Transcript Assessing Probabilities

Decision
Making
Under
Uncertainty
What’s in a decision?
Sven Roden
Unilever
Think Clearly – Act Decisively – Feel Confident
How to get senior managers interested in
decision analysis…
This is a demonstration
to illustrate all the key
fundamentals of
decision-making when
faced with uncertainty,
while still keeping it so
simple as to be
“obvious”.
Making it thoughtprovoking and
experiential
creates a high
impact event.
This example has been adapted from an exercise developed and
demonstrated by the Strategic Decision Group (www.sdg.com)
We will demonstrate the principles of
Decision Making Under Uncertainty using a
simple (but real) example
•
This is a personal investment
decision.
•
The outcome is uncertain.
•
The potential gains/losses are real.
What is the most that you are willing to invest?
Let’s create the most simple decision we can…
Decision
Uncertainty
Good
Outcome
Net Profit
Coin
Coin - £ X
Invest
–£X
Bad
Don’t Invest
Decision
0
0
Uncertainty
–£X
0
What is the value of the coin?
Ultimately, you have to work out what the coin is worth to you…
… but here is some information that may help you!
£240 to buy a 1982 minted ½ Krugerrand (based on £400 per ounce)
Source: http://www.taxfreegold.co.uk/krugerhalfdates.html
Krugerrands are legal tender in South Africa. The coin has a
face value of ~ £ 0.03. Source: http://www.reuters.com/finance/currencies
Spot price for 1 troy ounce of gold is
US$ 945
Source:http://www.ft.com/markets/commodities
The uncertainty is a simple(ish) call… do you think
the toy will end up inside or outside the circle?
Correct Call
Incorrect Call
Coin
0
You get to make the call
“inside” or “outside” after
the toy has been wound
up and allowed to run
Unfortunately, we can only offer this
investment opportunity to one person
We will sell this bond certificate to the
highest bidder…
“Random Walk” game rules
1.
The selected person plays the game once.
2.
The highest bidder will purchase the right to
play the game – no collusion between bidders.
3.
VISA
Payment is cash or cheque; no refunds.
4. I will “release” the wind up toy.
5. The person calls: “Inside the circle” or
“Outside the circle”.
NB: Should any part of the toy be touching or
outside the line, the toy is “outside the circle”.
6. If the call is correct, the person wins the coin.
7. If the call is incorrect, the person wins nothing.
8. I keep the amount paid to play, regardless of the outcome.
MasterCard
On your bid card please can you write…
Your Name
(so we can identify you!)
Your bid in £
(i.e. how much you are willing to pay for the
bond certificate)
How much the coin is worth to you
The certificate acknowledges the first
important “decision” of this session
We define a decision as an
“irrevocable” allocation of
resources with the purpose of
achieving a desired objective.
Probabilities quantify the person’s judgment
about the likelihood of winning
Correct Call
Probability = p
Probability = 1 – p
Incorrect Call
Probability is a measure of a person’s degree of belief in a
proposition based on all their previous information and
knowledge (including theoretical postulations).
The decision has now been made, so the
amount bid is a sunk cost; that’s behind us now!
Decision
Uncertainty
Correct Call
Outcome
Coin
p=
Invest
–£ Bid
1–p=
Incorrect Call
Don’t Invest
0
0
To evaluate if the decision was a good one,
we must establish a value for the deal
Deal
Decision
Uncertainty
Correct Call
Outcome
Coin
p=
Keep
1–p=
Incorrect Call
Sell
0
?
What is your minimum
selling price?
The value of the deal is the person’s minimum
selling price or “Certain Equivalent”
Deal
Uncertainty
Correct Call
Outcome
Coin
p=
Certain
Equivalent
1–p=
Incorrect Call
0
The person is indifferent between having the deal or its
Certain Equivalent.
It is important to recognise that good decisions
are not the same as good outcomes
Good Outcomes
Good Decisions
.6
.4
.7
.3
Preferred Results
What we would like!
40
–6
15
4
Balances the probabilities of
good and bad outcomes
consistent with preferences
What we need to do!
Another way to value the deal is to calculate its
“Expected Value” (probability-weighted average)
Deal
Uncertainty
Correct Call
p=
Outcome
V
(Value of coin)
Expected
Value
1–p=
Incorrect Call
0
EV = p x V + (1 – p) x 0
The Expected Value (or “mean”) is the average return
from each game if it were repeated many times.
The difference between “Expected Value”
and “Certain Equivalence” reflects attitude
towards risk
Certain Equivalents
£
EV
Risk
Averse
Risk
Neutral
Risk
Preferring
Risk Attitude
This is a matter of preference; there is no “correct” risk attitude for your
personal decisions. However, large commercial organisations would be well
advised to generally make risk neutral decisions.
Risk aversion should only become important if
the decision involves outcomes that are large
in relation to your wealth
Certain Equivalence
Risk neutral
line (CE = EV)
Snr
manager
Middle
manager
Jnr
manager
Expected Value
Risk averse people tend to risk neutrality when they feel
the stakes are small.
What is your call?
Inside the Circle?
Outside the Circle?
Several insights emerge from the demonstration
•
•
•
A decision is an irrevocable allocation of resources.
Probability is the quantitative language for
communicating about uncertainty.
Correct Call
Probability = p
Probability = 1 – p
Probabilities represent judgment, which includes
experience and information.
Incorrect Call
Certain Equivalents
€
EV
•
The value of an uncertain deal depends on its characteristics
and one’s attitude toward risk.
Risk
Averse
Risk
Neutral
Risk Attitude
•
We must distinguish between the quality of the
decision and its outcome.
•
Achieving alignment as a group is an additional challenge.
Risk
Preferring