(See also PS2.5f., 113f. In course pack)
Reminder: Study notes will go up this week
Hume:
1. MBS:
Make low-grade meat into sausage.
Need to “hedge away” risk.
If risk hedged away, = AAA bond (GNMA no longer exists)
How do I hedge risk?
Example: Fire, earthqakes
Both can be done by examining past frequence
Fires: Calculable, uncorrelated
Eartquakes: Calculable, correlated
Past frequency -> future frequency
Why? Why do we believe that the past predicts the future?
Are we justified in this belief?
What happened?
2 types of risk insurance: Prepayment, default
Irrational prepayment creates irrational option—in principle difficult, perhaps
impossible. More like fire
Default risk: in principle easy, but correlated
Solution: Use the market itself (the market’s beliefs) to calculate the risk of
correlation.
Market collapses in the face of massive unhedged and correlated risk
“Moral hazard”: Since lenders are borrowers are “disintermediated”, no one is
manning the bridge
Cf. http://archive.wired.com/techbiz/it/magazine/17-03/wp_quant
"Correlation trading has spread through the psyche of the financial markets like a
highly infectious thought virus," wrote derivatives guru Janet Tavakoli in 2006.
2. Induction in Aristotle
When, if ever, are we justified in inferring from the past to the future
Aristotle: See (Losee, pp. 6-7/coursepack 10)
All these things (cows, horses, humans) are mammals.
All these things have warm blood.
All mammals have warm blood
So long as: all these things  mammals (“convertibility”: these things are—or stand
in for—all the mammals)
3. Hume’s argument:
Intro claim: All our reasoning about unknowns is based on causality. Example:
Water on my kitchen floor. Am I indifferent? No! I want to know what caused it.
Why? Because I don’t want it to happen again.
I want to know: What was the prior event such that, if it hadn’t happened, I wouldn’t
have had water on my floor.
I can, it seems, only work this out on the basis of past experience.
Factors involved:
I – Temporal priority
II – Spatiotemporal Proximity (cf. Newton on gravitation)
III – Constant conjunction
Hume uses empiricist premise: we cannot know by merely by considering an object
(1) what effects it will produce
(2) what causes gave rise to it
These can be known only by experience (iv.1, p. 324)
But: it is one thing to say that
1. I have found that events of this kind (A) always give rise to events of this kind (B);
and
2. I predict that A-events will be followed by B-events
1: looks backwards
2: looks forward
Hume: “one may justly be inferred from the other”
In fact: “it always is inferred”
For us: process of induction
He continues: “the connection between these propositions is not intuitive”
“There is required a medium” (iv.2, p. 329)
The rationalist opponent
Rationalists like Leibniz believe that causal relations can be established by rational
investigations
Physics - once again - is a kind of geometry
But empiricists deny this:
“…knowledge of this relation [cause-and-effect] is not ... attained by reasonings a
priori; but arises entirely from experience …” (iv.1, p. 324)
Empiricist’s hope
So if knowledge of causes is not attainable by reason,
then it should be by experience
But that is just what Hume denies
If he is right, then experience cannot justify our causal statements
We speak of causes and effects without rational justification
Repetition
But: surely repetition of an experiment validates the inference.
But consider the individual case.
Can we identify the causal relation?
No!
So why would repeating the experiment change the facts?
We can’t “see” the cause in the one case
So why do 100 identical cases change our state of knowledge?
Hume’s attack
Hume: “this is the sum of all of our experimental conclusions:”
“From causes which appear similar we expect similar effects.” (iv.2, p. 331)
But: this is not a proposition based on reason
There are plenty of single cases in which it is false
There are lots of similar things (eggs) which produce distinct effects (tasty, rotten)
Inductive justification of induction
And we can’t justify it (“similar causes give rise to similar effects”) as inductively
supported
Hume: “It is impossible … that any arguments from experience can prove this
resemblance of the past to the future; since all these arguments are founded on the
supposition of that resemblance”
The assumption that “similar causes will [continue to] give rise to similar effects”
itself requires inductive support
Hume’s “sceptical solution”
Hume’s arguments raise an “asymmetry problem”
What is the difference between a person who has had many experiences, and one
who has not? (v.1, pp.335-336)
“He immediately infers the existence of one object from the appearance of the
other.”
Hume’s “sceptical solution”
“There is some principle which determines him to form such a conclusion. This
principle is custom or habit.” (ibid.)
What makes the cases of the experienced and inexperienced persons different is:
The experienced one is naturally inclined to infer one thing [effect] from another
[cause]
So what is causality?
Hume continues (v.2) with an analysis of “feelings” such as belief, which accompany
our thoughts
Some intensely felt ideas we believe
And there are “laws” or “principles” of connection among beliefs
E.g. resemblance, contiguity, causation
These “carry” the mind from one belief to another (v.2, p. 342)
Hume’s “sceptical solution”
The process which carries our mind from belief in the effect to belief in the cause (or
vice versa) parallels the “powers” in the world
“Here, then, is a kind of pre-established harmony between the course of nature and
the succession of our ideas …” (v.2, p. 345)
Problem:
If we take Hume at his word, then there is no reason to believe that successive
evidence objectively increases the likelihood of future behaviour.
All it does is increase our “degree of belief”
But I don’t want to know that I believe, I want to know whether I should believe.
Gaussian copula applied to CDOs
: “When the price of a credit default swap goes up, that indicates that default risk
has risen. Li's breakthrough was that instead of waiting to assemble enough
historical data about actual defaults, which are rare in the real world, he used
historical prices from the CDS market. It's hard to build a historical model to
predict Alice's or Britney's behavior, but anybody could see whether the price of
credit default swaps on Britney tended to move in the same direction as that on
Alice. If it did, then there was a strong correlation between Alice's and Britney's
default risks, as priced by the market. Li wrote a model that used price rather
than real-world default data as a shortcut (making an implicit assumption that
financial markets in general, and CDS markets in particular, can price default risk
correctly)."
http://archive.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all”