## Diversification of Risks

There are records showing that the power of diversification of risks was known to the ancients.  Investors who financed trading ships clearly favored taking fractions of a number of ships to owning all of a single ship.

The benefits of diversification are clear.  The math is highly compelling.  A portfolio of n risks of the same size A that truly independent have a volatility that is a fraction of the volatility of totally dependent risks.

Here is a simple example.  There is a 1 in 200 chance that a house will be totally destroyed by fire.  Company A writes an insurance policy on one \$500,000 house that would pay for replacement in the event of a total loss.  That means that company A has a 1 in 200 chance of paying a \$500,000 claim.  Company B decides to write insurance that pays a maximum of \$50,000 in the event of a total loss.  How many policies do you think that Company B needs to write to have a 1 in 200 chance of paying \$500,000 of claims if the risks are all totally independent and exactly as prone to claims as the \$500k house?

The answer is an amazing 900 policies or 90 times as much insurance!

When an insurer is able to write insurance on independent risks, then with each additional risk, the relative volatility of the book of insurance decreases.  Optimal diversification occurs when the independent risks are all of the same size.  For insurers, the market is competitive enough that the company writing the 900 policies is not able to get a profit margin that is proportionate to the individual risks.  The laws of micro economics work in insurance to drive the profit margins down to a level that is at or below the level that makes sense for the actual risk retained.  This provides the most compelling argument for the price for insurance for consumers, they are getting most of the benefit of diversification through the competitive mechanism described above.  Because of this, things are even worse for the first insurer with the one policy.  To the extent that there is a competitive market for insurance for that one \$500k house, that insurer will only be able to get a profit margin that is commensurate with the risk of a diversified portfolio of risks.

It is curious to note than in many situations, both insurers and individuals do not diversify.  RISKVIEWS would suggest that may be explained by imagining that they either forget about diversification when making single decisions (they are acting irrationally), or that they are acting rationally and believe that the returns for the concentrated risk that they undertake are sufficiently large to justify the added risk.

The table below shows the degree to which individuals in various large companies are acting against the principle of diversification.

From a diversification point of view, the P&G folks above are mostly like the insurer above that writes the one \$500k policy.  They may believe that P&G is less risky than a diversified portfolio of stocks.  Unlike the insurer, where the constraint on the amount of business that they can write is the 1/200 loss potential, the investor in this case is constrained by the amount of funds to be invested.  So if a \$500k 401k account with P&G stock has a likelihood of losing 100% of value of 1/200, then a portfolio of 20 \$25k positions in similarly risky companies would have a likelihood of losing 15% of value of 1/1000.  Larger losses would have much lower likelihood.

With that kind of math in its favor, it is hard to imagine that the holdings in employer stock in the 401ks represents a rational estimation of higher returns, especially not on a risk adjusted basis.

People must just not be at all aware of how diversification benefits them.

Or, there is another explanation, in the case of stock investments.  It can be most easily framed in terms of the Capital Asset Pricing Theory(CAPM) terms.  CAPM suggests that stock market returns can be represented by a market or systematic component (beta) and company specific component (alpha).  Most stocks have a significantly positive beta.  In work that RISKVIEWS has done replicating mutual find portfolios with market index portfolios, it is not uncommon for a mutual fund returns to be 90% explained by total market returns.  People may be of the opinion that since the index represents the fund, that everything is highly correlated to the index and therefore not really independent.

The simplest way to refute that thought is to show the variety of returns that can be found in the returns of the stocks in the major sectors:

The S&P 500 return for 2012 was 16%.  Clearly, all sectors do not have returns that are closely related to the index, either in 2012 or for any other period shown here.

Both insurance companies and investors can have a large number of different risks but not be as well diversified as they would think.  That is because of the statement above that optimal diversification results when all risks are equal.  Investors like the 401k participants with half or more of their portfolio in one stock may have the other half of their money in a diversified mutual fund.  But the large size of the single position is difficult to overcome.  The same thing happens to insurers who are tempted to write just one, or a few risks that are much larger than their usual business.  The diversification benefit of their large portfolio of smaller risks disappears quickly when they add just a few much larger risks.

Diversification is the universal power tool of risk management.  But like any other tool, it must be used properly to be effective.

This is one of the seven ERM Principles for Insurers

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### 2 Comments on “Diversification of Risks”

1. […] DIVERSIFICATION: Risks must be diversified. There is no risk management if a firm is just taking one big bet. […]

2. Good post with a lot of foundation that requires repeating. Thanks!

(also I am picking nits here but I calculated that Company B needs only 795 policies)