msb
Junior Member
Posts: 8
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Post by msb on Jul 19, 2012 12:18:29 GMT
Hey there, I saw your advice on a topic at "http://www.wilmott.com" about smoothing and was wondering if you could help me with my problem. I have a monthly return index as dependent variabel and want to regress it on monthly returns of other finacnial instruments. The problem I face ist that my monthly return index is smoothed, and therefore the volatility is lower than it should be. How can I desmooth the data? For your information I attach an excel file with the monthly log returns from my dependent index. It would be great if you could help me. Thanks in advance! Attachments:
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Post by willsmith on Jul 20, 2012 2:29:10 GMT
Hi. I think of smoothing as 'removing information' (think of an average - how can we recover the individual data only given the average? - we can't). Firstly I think you need to find out what smoothing function or algorithm has been applied to your data. Secondly, I opened your spreadsheet and loaded the 'monthly ln returns' into Matlab (I'm not sure what you want to do with the 'quarterly ln returns' series or where it comes from). I get the following summary statistics: EDU>> length(testdata)
ans =
290 i.e. about 24 years' of data. prices = ret2price(testdata) ; plot(prices) I have now recovered your price series so I can look at it, see the attachment. I agree that it looks smoothed. See how it goes up and down in jumps? That looks to me like its a windowed moving average. If an extremely high value enters the window it causes a jump up, and as that extremely high value exits the window, it cauess a jump down. I think you may be able to recover the original price data if you know your moving average window length. The difficulty will be seeding the initial values. Based on the look of the chart it's probably not crude oil (insufficient drop due to 2008) but perhaps could be gold. If you know what it is, it will be far easier to get the original data... Final question / idea : are you sure it's a price series, it looks very much similar to an inventory series. Attachments:
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Post by willsmith on Jul 20, 2012 2:42:54 GMT
One more thing. It's your price series that has been smoothed, I believe, not the return series.
If we look at your monthly returns, we see some extreme values such as +0.45 (i.e. 45% rise, t=11), +0.92 (t=47) and so on. If the return series themselves were averaged or somehow smoothed you would be unlikely to see such extreme monthly values.
Also if I look at the 1-period autocorrelation of your return data:
EDU>> corr(testdata,l(testdata))
ans =
0.0043
I see almost no auto-correlation from one month to the next. That's consistent with the efficient market hypothesis, again pointing to your prices having been smoothed - but not greatly, or we would see spurious +ve autocorrelation in returns.
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msb
Junior Member
Posts: 8
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Post by msb on Jul 20, 2012 13:59:30 GMT
Thanks a lot for your insights. You are right, the returndata is not smoothed, but it is derived from a smoothed price index. Unfortunately I have no information about the moving average windows length. The problem with the index is that it is created based on auction results where the liquidity is limited. the monthly return data is based on end of month index prices. The quarterly return data is based on the monthly data but I faced the problem that I needed midmonthpoints (eg. 15th of february 15th of may etc.) instead of end of month points. Therefore, to derive for instance to the quarterly return from 15th february to 15th may i took the average of the monthly index values of end of january & end of february AND the average of end of april & end of may and calcualted the reutrn then. Is that a valid procedure? As for my data analysis I just use return data, is it valid to control only the return data on autocorrelation? That would mean I only had to desmooth the quarterly return data. Or is the only valid method to check the Price data on autocorrelation, then first desmooth the the monthly price index and calculate the monthly and quarterly returns afterwards? Would I have to check on autocorrlation after the procedure agan?. Sorry for the many questions and thanks for your help again. I really appreciate it.
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Post by willsmith on Jul 23, 2012 1:59:31 GMT
Your quarterly return calculation assumes that prices moved linearly from 31st jan to 28th feb and so on. You have introduced further smoothing.
Autocorrelation might be a wrong track to go down. Some price series (like shipping indexes) based on assets that aren't easily tradeable exhibit (return) autocorrelation. You can't short a shipping contract today if you think the price will go down tomorrow. Housing prices also exhibit (return) autocorrelation because their sale and purchase takes so long. There's no logic in checking prices (not returns) for autocorrelation, if price today and price tomorrow are both positive (highly likely) then you have autocorrelation.
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msb
Junior Member
Posts: 8
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Post by msb on Jul 27, 2012 16:33:58 GMT
Hey again. Thank you, your answers are always very helpful. Im now on the track building a optimal portfolio (including traditional investments and commodities). So far I used the mean-variance analysis and found interesting literature about polynominal goal programming (PGP). It would be great for my work to include as well the higher moments and do a mean-variance-skewness-kurtosis analysis. however im not so familiar with programming, i was wondering if you have ever used PGP method. Is it possible to divide it in subparts to do it in excel? looking forward for your input..
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Post by willsmith on Jul 27, 2012 17:44:15 GMT
Sorry, I'm not familiar with Polynomial Goal Programming. I thought PGP was an encryption toolkit, showing my software roots!
Mean variance analysis makes intuitive sense - high returns with low risk. I'm not sure what the others would add. Maybe reducing kurtosis also makes sense - thin tailed returns are 'safer' than fat tailed. Excel has the SKEW() and KURT(). Beware, Excel's KURT is the EXCESS kurtosis (they don't make this very clear) i.e. EXCESS KURTOSIS = (USUAL KURTOSIS - 3.00)
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msb
Junior Member
Posts: 8
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Post by msb on Jul 30, 2012 0:25:12 GMT
hi thanks again for your help. I guess Polynomial Goal Programming goes beyond the scope of my research. I am back to prepare my data and desmoothed my commodity and housing index. But I also see autocorrelation for the t-bill returns used in my capm calculations. How should I deal with it? Shall I ignore the autocorrelation for my computation or should I also desmooth the risk free return (t-bill) If yes, is it applicable to use the same methodology I used to demsooth commodities and real estate returns?
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Post by willsmith on Jul 30, 2012 5:48:26 GMT
There's no reason to desmooth the t-bills - they are observed market prices so leave them as they are. How much autocorrelation do you get with daily t-bill returns? You could try plotting the returns on a scattergram (today against previous day) to look at the dependence structure. Is it just one or 2 outliers giving you the correlation?
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msb
Junior Member
Posts: 8
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Post by msb on Jul 30, 2012 9:52:08 GMT
Ah thanks for the hint! Now I found my problem. Whereas I derivced for my investments the total return index and calculated the log returns, for the risk free rate I just have the UK-T-bill YIELD available. So it is no surprise that there is autocorrelation as the yiueld is always positive ranging from 1% to 7%. I am wondering how to overcome this problem, as neither the yield nor the log return of the yoield would be appropriate but index values are not available. Thank you so much for your support
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msb
Junior Member
Posts: 8
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Post by msb on Jul 30, 2012 12:52:10 GMT
I checked again my data and found out that it was correct. I used the total return index from UK 3month t-bills and calculated the continiously compounding return. Thereby the autocorrelation does not seem to be a surprise as the t-biils which short maturities almost never will have negative returns. I attach graphs from the t-bill return index, and the autocorrelations of the logreturns against the 1 lag and time. So it can be seen that the autocorrelation is not due to a few outliers. But as the as the autocorrelation seems to be logically I can just ignore it and continue my computations? Attachments:
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Post by willsmith on Jul 31, 2012 16:24:31 GMT
You should never worry about autocorrelation with prices, only possibly returns.
In your case you have bond prices and you are converting them into rates, both flipsides of the same coin. Autocorrelation means nothing here as you note.
I mentioned "how much autocorrelation do you get with daily t-bill RETURNS", because you said earlier you had autocorrelation in the RETURNS.
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msb
Junior Member
Posts: 8
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Post by msb on Aug 1, 2012 13:14:39 GMT
hi sorry maybe my third graph led to confusion. The autocorrelation plots ARE from the return data. I just plugged the price index graph to show that it is no surprise that returns are inclusively positive and therefore the autocorrelation is no surprise, right? So anyhow do I have to be concerned about it? as the price index is on monthly basis steadily increasing, autocorrelations in the returndata seemes to me intuitively... So can I work with the returns even though autocorrelation is in place?
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Post by Terry on Aug 2, 2012 17:01:43 GMT
Hello Everyone, i have read the chat and so far you guys having been right about every thing especially what will smith said about the function kurt() on excel. i have a similar problem i.e desmoothing the returns of assets but this time it's hedge funds indices not real estate prices and i seem to miss the point where the returns are unsmoothed in your chat. can someone pls explain to me how i can do this on either excel or Matlab but preferably Matlab. thanks
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msb
Junior Member
Posts: 8
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Post by msb on Aug 2, 2012 18:29:32 GMT
well, even though it is no problem to calculate skewness or kurtosis for a single asset, the calculation for a portfolio proves far more difficult as hugh co-skewness and co-kurtosis matrices have to be calculated. I havent found a way yet. I guess matlab is suitable for it. For the chart you are right. The rerurnes are not unsmoothed. But as these represent risk free assets, t-bill returns, the question remains if s.th. has to be done against the autocorrelation. To answer your question I would recommend you the paper: Okunev, J. and D. White, 2003, ‘Hedge Fund Risk Factors and Value at Risk of Credit Trading Strategies'. There the methodology for unsmoothing hedge fund returns is explained
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Post by Terry on Aug 4, 2012 15:20:54 GMT
Thank you very much for your reply. i will look up the reference you have given.
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Post by alencherry on Oct 20, 2012 9:36:11 GMT
[Help] the code code how? What's the use? As Attachments:
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Post by edouard on Oct 20, 2012 10:07:46 GMT
[Help] the code code how? What's the use? As this is a piece of PHP code that seemingly destroys some variables, open a file, write in this file and close it.
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