Risk Of Ruin Formula Intuition

[Metronome]

This book excerpt explains risk of ruin in the context of a simple trading game. I am trying to gain an intuitive understanding of why the formula is what it is.

However, even in the degenerate case where [imath]C = 1[/imath], the formula does not seem to produce the correct result. If we divide a trading account into only [imath]1[/imath] part, then the risk of ruin should be the probability of losing the single trade, [imath]40[/imath]% if we borrow the number from the example. The formula would produce [imath]\frac{2}{3}[/imath] as an answer.

Likewise, the numbers in the table make very little sense to me, which is especially apparent in the first data column.

Why does this formula appear to give the wrong result, and how should I interpret it? My first attempt was to derive it as the solution to a difference equation which might be more intuitive than the formula itself. It kind of looks like the solution to a linear difference equation, being in the form of something to the power of a discrete exponent, but that would make [imath]C[/imath] the independent variable, and it is not clear to me how or even that different values of [imath]C[/imath] relate to each other in a way that could be written as a difference equation.

 

[JeffM]

This book excerpt explains risk of ruin in the context of a simple trading game. I am trying to gain an intuitive understanding of why the formula is what it is.

However, even in the degenerate case where [imath]C = 1[/imath], the formula does not seem to produce the correct result. If we divide a trading account into only [imath]1[/imath] part, then the risk of ruin should be the probability of losing the single trade, [imath]40[/imath]% if we borrow the number from the example. The formula would produce [imath]\frac{2}{3}[/imath] as an answer.

Likewise, the numbers in the table make very little sense to me, which is especially apparent in the first data column.

Why does this formula appear to give the wrong result, and how should I interpret it? My first attempt was to derive it as the solution to a difference equation which might be more intuitive than the formula itself. It kind of looks like the solution to a linear difference equation, being in the form of something to the power of a discrete exponent, but that would make [imath]C[/imath] the independent variable, and it is not clear to me how or even that different values of [imath]C[/imath] relate to each other in a way that could be written as a difference equation.

I agree that this excerpt is hard to decipher. It might be quite clear and sensible with more context, but what I am guessing is that the book is written by a dummy for dummies just as its title asserts. Words are being used in strange ways and simplifying assumptions are rampant. In particular, how ”expected return” is defined and how “probability” is defined are uncertain. Expected return is usually defined with respect to a probability distribution and no probability distribution is provided. And I wonder whether the author knows the distinction between odds and probability.

A starting point might be wikipedia rather than a book that explicitly admits that it is directed toward idiots.

Risk of ruin - Wikipedia

en.wikipedia.org