Primer to Risk and Returns – I

Understanding Risk — Why diversify?

How is it that a large portfolio, say the Sensex is much less risky than its individual component stocks considered individually? We can elaborate on this by understanding the concept of risk and its types.

Risk, or volatility, has quite a negative connotation in every field, not just finance. Considering it from an unbiased perspective, it implies unpredictable gains or losses from holding a particular security. Let us consider risk as follows:

1. Common risk
2.  Independent risk

Cyclone versus Theft Insurance

For a given home in Nariman Point – Mumbai, let us consider two types of home insurance, one for a house break and the other for a cyclone. Say each year, there is a 1% probability of the house being broken into and a 1% probability of the house being damaged by a cyclone. Say 10,000 insurances are sold for each type, with the same insurance company.

It is easy to see that if a cyclone occurs, it affects large regions, thus the insurance company would have to pay coverage not just that one house but on all the policies written for surrounding houses in the neighbourhood, meaning all 10,000 insurance claims will be filed. Conversely, if no cyclone occurs, claims are filed by none, making it an all or nothing scenario.

In the case of theft, 100 claims will be filed where the probability of theft is 1% across 10,000 houses, given that the probability of a house being broken into is independent of thefts in other houses. In certain years it could be 750 or 1250, but it would on average be 100.

Which is then riskier? The insurance policy on cyclone or theft?

Those of you who guessed cyclone, you are quite right, even if you guessed it by its literal sense. Now let us answer the question — Why are the portfolios of insurance policies so different when the individual policies themselves are quite similar?

It is the type of policy that makes the difference. A cyclone would affect all houses simultaneously, meaning that the risk is perfectly correlated across homes — this is called common risk. On the other hand, the theft risk is uncorrelated and independent across homes, this is called independent risk, i.e., for 10,000 houses around 100 will file claims

The averaging out of independent risks is called diversification. However, there is no escaping common risk.

The principle of diversification is commonly used in the insurance industry. Theft, life, health, and auto insurances generally make use of the fact that normally, claims in these fields are independent of each other as risks are uncorrelated Thus, the larger the number of policies sold by the insurance company, the more is the degree of diversification, so much so that in the end, the insurer faces almost no risk at all.* Even in cases of natural calamities, diversification can be obtained to a certain degree — it can be achieved by selling policies in different geographical regions. You would notice that most farmers try to plant more than 1 type of crop, in order to reduce the risk from the failure of any individual crop, this is an example of diversification!

This means that individual risks can be diversified whereas common risks cannot. We will see next what are the examples of common and individual risks when it comes to financial markets, in the next blog https://sanyojit.com/primer-to-risk-and-returns-ii/

*This is mathematically proven by the formula of Standard Error (SE), as the square root of the number of observations increases, the standard error (standard deviation of the average) decreases.
SE (Percentage theft claims) = SD (Individual claims) / √ (Number of Observations)