On my last post on Probability in Finance, Murali raised a question as to whether the subjective probabilities could be based on past occurrences (relative frequencies). My answer would be yes, but in Finance the subjective probability can not be based only on relative frequencies. One needs to combine his/her judgement with the relative frequencies. Let me explain with the following examples.
A probability distribution of defective parts per 1,000 in a manufacturing process is developed based on repeated observations in the past. Now if you want to predict the probability of 10 defectives per 1,000 during the next production run, you would immediately refer the distribution that is already developed. Here your chances of being correct are relatively high.
Now, assume that you develop a probability distribution of rates of return per annum generated by a stock by observing sufficiently long period of time (say last 50 years). If I ask you what is the probability that the same stock would generate 20-25% returns during the next year, I am sure, you wouldn't feel very comfortable to base your answer completely on the frequency distribution. You would definitely use the distribution, but add to it your judgement on various other factors that you feel would influence the returns. This is where the subjectivity creeps in.
A probability distribution of defective parts per 1,000 in a manufacturing process is developed based on repeated observations in the past. Now if you want to predict the probability of 10 defectives per 1,000 during the next production run, you would immediately refer the distribution that is already developed. Here your chances of being correct are relatively high.
Now, assume that you develop a probability distribution of rates of return per annum generated by a stock by observing sufficiently long period of time (say last 50 years). If I ask you what is the probability that the same stock would generate 20-25% returns during the next year, I am sure, you wouldn't feel very comfortable to base your answer completely on the frequency distribution. You would definitely use the distribution, but add to it your judgement on various other factors that you feel would influence the returns. This is where the subjectivity creeps in.
Thank you very much for your thoughts and input sir..again i have a doubt..if I have bunch of individual stocks in a portfolio, I can summarize the quantitative aspects of those individual stocks. How can I summarize the qualitative (subjective) aspects for that portfolio? (first of all do i need to summarize qualitative aspects as well?)
ReplyDeleteThanks for posting article on Probabilities Sir; it reminds me about my recent discussion on whether financial decisions should be based on quantitative factors and numbers, determined by the patterns of the past, or more on subjective degrees of belief about the uncertain future
ReplyDeleteI believe there is always blame on statistical tools for any quantitative failure in the system. Investors fail to recognize the basis and the assumptions of the model and fail in their decisions based on the tool. Most of the financial and statistical models are based on the assumption that the market is normally distributed. The models are constructed based on the various assumption and the onus lies on the users to make best use of it. The data used in statistical tools are based on past data, with limited sample size, errors and many assumptions. Given this, risk factor change over period, whether it is internal controllable risk factors of a particular asset class or external uncontrollable risk factor (Good example would be the mortgage crisis in US where regulating agencies fail in there analysis, as we saw many asset class worse than junk bonds were ranked ‘AAA’), as with new additional risks the existing model becomes outdated and needs to be upgraded. But the management relies on these out dated model and takes up huge risks.
Thus we believe in 99% probability and ignore the chance of 1%. But we fail to analyze the magnitude of the 1% risk; being rational we look at the brighter side and end up taking huge risks. Thus we forget the 1% tail risk a ‘Black Swan’. Thus I think numbers backed up with subjective approach and also behavioral finance would help in making better investment decisions.
Thank you Murali, I shall soon come back with a detailed response. Sushma, I am extremely happy to see that you have gone way above what we taught you here in SIT. It gives me immense happiness to read your comments. Let me quote from John C Hull, "Stress Testing can be considered as a way of taking into account extreme events that do occur from time to time, but are virtually impossible according to the probability distribution assumed for market variables. A 5-standard deviation daily move in a market variable is one such extreme event. Under the assumptions of a normal distribution, it happens about once every 7,000 years, but in practice, it is not uncommon to see a 5-standard deviation daily move once or twice every 10 years" (Options, Futures & Other Derivatives, Chapter VaR). This is exactly what you talked about in your comment. Thanks Sushma for sharing your views.
ReplyDeleteThanks Sir, Some how my recent discussions and your thoughts on finance are on same page:-) I am also sorry for dragging the conversation from probability/returns to risk and quantitative tools.You were very right in your quote Sir, my comments were majorly focused on the use of VaR (which is a product of probability thus I bought in the discussion). Also I was under the impression that 3 to 4 standard deviation would trigger an extreme event but thanks for the information Sir I have to check out the standard deviation confidence interval breakup in a bell curve.
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