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help on cross hedge optimal hedge variance ratio

2 messages · Krishna Kumar, Spencer Graves

Original
Krishna Kumar
# 
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
1 day later
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: