Mcdonald Equations

[hellohi]

I want to ask, in Financial Markets and Product topic (GARP officail books), the Robert McDonald chapter, at the end of this chapter under "hedging jet fuel with crude oil" the writer put equations included numbers - the equations 12.12 and 12.13 - and I dont know where these numbers come from, may you help?

best regards
Nabil

 

[Dr. Jayanthi Sankaran]

Hi @hellohi,

As far as I can see equations 12.12 and 12.13 pertain to hedging jet fuel with crude oil futures. It so happens that jet fuel futures do not exist in the US. As a result, the closest substitute is the crude oil futures. Also, crude oil is used to produce jet fuel - and so it makes perfect sense to use it as a hedging instrument.

Equation (12.12) is the mark to market profit of this hedge which is:

(Pt - Pt - 1) + H(Ft - Ft - 1)

where (Pt - Pt - 1) is the change in the jet fuel price
(Ft - Ft - 1) is the change in the crude oil futures and
H = hedge ratio

In order to estimate the hedge ratio H, we regress the change in jet fuel price (Pt - Pt - 1) against the change in the crude oil futures price (Ft - Ft - 1). Running this regression using daily data between January 2006-March 2011 gives:

(Pt - Pt - 1) = 0.0004 + 0.8379(Ft - Ft - 1) R-square = 0.596 .......................Equation (12.13)

The coefficient of 0.8379 tells us that when the crude oil futures price increases by $0.01 per gallon, a gallon of jet fuel price increases by $0.008379.

Hope that helps

 

[hellohi]

Hi @hellohi,

As far as I can see equations 12.12 and 12.13 pertain to hedging jet fuel with crude oil futures. It so happens that jet fuel futures do not exist in the US. As a result, the closest substitute is the crude oil futures. Also, crude oil is used to produce jet fuel - and so it makes perfect sense to use it as a hedging instrument.

Equation (12.12) is the mark to market profit of this hedge which is:

(Pt - Pt - 1) + H(Ft - Ft - 1)

where (Pt - Pt - 1) is the change in the jet fuel price
(Ft - Ft - 1) is the change in the crude oil futures and
H = hedge ratio

In order to estimate the hedge ratio H, we regress the change in jet fuel price (Pt - Pt - 1) against the change in the crude oil futures price (Ft - Ft - 1). Running this regression using daily data between January 2006-March 2011 gives:

(Pt - Pt - 1) = 0.0004 + 0.8379((Ft - Ft - 1) R-square = 0.596 .......................Equation (12.13)

The coefficient of 0.8379 tells us that when the crude oil futures price increases by $0.01 per gallon, a gallon of jet fuel price increases by $0.008379.

Hope that helps

thanks a lot dr.Jayanthi

your explain help me a lot to understand well the subject og the paragraph, but stell need answer where 0.0004 and 0.8379 come from?

 

[Dr. Jayanthi Sankaran]

Hi @hellohi,

Equation (12.13) is the Linear Regression Model with a Single Regressor. It is of the form:

Yi = b0 + b1Xi

where
the suscript i runs over observations, i = 1,...,n
Yi is the dependent variable which in our example is (Pt - Pt - 1) = the change in the jet fuel price
Xi is the independent variable which in our example is (Ft - Ft - 1) = the change in the crude oil futures price
b0 = intercept of the sample regression line which in our example = 0.0004
b1 = the slope of the sample regression line which in our example = 0.8379

I suggest that you please read Chapter 7, GARP Part I Readings, T2 - Quantitative Analysis!

 

[hellohi]

Hi @hellohi,

Equation (12.13) is the Linear Regression Model with a Single Regressor. It is of the form:

Yi = b0 + b1Xi

where
the suscript i runs over observations, i = 1,...,n
Yi is the dependent variable which in our example is (Pt - Pt - 1) = the change in the jet fuel price
Xi is the independent variable which in our example is (Ft - Ft - 1) = the change in the crude oil futures price
b0 = intercept of the sample regression line which in our example = 0.0004
b1 = the slope of the sample regression line which in our example = 0.8379

I suggest that you please read Chapter 7, GARP Part I Readings, T2 - Quantitative Analysis!

thanks DR

thanks for clear clarification, I know this is a linear regression, I can extract from your clarification that these number just an examples and not part of the equations.

best regards,
Nabil