[R] help on cross hedge optimal hedge variance ratio

[Spencer Graves]

	  You have not told us what software you used to get the results you 
present.  My first question is whether you are working with prices or 
log(prices)?  If the former, I suggest you consider the latter;  price 
changes tend to be much better behaved, more nearly normal, etc., on the 
log scale than in dollars, Euros, Rupias, or whatever.

	  Secondly, have you made a normal probability plot of the residuals, 
preferably using "studres" in library(MASS)?  (If you don't have 
Venables and Ripley 2002 Modern Applied Statistis with S, Springer, I 
recommend you get it and spend some time with it.  In addition to 
"studres", it has an excellent chapter devoted to an introductory 
discussion of time series analysis.)  Outliers suggest you may need to 
be working with some of the more sophisticated Rmetrics tools, but I'm 
not sufficiently familiar with those to say much more about that at the 
present time.

	  If I had outliers, I might just delete them initially.  However, I 
would definitely want to come back to them later, because the outliers 
could provide more information than other observations to predict, for 
example, a structural change in the market.  Modeling and reacting 
properly to such signals could make the difference between stellar 
performance and disaster in managing a hedge fund.

	  Thirdly, have you made acf and pacf of the residuals?  Also, have you 
computed the Box-Ljung statistic (function Box.test)?  If no, I suggest 
you do that as a next step.  If they indicate some kind of 
autocorrelation structure, I might then try to model and estimate that 
along with your regression model using function "arima".

	  If you still have questions (which I suspect), then feel free to ask 
another question.  However, before you do that, PLEASE do read the 
posting guide prior! "http://www.R-project.org/posting-guide.html". 
Many people find answers to their own questions in the process of 
working through the posting guide.  Questions posted following that 
process tend to be clearer, easier for others to understand and respond 
to.  On average, this tends to increase the speed, volume and utility of 
replies.

	  spencer graves

Krishna wrote:

> Hi everyone
> 
> I am trying to estimate the optimal hedge variance ratio for cross
> hedging two commodities. the price levels are used (compared to price
> change and % price change) and used the OLS with dummy variable for
> estimating the co-efficients. the equation looks like this
> 
> Y = B + B1*D1 + B2*X + B3*(X*D1)
> 
> Where Y = Daily Cash market price
> D1 = Dummy variable taking value 1 for period Oct-Mar and 0 for Apr-Sep
> X = Daily futures market price on which cross hedging is done.
> B,B1,B2,B3 are the slope co-efficients. 
> 
> The results look like this 
> Regression Statistics
> Multiple R		0.948702709
> R Square		0.900036831
> Adjusted R Square	0.89981135
> Standard Error		25.52050965
> Observations		1334
> 
> 
> 	Coefficients	Standard Error	t Stat	P-value
> Intercept	53.817		4.375		12.300	0.000
> X	0.986		0.012		80.283	0.000
> D1	27.399		6.106		4.487	0.000
> D1 * X	-0.100		0.017		-5.820	0.000
> 	
> It is understood the slope co-efficients for different periods are
> significant as indicated by t-table value. But I feel suspicious on
> the reliability of this values.
> 
> I have used 5 years of daily price data for running the regression,
> and I feel suscpicious becasue, the monthly correlations (pearson
> correlation co-efficient) are highly varying between spot and futures
> and some times even negative.
> 
> Can someone suggest me 
> a) the tests to judge the reliability of hedge-variance values
> b) Is there any other better method than described here for estimating
> the hedge-variance values
> 
> Thank you for the attention and look forward for an early reply
> 
> rgds
> 
> snvk
> 
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