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I am attempting to recreate the S&P Dynamic Asset Exchange using the methodology outlined in this paper.

I am struggling to 'normalize' the prices of the assets properly. On page 6 of the aforementioned paper,

Price A(t) = Price of asset A normalized to equal 100 on the last trading day of the preceding year

Price B(t) = Price of asset B normalized to equal 100 on the last trading day of the preceding year

-- What methodology is implied for 'normalize' -- the standard Random Variable normalization? (Random Variable - Mean)/(Standard Deviation)? Or is there an alternative method?

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2 Answers 2

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I think in this case no fancy normalization techniques are implied. At least from what I understand from the cited part, they just scale the variables so that they are equal to 100 in the base period (end of preceding year) - something like computing a deflator, commonplace in macro analysis.

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Hi Karol, Thank you for the answer. So, just to verify what you are saying: if the final return on the last trading day of the year was equal to 500, I would subtract 400 from all of the data points going forward? So, 12/31/2010 return is 500 -- I would subtract 400 from the return for the next trading day, say, 1/1/2011? If this is what you are describing, I have actually tried this and I have run into a number of problems. Primarily, I have run into negative returns (after they have been 'normalized'), which in turn causes problems at the ln(Price B / Price A) -- ln is undefined <0. –  user2188190 Jun 24 '13 at 12:30
    
Are you talking about returns or price levels? Your question and comment differ in that regard. And no, I had another procedure in mind - just try to adjust the variable through multiplying by a scaling factor. E.g. $$P_{t_0}=25 \wedge P_{t_{+1}} = 30 \Rightarrow P_{t_0}^*=100 \wedge P_{t_{+1}}^* = {100\over25} \times30=120$$ At least that's what I think they meant by normalizing. –  Karol Piczak Jun 24 '13 at 14:12
    
Thank you, Karol! Your answer seems reasonable to me -- and, importantly, results in valid data points (i.e. no negative data). Approaching this from a statistical background, in a problem that uses correlation, covariance, std, I assumed normalization in the sense of fitting the data to a normal distribution. Regarding Returns vs. Price Levels: it is my understanding that the 'Price', in this particular formula, is a function of the daily returns of various indices -- in my case, I am using the S&P 10 Year U.S. Treasury Note Futures Total Return Index to derive my Price B. –  user2188190 Jun 24 '13 at 14:43

On page 6 of the document there is the formula "Ct_DeltaAB = Equation #1 evaluated for changes in Price A and Price B". How can I know what the changes are in Price A and Price B? I know the correlation between A and B but that does not mean that I can derive the changes of A and B. How do I solve this problem?

Rick

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This needs to be a separate question, not an answer. –  chrisaycock Jul 17 '13 at 16:02

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