He had testified to the Senate committee on June 13, 2012.
This was in regards to JP Morgan’s trading in financial derivatives gone wrong.
I had noticed the following blog post by dy/dan:
This applies even double to politicians who oversee risk management of too big to fail banks.
I submitted although it has not posted the following comment to his blog.
I think requiring them to take math tests is an excellent idea. Especially ones on the financial oversight committees. When Goldman Sachs executives testified in 2011, Senator Levin said that value at risk was a well respected method. VAR is a way of measuring tail risk. However, Goldman does VAR over a 1 day interval. This time interval is not long enough, since they can’t liquidate their positions in one day.
In constrast, life insurance companies use a 30 year time interval. I think the senator was completely unaware of this. If he had to take an algebra II exam with some stats it might get him closer to being able to ask the right questions of Goldman guys.
Last Saturday I head Andrea Mitchell was interviewing Tim Geithner. This was a rebroadcast of a June 13 2012 interview.
She was saying Geithner was not doing a good job educating the public on what is being done in risk management. I would like to see Geithner’s scores on a recent math test as well. More so than Arne Duncan.
This would have been around 41 on his list.
Suppose a bank borrows 100 dollars and invests it into a stock index. Suppose the stock has a standard deviation on an annual basis of 15 percent. We should use logs, but we ignore that. So the two standard deviation loss is the stock is worth 70 cents on the dollar after 1 year. The loss is 30 dollars on the position. So the value at risk at the minus two standard deviation level is 30 dollars.
If we require the bank to hold capital based on annual VAR on this position, it would need to contribute 30 dollars of shareholder equity plus enough to make up for the difference of the interest on the borrowing minus the dividend yield of the stock taking into account the appropriate portfolio math. The interest on the capital would also partly offset the interest paid on the borrowing by the bank.
This type of calculation fits into an algebra course and into financial courses offered at some high schools and certainly colleges. It is an interesting application because it relates to a hot topic in current affairs.
Moreover, the financial oversight committees are not strong on this type of math, despite it not being very difficult.
VAR is not difficult to understand or apply in simple cases. It is used by financial institutions and is highly relevant to headlines in the media. So VAR is a great application for algebra or any other course that does the arithmetic in VAR calculations. So it can also be covered in a general math course or practical finance course or as arithmetic before getting to algebra.
==Some more detail on VAR example.
We have to hold sufficient capital x so that if the stock loss is 2 standard deviations down, we break in at the end of a year. Assume 5 percent interest is earned on capital and paid on the borrowing. The stock is worth 70 at the end of the year. Assume zero dividend on the stock. The breakeven condition on x is
-100*1.05 + x*1.05 + 70 = 0
Solving for x, we get
x = 100 – 70/1.05
70 / 1.05 = 66.6666667
100 – (70 / 1.05) = 33.3333333
So we hold more than 30 dollars.
Because we have borrowed 100 and are lending the capital both at 5 percent, so we need some extra capital to pay this cost of borrowing.
We can add in a dividend on the stock. We can also treat the two standard deviations down to 70 as after the dividend is paid.
We can work with the change in stock price in logs and subtract 2 *.15 = .3, so we have
log y = log 100 – .3
y = 100 * exp(-.3) = 100 * 0.740818221 = 74.0818221
The problem can be reworked with this as the final stock price instead of 70.
This type of application can also be used for the practical applications of math course. Timothy Gowers discusses such a course for the UK.
Value at risk is full of good examples for the type of course Timothy Gowers discusses for practical math applications.
If the course is to teach ingenuity, the problem of measuring trading risk can be given without first giving the value at risk approach. Or after consider a basic application without interest or dividends or using logarithms, the additional complications can be added.
The growth of risk like the square root of time can also be discussed and alternatives discussed as part of the course work.