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Aug
29
comment St Petersburg lottery pricing & short investing horizons
Ok! I'll look out for your question. There are many people here who are excellent teachers and I'm sure someone will be able to help.
Aug
29
comment Appropriate method for calculating negative returns on a trading strategy?
I'm tired of my answer being used to stage a witchhunt. I refuse to "confess" that moving from -100 to -90 is anything other than a -10% change. Here's Wolfram Alpha demonstrating that basic math yet again. What more can I do? This discussion is over.
Aug
29
comment What distribution to assume for interest rates?
"Interest rates in general are far from independent and identically distributed" -- a statistician's least favorite phrase, but so very true in this case.
Aug
29
comment St Petersburg lottery pricing & short investing horizons
Hi Tim -- Taleb's reasoning is actually slightly different. His calls these impactful outliers "black swans". His option strategies take advantage of the fact that stock returns are usually assumed to be log-normally distributed, meaning such outliers are ignored in pricing options, and so they're too cheap. Therefore, it's a form of "model arbitrage". To quantify it, you could examine option prices under non-normal distributions accounting for excess kurtosis and skew. It is partially diversifiable since there are instruments correlated with the strategy -- so some risk can be mitigated.
Aug
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awarded  Organizer
Aug
29
revised St Petersburg lottery pricing & short investing horizons
edited tags
Aug
29
revised St Petersburg lottery pricing & short investing horizons
Increased the directness of the answer
Aug
29
answered St Petersburg lottery pricing & short investing horizons
Aug
27
comment What is the meaning of subadditivity in a risk measure?
@Chang, upon browsing your other questions I've noticed that you appear quite familiar with coherent risk measures. I apologize if my answer is too basic for you in its treatment of such measures; hopefully it will still benefit others.
Aug
27
awarded  Commentator
Aug
27
comment Appropriate method for calculating negative returns on a trading strategy?
Totally agree and I like your thought a lot.
Aug
27
revised What is the meaning of subadditivity in a risk measure?
Clarified what a portfolio is less volatile than
Aug
27
revised What is the meaning of subadditivity in a risk measure?
added 4 characters in body
Aug
27
answered What is the meaning of subadditivity in a risk measure?
Aug
26
comment Appropriate method for calculating negative returns on a trading strategy?
Upvoted because normalizing with capital or margin is definitely the way out of this mess. One hesitation on normalizing with max drawdown, though, is that that some of the pnl numbers are being adjusted by a value not known at the time of that pnl. That could be problematic, for example, if in the future the max drawdown were even larger. In that case, running the same analysis would give different percent returns for these observations. If this is a one-time analysis, maybe it's not an issue, or perhaps it could be fixed by dividing pnl at time t by the max drawdown observed at time t.
Aug
26
comment Appropriate method for calculating negative returns on a trading strategy?
On further thought, it is interesting to me that the answer you're campaigning to have accepted contains the exact math you find so shocking in mine. If the OP implements your answer, he will wind up with -1.64% as his final change, subject to rounding. In any case, since our private argument has added nothing constructive to this question, I suggest we put it aside.
Aug
26
comment Appropriate method for calculating negative returns on a trading strategy?
That's right... and you do too, in fact: in your own answer you write the percent change equation [r(t) / r(t-1) - 1], which for a move from -100 to -90 yields -10%! If you'd bothered to read my answer you'd see my second sentence: "I disagree with the use of any form of percent returns... because they are nonsensical for negative equity values." Negative percent changes move values toward zero, not toward negative infinity. That is not up for debate. If you choose to get around it, say with absolute values, then your price series can't be trivially reconstructed from the changes.
Aug
24
answered Basic question about Black Scholes derivation
Aug
23
comment How to normalize different instruments by volatility?
I agree that price vol can be used to normalize (though I wouldn't), but I strongly disagree that "mathematically [it] is in no way sub optimal" -- the price series is the integral of the return series, which is where the generative process is defined and where all analysis should take place. That's why things like stock splits and dividends don't matter in practice -- we just rebase the price. But if you based all analysis on price vol, then (for example) a price-vol based derivative immediately following a stock split would have a very different price, creating arbitrage opportunities.
Aug
23
comment How to normalize different instruments by volatility?
@Freddy consider a \$1 stock and a \$100 stock with identical returns. Note that I can perfectly replicate the high stock with 100 shares of the other. Now price a return vol derivative on each one, say a 10% OTM call. Again, the 100 units of the low call replicate the high one. Now use a price vol derivative instead: 100 low derivatives would not form a replicating portfolio because vol is different for each stock, even though one perfectly replicates the other. This is a violation of the no-arbitrage theorem and is why stationarity assumptions are so important in mathematical finance.