Day: December 16, 2010

Special Birthdays for Nerds (like me)

Special Birthdays for Nerds (like me)

I called my bank today to try to straighten out something.? In the process, they asked my birthday for verification purposes.? I said, ?Twelve, Five, Sixty.? My birthday is special.? It multiplies.?

After a longish pause, the guy on the other end said, ?Huh, it does multiply.? Cool, I wonder how common that is.?? I replied, ?Good question.? I have known that my birthday multiplied since I was seven, but I never thought of that question until you asked it, and I must say that I don?t know.?

Well, now I do know.? Part of the question here stems from two digit date fields ? mm/dd/yy, in the American system. 12 X 5 = 60.? How common is that?

Over a 400 year period, there are 146,097 days.? (365.25 * 4) – 3 days.? No leap years in 1700, 1800, and 1900, but yes, leap year in 2000.

Month Possible Days
1 31
2 28
3 31
4 24
5 19
6 16
7 14
8 12
9 11
10 9
11 9
12 8

In this situation, over 100 years, there are 212 days where the month and day multiply to be the year.?? That?s 848 over a 400 year period.? February 29th would work in XX58, but that is never a leap year.

Then I said, why limit it to multiplication, why not consider addition, subtraction and division?? With addition, any combination of month and year will produce a year, so over a 100 year period, there should be 365 additive special birthdays.? February 29th would work in XX31, but that is never a leap year.? So, 1460 over 400 years.

Subtraction is more scarce for special birthdays.? The potential number of special birthdays in any month is the month number itself.? All of the special days would pack into the beginning of a century, for us ending at 12/1/2011.? 78 per century, or 312 over 400 years.

Finally there is division, which is the rarest.? The number of days in a given month is equal to the number of factors for a month.? In order that would be 1, 2, 2, 3, 3, 2, 4, 2, 4, 3, 4, 2, 6.? That makes 35 over a century, or 140 over 400 years.

So how many mathematically special birthdays are there in total?? Wait, we have to net out double counting.? Without boring you with the math, double counting happens with multiplication and division when the day is one. 02/01/2002 is special for division and multiplication.? Addition and multiplication match for 02/02/2004.? Over 400 years, there are 52 days of overlap in total.

This brings us to the final table:

Addition Multiplication Subtraction Division Total
Denominator 146,097 146,097 146,097 146,097 146,097
Special days 1,460 848 312 140 2,708
Percentage 1.00% 0.58% 0.21% 0.10% 1.85%
One in 100 172 468 1,044 54

So, by my definition, one in 54 have mathematically special birthdays.? I?m sure there are other ways to view this, and I look forward to comments from those that will broaden my mind, and/or correct my errors.

Flavors of Insurance, Part XI (Banks and the Insurance Business)

Flavors of Insurance, Part XI (Banks and the Insurance Business)

My bias in understanding banks in the insurance business is that banking and insurance are fundamentally different businesses, but there are areas of overlap where the participation of banks sense. In Europe, indiscriminate mingling of the two businesses has usually led to losses. Why?

Though banking and insurance are both described to be financial services, they are different in the terms of financing done, arid service provided. Here are some of the key differences:

  • Product complexity: Insurance liabilities are typically more complex than bank liabilities; there are more factors that can affect the overall cost of the promises that an insurer makes to a policyholder, than a bank makes to a depositor.
  • As a result, the liabilities underwritten by an insurance company are usually riskier than those underwritten by a bank.
  • Because of the relative riskiness of the asset and liability structures, including the greater length of guarantees made, insurance companies generally run at a higher ratio of book equity to assets.
  • With the longer liability structures, and a highly competitive environment, the investment policy of most insurance companies is more aggressive than that of most banks. Interest rate risk is not generally a problem; most companies attempt to squeeze out interest rate risk by approximately matching assets and liabilities. Most of the risk comes from investing in equities, lower grade corporate debt, and equity risk from the writing annuities. (As the market rises and falls, so do fees received.)
  • Liabilities are more expensive to originate and service at insurance companies.
  • There is a high amount of idiosyncratic expense associated with running an insurance company. When a bank buys an insurance company, there are usually few expense savings.
  • Though there are diversification advantages from a holding company owning both banks and insurers, this advantage often outweighed by the different skills needed to manage the different entities well.

The European experience with banks and insurance companies under the same roof has been mixed. One success has been banks coming to dominate distribution of life insurance products. Banks distribute more than 50% of all life insurance policies in most countries in developed continental Europe. The tendency for banks to sell insurance is strongest in countries where banks are dominant financial institutions aside from insurance.

But there have been failures as well. Most of the failures have been due to a lack of understanding of how different banking and insurance really are. Others have been due to taking too much risk, particularly in unfamiliar countries. Here are some examples:

  • CSFB buying Winterthur did not grasp how sensitive the performance of Winterthur was to the performance of the equity markets. When the equity markets fell, CSFB had to pump in $2.4 billion of capital.
  • Allianz did not grasp the poor asset quality of Dresdner, particularly in the midst of a bad market for investment banking
  • Zurich Financial Services was overly aggressive in the expansion plans in the US, leading them to overpay for marginal asset management companies like Kemper and Scudder.
  • Aegon, ING, and Prudential plc all suffered by building up leverage through 2000, particularly in their US life insurance subsidiaries, and then got whacked by the combination of the bear markets in equity and credit.

To summarizing the European experience positively, if a bank has strong customer relationships, it can earn additional margins through distribution of insurance products. Negatively, conservatism pays in entering new lines of business and new countries.

The US experience with banking and insurance together has been more limited, due to laws such as McCarran-Ferguson and The Bank Holding Company Act. McCarran-Ferguson, passed in 1945, entrenched the exclusive authority of the states to regulate insurance. The Bank Holding Company Act of 1956, amended in 1970, restricted the insurance activities of bank holding companies.

Until HR 10 was passed in 1999, the Federal Reserve gradually relaxed regulations on bank involvement in insurance companies so long as earnings from insurance activities remained below a threshold. In April of 1998; the merger announced between Citicorp and Travelers forced the need for structural legal change, leading to the passage of HR 10, otherwise known Gramm-Leach-Bliley. HR 10 allowed for the formation of financial holding companies that could engage in banking, investment banking, and insurance, with regulation of mixed entities to be done functionally down at the operating companies, in much the same way it would be done for standalone entities.

When HR 10 was passed, there was a lot of expectation in the insurance industry that the new law would have no large effect. Some observers suggested that life and personal property/casualty insurers might be bought by banks because of investment and product marketing synergies. But most thought that banks would not buy insurance companies, and insurance companies would not buy banks. This expectation has largely been met. Aside from Citicorp, only Bank One has acquired an insurance underwriter of significant size.

Even with Citigroup (ne? Citicorp) the acquisition of Travelers was re-thought. In 2002, Citigroup spun the property/casualty operations off as Travelers Property Casualty, which had a short-lived existence as a standalone company before merging with The St. Paul. Citigroup kept the Travelers life and investment operations (and the logo).

Bank One acquired the US life insurance operations of Zurich Financial Services. This allows Bank One, soon to be a part of JP Morgan Chase, to underwrite life insurance. They presently use it to sell term insurance and annuities.

So, why didn’t banks attempt to enter the life and personal property casualty lines, in general? The quick answer was that they didn’t need to; many already had the benefits that come from distribution of insurance products, without the additional risk of underwriting, the additional hassle of state regulation, and the complexities of managing two disparate businesses. Additionally, the sale of insurance products has tended to be a high ROE business, whereas underwriting, given the stiff capital and reserving requirements, tends to be a low ROE business.

Banks sell 23% of all annuities sold. At present, most of the insurance business that banks do is the sale of annuities. Here is a breakdown of insurance sales done by banks in the US (from LIMRA, as reported in the National Underwriter):

Product

Percentage of Sales
Annuities 68%
Benefits and other commercial lines 16%
Personal Property-Casualty 7%
Credit 5%
Individual Life and Health 4%

Aside from annuity sales, the other major area of insurance activity for banks is the brokerage of employee benefits and commercial insurance. Banks have been aggressive buyers of local insurance brokers; one-third of all sales of local insurance brokerages since 1995 have been sold to banks.

There is logic to banks engaging in insurance brokerage. It deepens commercial relationships within a bank’s footprint, and can even lead to opportunities to expand the geographic scope of a bank as it buys insurance brokerages outside its footprint. Insurance brokerage relationships can lead to new banking clients, and vice-versa.

There are two banks among the top ten insurance brokers in the US: Wells Fargo is fifth, and BB&T is sixth, behind the big insurance brokerage specialists Marsh and McClennan, Aon, Arthur J Gallagher, and Brown and Brown. There are cultural differences between banking and insurance brokerage. A large commitment to insurance brokerage by a bank implies that the brokerage arm will behave like the big insurance brokerage firms that they compete with. Banks with a small commitment to insurance brokerage tend resemble the small brokers that the bank acquired. And in general, insurance brokerage tends to be a more aggressive sales- and customer service-driven culture.

We are not yet at the end of the involvement of banks in the insurance business. Intelligent bankers will use insurance as yet another way to deepen the relationships that they have with commercial, and to a lesser extent, retail clients. In general, we do not expect many banks to take on underwriting risk.

-==?=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Bringing it to the Present

All of this is still true today, and banks don’t know what to do with insurance, aside from a few of them selling annuities, like CDs, and being insurance brokers through their business banking relationships.

The last major bit of the Travelers acquisition was unwound as well, as MetLife bought the Life & Annuity business of Travelers for an attractive price.

One correction: in general, we now know that insurers do asset-liability management far better than the banks, and that the banks were considerably overlevered compared to the stable insurers.

I still think the best summary here is: banks can be good marketers of insurance.? They are a logical distribution channel for many lines.? But they don’t do a good job managing insurers.

Insurers may be better at managing their own pup banks, like Allstate and MetLife, but the length of the time of success is too short to be definitive.? Be skeptical of large efforts to blend banking and insurance; it usually doesn’t work.

Full Disclosure: Long ALL

Theme: Overlay by Kaira