jlowin
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 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. Aug 23 comment What is the reference python library for portfolio optimization? I have had a demonstration of it but I have not licensed it myself. Aug 23 answered How to annualize dividends paid at varying intervals? Aug 23 answered What is the reference python library for portfolio optimization? Aug 23 comment How to normalize different instruments by volatility? Mathematically they aren't equivalent at all. Returns can be stationary processes and levels can not (as the integral of a stationary process is not stationary) -- therefore volatility measures simply can not be equivalently descriptive for returns and levels. See this SE question for more, including helpful pictures. Aug 23 comment Appropriate method for calculating negative returns on a trading strategy? @Freddy I can't tell if you're joking... so let's start with round numbers. (A) A stock is at \$100 and moves to \$99. It is now -1% from its previous value. Agree? Of course you do, because 100 * (1 + -0.01) = 99. (B) Now with the numbers from your answer: An equity balance moves from 5.2735 to 4.3922. The new value is -16.71% lower than the old. Let's check your work: 5.2735 * (1 + -.1671) = 4.3922. (C) Now my numbers: A negative equity balance starts at -7.30 and moves to -7.18. It is therefore -1.64% from its starting place. Let's prove it: -7.30 * (1 + -.0164) = -7.18. Aug 22 awarded Supporter Aug 22 comment Appropriate method for calculating negative returns on a trading strategy? Freddy, can you be more specific? I see I overlooked a negative sign in the third paragraph, but that's not a calculation -- Since the only percent I do calculate is unquestionably -1.64%, is it possible that you are confusing my natural logs for base-10 logs? That's pretty standard notation. Aug 22 awarded Editor Aug 22 revised Appropriate method for calculating negative returns on a trading strategy? Added missing negative sign to -7.30 in third paragraph Aug 22 answered Appropriate method for calculating negative returns on a trading strategy? Aug 21 awarded Teacher Aug 21 answered Implied forward rates puzzle