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Oct
6
comment Howto Calculate An Error's Partial Derivative in ANN
In your reference, note how the "error signal" at each neuron is the weighted sum of the error signals in the following layer. That error signal gets multiplied by the neuron's derivative and its input to find the weight update -- therefore the total gradient (i.e. the weight update) for that neuron is dependent on results in later layers.
Oct
6
comment Howto Calculate An Error's Partial Derivative in ANN
Hi @Nutritioustim, sorry if I wasn't clear -- an example will help. Say you're building a 2-layer neural network. Now suppose all the weights in your second layer are 0. Then the gradient for all the weights in your first layer must be 0, because no matter what you set them out, their output is going to be multiplied by 0 in the second layer, eliminating their impact. That's why backprop is such an important algorithm -- it takes the error back through each layer. Note that from a mathematic perspective, it's basically just a chain rule application.
Sep
10
comment Quantitative Analysis Games on Investing?
Kaggle is a great site.
Sep
6
comment VIX = Vega of S&P500 options?
@Strage I think we're talking about two different things, and I'm sorry for the confusion -- I was trying to leave variance swaps completely out of my answer because the original question and subsequent comment ask specifically about vanilla equity options. However, to clarify -- when I said hypothetical floating strike, I was referring to the "always-ATM" equity option for which VIX represents the implied vol, not a variance swap strike. I didn't realize you were referring to swaps and I see my comment doesn't make any sense in that context.
Sep
4
comment VIX = Vega of S&P500 options?
@vanguard2k You could try, but there are quite a few hurdles to replicating VIX with available SPX options: first, it would have be a very dynamic replication; the required options (not to mention quantities thereof) change every minute and rebalancing on any timescale would be difficult and expensive. Second, compounding the first, note that the calculation uses mid prices, and even half the bid/ask spread can have a meaningful impact on implied vol.
Sep
4
comment VIX = Vega of S&P500 options?
@Strange that makes sense because VIX references a hypothetical floating strike (ATM), not fixed.
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
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
comment Appropriate method for calculating negative returns on a trading strategy?
Totally agree and I like your thought a lot.
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
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 Python library for Portfolio Optimization
I have had a demonstration of it but I have not licensed it myself.
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.