Delta normal Var/Stulz Var impact

[sdoshi004]

Hi David

I had gone through the screen cast MArket C- part 1 and came across the captioned concepts. However while going through the related edit grids, I got lost since the formulas used by you in the calculation (for e.g. portfolio Variance capturing covariance) was going above my head. There is a high probability that you would have explained this in your earlier screen cast but I might have forgotten it. It happens at times when you mover further in the syllabus, u bound to forget old stuff and thats where repetative reading helps. However, is it possible for you to give reference to the formulae in the edit grids which help us to go back to the concept and refresh our memory?

Would appreciate your response.

Thanks

Sumit

 

[David Harper CFA FRM]

Hi Sumit,

The Stulz small project VaR is among the more involved calculations. The testable elements relate to the second half of the sequence, but I agree it is good to be able to follow the whole sequence b/c the first half is essentially the same as Jorion's (Ch 7) Portfolio VaR concepts.

What I just did is add formula images to the second half @
http://www.bionicturtle.com/premium/editgrid/2008_frm_stulz_var_impact_of_small_project/

see at rows 26+, to the right, i pulled in the images of the Stulz formulas...

(unfortunately, the File > Export As will not copy the images to the Excel export)

Can you tell me if this is what you mean, if this is helpful? If so, I will do the same for first half of small project and large project...

Thanks, David

(not to replace your point, but if you'd like additional help on the portfolio variance with matrix, i just did a 10 min screencast on that @ http://www.bionicturtle.com/learn/article/how_to_get_portfolio_variance_from_covariance_matrix_10_min_screencast/)

 

[David Harper CFA FRM]

I've gotten a few questions about the use in Stulz of the $1.11 assumption for the marginal cost of VaR. I personally find this a mind-bender so I put the explain below into the XLS.

The initial assumption is that a reduction of $1 in equity corresponds to a $0.10 increase in firm value
(i.e., higher leverage increases firm value by lowering the WACC). This 10% assumption is given.

Then, what happens if the "VaR impact of the trade" reduces the firm's VaR (as in this example)?
Now the firm can reduce its equity to restore its probability of distress to the pre-trade level; i.e., the trade has created "excess VaR" above an optimal level.

So, lower VaR allows the firm to swap debt-for-equity. This lowers WACC and increases firm value!
If the impact of the trade is to reduce the VaR by $1, how much can equity be reduced? (to restore the PD to pre-trade level)(again, under the assumption that a $1 reduction in equity creates +$0.10 additional firm value)

Equity can be reduced by $1.11 or $1/(1-10%). Because if equity is reduced by 1.11 then firm value is increased by (10%)(1.11) = $0.11. The equity drop of (-) $1.11 is offset by the increase in firm value of (+) 0.11, so that VaR is increased by $1.

So, to restore the VaR, we can summarize:

A trade that reduces the VaR by $1 means equity can be reduced by $1.11 (i.e., debt increased) to restore to the pre-trade VaR level,
A trade that increases the VaR by $1 means equity must be increased by $1.11 (i.e., debt reduced) to restore to the pre-trade VaR level


That gives us the equity change that corresponds to "preserving" the VaR level,

Now we multiply that by 10% to get the corresponding change in firm value.

And that's why Stulz has the marginal cost of VaR = $0.111 = 10% * $1.11

Again, why?
Because for every dollar in reduced VaR, the firm can "afford" to swap debt-for-equity at + $1.11 per $1 VaR.
And 10% of this newly reduced equity ($1.11) corresponds to an increases firm value (due to leverage)

David