Taleb has a good point about people mistakenly interpreting standard deviation (sigma) as Mean Absolute Deviation (MAD). I like that he gives some conversions (sigma ~= 1.25 * MAD, for Normal distribution).
I think it's rather silly to talk about "retiring" standard deviation, but we can't blame Taleb - the publication itself posed the question "2014: What Scientific Idea is Ready for Retirement?" to various scientific personalities.
What Taleb failed to mention is that, once properly understood, standard deviation has distribution interpretations that can be much more useful than MAD. For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.
Not everything is approximately normally distributed, but a lot of phenomena ARE normally distributed. It's a well known fact that the phenomena which Taleb is most interested in (namely, financial return time-series) are not normally distributed. But I would like to know how Taleb proposes to "retire" volatility (sigma) from financial theory and replace it with MAD? Standard deviation is so central in finance that even the prices of some financial instruments (options) are quoted in terms of standard deviation (e.g. "That put option is currently selling at 30% vol"). How do we rewrite Black-Scholes option pricing theory and Markowitz portfolio theory in terms of MAD and remove all the sigmas everywhere? Surely Taleb has already written that paper for us so that we can retire standard deviation?
I think his point is that Black-Scholes et al are holed beneath the waterline precisely because they involve standard deviations. In his world, you're better off being unable to price an option than you would be with Black-Scholes. Your example of "That put option is currently selling at 30% vol" is actually an example of why the system is so completely broken: if volatility as standard deviation was valid, all options against the same underlying instrument would have the same implied volatility. The volatility smile shouldn't exist.
This wouldn't matter if the down-side wasn't so crippling.
I don't think Taleb has to be the one to propose a replacement for portfolio theory, and I think criticism of him for not doing so is pointless. You don't need to have a spare tire handy to point out that your neighbour's car has a flat, and you don't have to run an airline to tell people not to get on a plane with the engines visibly on fire.
I've never understood this part of Taleb's argument. Of course, constant vol Black-Scholes does not hold. BUT NO ONE USES THIS. Everyone in the financial industry is well aware of the volatility skew, and spends lots of time adjusting for it.
B-S vols are putting the "wrong number into the wrong equation to get the right price" as Rebonnato famously said.
> For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.
Could you sketch out why similar statements couldn't be made about MAD? My (possibly flawed) intuition is that the expected proportion of observations within n\*MAD should be similarly independent of the parameters of the normal distribution.
I think it's rather silly to talk about "retiring" standard deviation, but we can't blame Taleb - the publication itself posed the question "2014: What Scientific Idea is Ready for Retirement?" to various scientific personalities.
What Taleb failed to mention is that, once properly understood, standard deviation has distribution interpretations that can be much more useful than MAD. For example, if the data is approximately normally distributed, then there is approximately a 99.99% probability that the next data observation will be <= 4 * sigma.
Not everything is approximately normally distributed, but a lot of phenomena ARE normally distributed. It's a well known fact that the phenomena which Taleb is most interested in (namely, financial return time-series) are not normally distributed. But I would like to know how Taleb proposes to "retire" volatility (sigma) from financial theory and replace it with MAD? Standard deviation is so central in finance that even the prices of some financial instruments (options) are quoted in terms of standard deviation (e.g. "That put option is currently selling at 30% vol"). How do we rewrite Black-Scholes option pricing theory and Markowitz portfolio theory in terms of MAD and remove all the sigmas everywhere? Surely Taleb has already written that paper for us so that we can retire standard deviation?