A few weeks ago the news where reporting that silicon valley...

A few weeks ago, the news where reporting that Silicon Valley Bank (USA) failed due to risks materializing in their bond portfolio. Shortly before, a few negative news led to the fact that many customers started to lose confidence in the bank. They created a bank run, where many depositors of the bank demanded their deposits back. In order to satisfy this demand in cash, the bank had to sell a large number of their long running bonds (their own investment into bonds issued by others) at a large loss and thus became insolvent. (i) Please explain how it can happen that bonds, which are supposedly a relatively safe investment, are traded much under their face value.

Transcript

00:01 Or tax -free cash isas, when they processed, had more errors than the other type.

00:08 So there was a sample of 800 total accounts, 400 taxable bonds, 400 cash -is -a accounts, and the number of errors or incorrect applications, incorrect applications were observed.

00:23 That's what this table is.

00:24 This is our observed values here.

00:30 And what we're going to do, we're going to see if there's a, some sort of dependence upon the whether things are correct or incorrect and what type of bond it is.

00:39 So we're going to do a kai squared test for independence.

00:43 So the null hypothesis is that bond type and correct and correct versus incorrect is are independent.

01:04 And we'll say incorrect processing.

01:25 Oops, are independent.

01:26 So the bond type and incorrect processing of the bonds are independent.

01:42 The alternative is that they're not independent.

01:48 So we'll just write not independent.

02:02 And like i said, it's a kai squared test for independence.

02:04 So we're going to go our kai squared statistic, which is given as the sum of the observed values, minus the expected values squared, all over the expected values.

02:14 And the expected values are calculated by taking the total, in the row multiplied by the total in the column divided by the total sample.

02:27 So for example, for the expected values, the way we get 365 here is we take 400 times 730 divided by 800.

02:37 And these marginal totals were given just by taking the sums of the rows and sums of the columns.

02:44 So 730 times 400 divided by 800 is 365.

02:47 And it ends up being the same for the cache as well.

02:53 Incorrect.

02:55 It's this, you know, this cell is 400 times 70 divided by 800.

02:59 Oops, sorry.

03:00 Yeah, that's right.

03:02 And then that's 35.

03:04 Okay...