To specialists in the theory of probability. I have a portfolio of 10 stocks. What is the probability that 2 of my 10 companies will go bankrupt next year? - page 6

[Aleksey Nikolayev]

Maxim Kuznetsov:

it was just a complete quote from the topic. It is underlined what is a condition and noted what is relevant to the subject area

where do you see conditional probabilities here? there are none. There are statistics from last year.

there's not even a total number of companies at the time of investment, it's unknown and by the way unimportant.

PS/ not even surprised that tractors plough the oceans and GAs beat random :-)

not only everyone knows how to write / and read / TK)

[Aleksey Mavrin]

Now I wonder - question/suggestion to TC - there are a bunch of rating agencies and just methodologies that rate companies, including insurance against default.

Find them for your companies... and compare it with this approximation :)

That way you will probably assess the quality of your portfolio.

[Vladimir Suschenko]

igrok333:
Last year, 50 out of 5,000 companies went bankrupt in the US market. So the probability of a company going bankrupt is 1/100.

I have a portfolio of 10 stocks.

What is the probability that 1 of my 10 companies will go bankrupt in a year? It's easy to calculate.
The probability of one company going bankrupt is 1/100. And we take 10 companies, so we increase the odds of the event occurring by a factor of 10.
So we get a probability: 1/100 * 10 = 1/10.

What is the probability that 2 of my 10 companies go bankrupt in one year? How do we calculate this?

With this formulation of the question, the problem has no solution.
However, if we make some hypothetical (unrealistic) assumptions, we can formalise the problem and reduce the solution purely to probability theory.
Assumptions:

1 - The market blindly, with its inexorable hand, bankrupts companies regardless of their field of activity, assets, management capacity by random poke, purely on the principle of "50 out of 5000 must go";

2- You purchased your shares completely unknowingly by running a random number generator, selecting 10 items from the list of 5,000.

These assumptions are not mutually exclusive and both are self-sufficient to reduce the solution of the problem to a probabilistic method.

We get it - last year you had 10 stocks (N) from the list of 5000 companies (G2019), by market decision 50 (M) went bankrupt. In general, from last year's history we have that the probability (V) of bankruptcy of each company from the list was V=(M/G2019)x100%=(50/5000)x100%=1% . Now we come to the key point which should be understood and taken into account for further search of solution of the problem - in the formula for finding probability of bankruptcy of one of your shareholders the number of them (N) ABSOLUTELY DOES NOT MEAN, as probability is the same as for any company from the general list - V=(M/G2019)x100%=(50/5000)x100%=1%. In other words, the probability of each stock in your portfolio going down the drain (irrespective of their total number N) will be 1%. Now, if thebasic principle of market approach to bankruptcy of the companieswill be kept in the current year, the probability of one of your shares flying out of the market (still irrespective of their number in your portfolio) will remain unchanged - 1% (the second quasi paradox will be that the current number of companies in the list, conditionally G2020 will not affect this value either). The probability of 2 stocks leaving would be 0.5% respectively, 3 stocks 0.3333% etc.

Of course, as already stated, this solution is hypothetical in absolute isolation from reality. To find real values of probability of bankruptcy of any shareholder in your portfolio it is necessary to operate with statistical data on all companies from the list and determine which of the criteria are common (significant) in the list of bankrupts, determine weights of significance of these criteria, then analyse shares in your portfolio by presence/absence of these criteria and only after that calculate probability individually for each share.

[igrok333]

Aleksey Mavrin:

Now I wonder - question/suggestion to TC - there are a bunch of rating agencies and just methodologies that rate companies, including insurance against default.

Find them for your companies... and compare it with this approximation :)

That way you will probably assess the quality of your portfolio.

there was kodak, then they invented digital camera technology - kodak went bankrupt. you don't see that coming.

[igrok333]

Aleksey Nikolayev:

exactly two: 0.004152351

at least two: 0.0042662

I got the same result.

[igrok333]

This task is to understand what the minimum acceptable portfolio size should be. Is 10 shares too small?

(we can argue about how to calculate the probability of bankruptcy of a firm. but the easiest way is to take the total number of firms and divide by it the number of firms that go bankrupt on average per year)

A portfolio of 10 firms.

The event "one firm in the portfolio goes bankrupt" will occur every 10 years.
What will happen then?
The portfolio will lose 10% of its capital. But the other 9 companies will give 9% profit for that year. The result for the year is -1%.

The event of two portfolio companies going bankrupt will occur once every 200 years.
What happens then?
The portfolio will lose 20% of its capital. But the other 8 companies will give 8% profit for that year. The result for the year is -12%. Not too bad, the loss will be recouped over the next year.
200 years is a very long period. But if you consider that portfolios are passed on to children, then to grandchildren... I would like this unpleasant event to happen as infrequently as possible.

The 'bankruptcy of 3 portfolio companies' event will occur once every 10,000 years.
It's a huge period, so I won't even look at it in detail.

The main thing is that the probability of losing the whole capital (bankruptcy of all 10 companies) is minuscule. Even the probability of 50% capital loss is negligible.

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If the portfolio consists of 1 share, then (according to my simple calculation of probability of bankruptcy of one company), this share will depreciate once in 100 years. And once every 100 years, the family will lose capital.

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10 companies is a bit small. it's better to increase the number.

You can also have 100, but it takes a lot of time to thoroughly analyse 100 companies, and it is very difficult to monitor the activities of 100 companies.

[Aleksey Nikolayev]

igrok333:
A portfolio of 10 companies.

The event "bankruptcy of one company in the portfolio" will occur once every 10 years.

The event "bankruptcy of two companies in the portfolio" will occur once every 200 years.

Not really. The probability of two bankruptcies in 22 years will be higher than the probability of one bankruptcy in 10 years. I am too lazy to calculate exactly (it is impossible for one firm to go bankrupt twice), but the values are in the order of 0.65 and 0.63.

It is clear, that the given calculations on such big terms have no special sense - for 20 years there will certainly be global crises and technological leaps.

PS. made a mistake, it is possible to calculate precisely

p_2_in_22_years <- 1-dbinom(0,220,0.01)-dbinom(1,220,0.01)
p_1_in_10_years <- 1-dbinom(0,100,0.01)

p_2_in_22_years; p_1_in_10_years

0.6468995; 0.6339677

[Aleksandr Yakovlev]

If you put a monkey in eternity and give it a pen and paper, sooner or later

it will write War and Peace.

The probability of 10 companies going bankrupt next year is 100%.

[igrok333]

Aleksandr Yakovlev:

If you put a monkey in eternity and give it a pen and paper, sooner or later

it will write War and Peace.

The probability of 10 companies going bankrupt next year is 100%.

is in your case.

[Aleksandr Yakovlev]

igrok333:
That's in your case.

What makes you think that you have chosen the 10 companies that cannot go bankrupt and assume the probability that among them

there might be one or two companies that will go bust. You don't take into account that you chose companies that will all merge next year.

That's what I'm talking about. And don't take it personally. You ask a question, you get an answer.