any individual lines, please contact Dr Ben Zehnwirth or David Munroe.