9. “The demand for certainty is
one which is natural to man, but
is nevertheless an intellectual
vice. If you take your children
for a picnic on a doubtful day,
they will demand a dogmatic
answer as to whether it will be
fine or wet, and be disappointed
when you cannot be sure...”
10. ...but so long as men are not
trained to withhold judgement
in the absence of evidence, they
will be led astray by cocksure
prophets...For the learning of
every virtue there is an
appropriate discipline, and for
the learning of suspended
judgement the best discipline is
philosophy.
11. “The message is: That there
are known knowns, There are
things we know that we know,
There are known unknowns,
That is to say there are things
that we now know, we don't
know. But there are also
unknown unknowns, There
are things we do not know we
don't know. And each year we
discover a few more. Of those
unknown unknowns.”
22. Probability of “heads” coming up on a toss of a
fair coin is ½.
That is, when the coin is tossed many times, we
can expect “heads” to come up in
approximately one-half of tosses.
23. Expected value of game with a number of uncertain
outcomes: is the size of the prize that player will win on
average.
On a single toss of a coin, Jones pays Smith €1 (X1 = + €1) if
a tail comes up. Smith will pay Jones €1 (X2 = - €1) if a head
comes up, the expected value of a game for both players is
24. If game changes so that, from Smith’s point of view, X1 =
€10, and X2 = - €1, the expected value for Smith would be:
Because Smith would stand to win €4.50 on average, she
might be willing to pay Jones up to this amount to play.
• Fair games are games that cost precisely their expected
value.
25. When people face risky but fair situations, they
will usually choose not to participate.
Risk aversion is tendency for people to refuse
to accept fair games.
27. Utility
U
0 20 30 33 35 40 50 Income
(thousands
of euros)
28. Current €35,000 provides utility of U3.
Utility of €5,000 bet is the average of the utility of
€40,000 (if a player wins) and utility of €30,000 (if a
player loses).
Average utility is U2< U3.
The utility (U1< U2) of the €5000 bet is the average
of the utility of winning (€50,000) and losing
(€20,000).
29. Utility
U
U3
U2
U1
Income
0 20 30 33 35 40 50 (thousands
of euros)
34. Utility
U2 U
U1
Income
0 20 25 27.5 35 (thousands
of euros)
35. Utility
U2 U
U1
U0
Income
0 20 23 25 27.5 35 (thousands
of euros)
36. Some risks are so unique or difficult to
evaluate that insurers are unable to set
premium rates - risks become uninsurable.
If events are so infrequent or totally
unpredictable (such as wars, “Acts of God”
etc.) then insurers have no basis for
establishing premiums.
37. Diversification: is an economic version of “Don’t put
all your eggs in one basket.”
• Diversification spreads risk among several options
rather than choosing only one.
Suitably spreading risk may increase utility above that
obtain by a single transaction.
38. Investing in 15,000 shares of company A yields
a 50 percent chance of having €50,000 and a
50 percent chance of having €20,000.
Yields a utility level of U1.
If the person invests in 7,500 shares of each
company, they face four possible outcomes
shown in Table 5-1.
39. Utility
U
U1
Income
0 20 35 50 (thousands
of euros)
40.
41. Each of four outcomes is equally likely; with half of
cases, the investor ends up with the original
€35,000.
Diversification strategy, while it still has an expected value
of €35,000, has less risk.
Figure 5-3, point C represents when B does poorly, and D
represents when B does well.
Point E, (the average of C and D) results from
diversification, and yields utility U2 > U1.
