Question 6.7 (Chapter 6 Page 33)

[Purp1euk]

I'm a little confused about the answer given for 6.7.

I was under the impression that E[ s^2(theta) ] represented the average variance in the data for a single risk.

However, and this may be because this is a question on EBCT Model 2 rather than EBCT Model 1, but the answer states that E[ s^2(theta) ] represents the average variance in the data for different risks.

Please could someone clarify this point?

 

[John Potter]

Hi Purp1euk

You can't really have the average variance for a single risk, there's nothing to average. It would be like saying, what's the average of 5? Well, 5.

We look at the variance for each of the N individual risks (see page 30 Tables for formula) and then take the average of these. Now, we're saying what's the average of 5, 6 and 7? Even I can do that one, 6 ;-)

The same is true for EBCT Model 1 (see page 29 Tables)

Hope this helps,
John

 

[Purp1euk]

Thanks John.

This is why I'm confused, because page 15 of Chapter 6 states that E[ s^2 (theta) ] is the average variability of data from year to year for a single risk.

Could you explain this point further and whether this statement on page 15 is misleading?


Kind regards,

Matt

 

[John Potter]

Hi Matt,

Yes, this isn't the best CR sentence I've ever seen. I think it's meant as:

the average ACROSS THE RISKS OF (variability of data from year to year for EACH single risk.)

To be fair it then does say "the average variability within the rowS of Table 1" (plural on rowS), which might clear up the ambiguity given that average does need to average something. However, I agree that we shouldn't really need to do a detective job on what should be a simpler sentence!

I'm sorry for the confusion. I think your understanding of the situation is good, which hopefully means you can handle the exam questions on the topic

John

 

[Purp1euk]

Thanks for that John - that definition now makes a lot more sense given the form of the formula in the tables.

However, I am now struggling to understand paragraph (iii) from Chapter 6 page 15 as a result. It states that increasing E[ s^2 (theta) ] relative to Var[ m(theta) ] is a sign that the sample data for the individual risk is more variable and less reliable relative to the collateral data which covers all risks.

However, if we consider sample data for risk 1, surely E [...] relative to Var [..] could increase solely due to the variability of, say, the data for risk 2 increasing? In this case the sample data could be seen to be more reliable, not less, relative to the collateral data.

Could you expand on this point and perhaps shed light on where I am going wrong?

Thanks for your time.

 

[Purp1euk]

Hi John,

Actually I think I have worked out why.

In the case of EBCT Model 2 I think my previous response is valid, as you calculate individual Z's for each risk.

However, as a single Z is used as the credibility factor for all risks for EBCT 1, any increase in the variance of one set of risk data would mean that (for that risks's component of the calculation of Z), we place less confidence in the sample data we are considering relative to the larger collateral data set. This then reduces the value of Z that is applied for all risks.

Please let me know if you agree...

 

[John Potter]

Hi Matt,

It took me a while thinking about this one and I think I went through the same circle of confusion that you did! However, yes, I agree with your final conclusion,

John