What is meant by law of large numbers in insurance?
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A theorem that describes the result of repeating the same experiment a large number of times Show What is the Law of Large Numbers?In statistics and probability theory, the law of large numbers is a theorem that describes the result of repeating the same experiment a large number of times. The large numbers theorem states that if the same experiment or study is repeated independently a large number of times, the average of the results of the trials must be close to the expected value. The result becomes closer to the expected value as the number of trials is increased. The law of large numbers is an important concept in statistics because it states that even random events with a large number of trials may return stable long-term results. Note that the theorem deals only with a large number of trials while the average of the results of the experiment repeated a small number of times might be substantially different from the expected value. However, each additional trial increases the precision of the average result. Example of Law of Large NumbersThe simplest example of the law of large numbers is rolling the dice. The dice involves six different events with equal probabilities. The expected value of the dice events is: If we roll the dice only three times, the average of the obtained results may be far from the expected value. Let’s say you rolled the dice three times and the outcomes were 6, 6, 3. The average of the results is 5. According to the law of the large numbers, if we roll the dice a large number of times, the average result will be closer to the expected value of 3.5. Law of Large Numbers in FinanceIn finance, the law of large numbers features a different meaning from the one in statistics. In the business and finance context, the concept is related to the growth rates of businesses. The law of large numbers states that as a company grows, it becomes more difficult to sustain its previous growth rates. Thus, the company’s growth rate declines as it continues to expand. The law of large numbers may consider different financial metrics such as market capitalization, revenue, and net income. Practical ExampleLet’s consider the following example. Company ABC’s market capitalization is $1 million while Company XYZ’s market capitalization is $100 million. Company ABC experiences a significant growth of 50% per year. For ABC, the growth rate is easily attainable since its market capitalization only grows by $500,000. For Company XYZ, that growth rate is almost impossible because it implies that its market capitalization should grow by $50 million per year. Note that the growth of Company ABC will decline over time as it continues to expand. Related ReadingsCFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)™ certification program, designed to transform anyone into a world-class financial analyst. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:
Insurance is about covering risks and not certainties. But even while covering an uncertain event, it is important for the insurer to know the probability of that risk actually becoming a reality, to be able to price the product right. Insurers rely on the law of large numbers to predict the risks. Large numbers in real life According to this law, the average of the results obtained from a large number of trials will move closer to the expected result as more and more trials are performed. Let’s explain this through a popular example. When you flip a coin, the chances of it landing head upwards are 50%, as the coin has two sides and it could show either head or tail. By this logic, a person flipping a coin six times should get tails at least three times, but when a coin is flipped just six times, the person may get five tails in a row. But flip that coin 60 times, and the number of tails would be closer to the 50% mark. As you increase the number of trials of an event, the number of occurrences of that event get closer and closer to the average chance of the event taking place. Why do insurers apply this law? An insurer can predict the chances of a specific risk taking place more accurately through this law. For example, as the number of people in a group (who want an insurance cover against a common risk such as car theft) increases, the real-life instances of that disaster come close to the expected average of that event occurring. In other words, the deviation of the actual event from the expected average will reduce, as the number of people in the pool increases. So, larger the sample size, the greater is the predictability for insurance when doing the premium rating. By having a larger pool, the insurer can accurately predict the probability of an event and price the policy accordingly
Catch all the Business News, Market News, Breaking News Events and Latest News Updates on Live Mint. Download The Mint News App to get Daily Market Updates. More Less What is the law of large numbers simple definition?The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.
What is law of large number example?Example of Law of Large Numbers
Let's say you rolled the dice three times and the outcomes were 6, 6, 3. The average of the results is 5. According to the law of the large numbers, if we roll the dice a large number of times, the average result will be closer to the expected value of 3.5.
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