Error in A2000, Q1(i)??

You are asked to set out the equation for the expected return on the Arbitage Pricing Theory model.

Solution says:



but to me this is fundamentally flawed. The n macroeconomic factors are assumed to be random variables with zero mean under the APT model, so this is can't be right.

 

it's completely wrong, see http://www.econ.rochester.edu/Wallis/Renstrom/Eco217/Lect_9.pdf

 

The theory gives a set of indices I1, I2, ..., IL

These aren't assumed to have mean zero, but it is assumed that:
E[ci(Ij - E[Ij]] = 0

The expectation is just what is given in the answer. The only part with zero mean is the random component in the equation.

 

hmm interesting, the institute seem to formulate the APT in a different way to the textbooks.

 

Yup, looks like it.

Now if only I knew how to pass this paper.

 

i've tried to apply the above paper, to the version of the APT model in the core reading, which seems to imply some interesting things.

If anyone's got time to read, have a look at the attached pdf.

 

The profession's suggested additional reading for CT8 is shown at:

http://www.actuaries.org.uk/Display_Page.cgi?url=/students/CT_reading.html#8

APT is covered in Elton, Gruber, Brown et al and my 5th edition is consistent with the CT8 formulation. The special case where the indices are adjusted to have zero mean is covered later on in this textbook. So it's not as though the CT8 Core Reading authors have made up their own unique way of doing things just to upset you Gareth!

Let's hope the examiners haven't either!

I've had a look at your pdf attachment and, despite there being a few typos, I agree with your conclusion that "lambda(0)=r". This is most easily seen by considering an asset with b(i)=0. The result follows immediately then, since the expected return on a zero-beta portfolio must be r. The lambda(1) result is also correct.

Best wishes for Wednesday

 

thanks Mike, i found this topic was quite confusing from the core reading, as there was no real example of what the lambda's actually represented.

Sorry about the typos, my latex skills are pretty rusty...been a while since uni...

A good addition to the ActEd part of the notes would be a concrete example of the arbitrage pricing model, using a single index (perhaps as an extra Q&A question). I mean one which shows the theorectical basis of the model, rather than a numerical example.

I found that I needed to look elsewhere to really get to the bottom of this topic (and then by chance the two sources I looked at used the zero adjusted version, which just added to the confusion!)

 

OK - I've just forwarded this on to the tutor who's updating the CT8 CMP for 2007.