“…it should be understood that forecasts have no
intrinsic value. They acquire value through their
ability to influence the decisions made by users of
the forecasts.”
Allan H. Murphy, 1993
“What is a Good Forecast? An Essay on the
Nature of Goodness in Weather Forecasting”
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MBA elective - Models for Strategic Planning - Session 7
The Value of Information
Essential ideas
Information must influence your decisions to have any value
Value of Information = the increase in Expected Value from
having information over not having it
Real information is often incomplete, unreliable:
‘Perfect Information’ provides an upper bound on information value
Value of Information determines an optimal information search,
rather than a perpetual plea that “more research is needed”
Real Options share close similitude with Perfect Information:
both derive their value from avoiding the downside,
or capitalizing on the upside, of a risk
© 2009 Ph. Delquié
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• Information Any piece of knowledge liable to alter your beliefs
about the uncertainties you are facing
Ex: forecasts; experts’ opinions; results of market studies, surveys,...
• Reliability of information
- Real information is less than perfectly reliable:
Prob[ X happens given Information predicts so ] < 100%
Forecasts contain error; Survey results inaccurate; Experts fallible1
- However, not always possible to assess reliability of information
- Thus, introduce the concept of “Perfect” information
• Perfect information
- Predicts outcomes with 100% reliability
- The value of perfect information will provide an upper bound
on the value of any information
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Example: Marketing Strategy (from Exercise Set)
The management of a motion picture studio has determined the following payoff
table for marketing choices for a new film (the amounts are in millions of dollars):
Box Office
Result
Distribute as
‘A’ Feature
Distribute as
‘B’ Feature
Sell to
TV network
Success
25
15
5
Failure
-10
-5
5
The probability that this new production will be a hit has been judged initially at 30%. The
studio is considering to obtain a pre-release forecast based on various studies (such as a
series of sneak previews, or opinion markets, e.g., www.hsx.com) before deciding how to
market the new film. Historically, it has been found that favorable forecasts have been
obtained for 70% of all successful films, while unfavorable forecasts have resulted from
80% of the box office failures subjected to such experimentation.
a) Build a decision tree model to analyze this problem.
b) What probabilities should be assigned to box office success, if the sneak preview is
favorable? If the sneak preview is unfavorable?
c) If a sneak preview results in a net cost of $500,000, would you recommend it be taken?
(Assume that choices are based on expected values.)
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Calculations – Value of Perfect Information
Decision with Perfect Information
Decision without information
Decision
Uncertainty
Suppose a “Clairvoyant” could foretell
the outcome with 100% reliability1
Perfect
Information
Payoff
Information Message
Decision given Information
0.3
Box-office Success
25
25
Distribute as A feature
0.3
1Box-office Success!
EV = 0.5
0.7
Box-office Flop
Distribute as B feature
1
-10
Sell to TV network
Clairvoyant
affirms1
15
5
11
Distribute as B feature
EV =
15
25
0.3
Box-office Success
3
Payoff
Distribute as A feature
Distribute as A feature
-10
1
0.7
Box-office Flop
0.7
1Box-office Flop!
Distribute as B feature
-5
3
-5
5
Sell to TV network
Sell to TV network
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EV =
5
5
EV without information = $5M
≤
EV with perfect information = $11M
Expected Value of Perfect Information (EVPI) = ∆EV = 11 – 5 = $6M
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Calculating the Expected Value of Perfect Information (EVPI)
1. Draw the tree of Perfect Information messages + their
subsequent decisions
2. Calculate EV of above tree: that’s EV with Perfect Information
3. Calculate increase in EV due to perfect information:
EVPI = EV with (costless) Perfect Info − best EV without info
Perfect Information is, by definition, the highest quality information,
therefore EVPI provides an upper limit on the value of any information
about the uncertainty at hand.
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Calculating EVPI (cont’d)
In a decision tree, obtaining Perfect Information amounts to
inverting the decision–chance sequence:
without PI
with PI
Decide, then find out
Find out, then decide
→
EV without information
≤
EV with perfect information
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Calculating the Expected Value of Imperfect Information (EVII)
•
EVII defined similarly as EVPI:
EVII = EV with (costless) Imperfect Info − best EV without the Info
•
Notes:
- Cost of Imperfect Info is not included in calculating EVII.
- EVPI ≥ EVII ≥ 0
•
(always!)
Information is worth acquiring if its value exceeds its cost,
that is, if: EVII > Cost of Information
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Calculations – Value of Imperfect Information
Im perfect
Inform ation
Inform ation Message
Decision given Inform ation
Uncertainty
Payoff
0.60
Box-office Success
25
Distribute as 'A' feature
11
0.40
Box-office Flop
-10
0.60
Box-office Success
0.35
Favorable
15
1
Distribute as 'B' feature
11.00
7
0.40
Box-office Flop
-5
Sell to TV network
5
Run Sneak Previews
5
0.14
Box-office Success
7.10
25
Distribute as 'A' feature
EV with imperfect
information =
$7.10M
-5.15
0.86
Box-office Flop
-10
0.14
Box-office Success
0.65
Unfavorable
15
3
Distribute as 'B' feature
5.00
-2.23
0.86
Box-office Flop
-5
Sell to TV network
5
5
Expected Value of Imperfect Information (EVII) = 7.10 – 5 = $2.10M < EVPI
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Practical interest of EVPI
•
Provides a quick upper bound estimate on whether
real information may be worth acquiring
•
No need to know actual information reliability
to calculate EVPI
•
When facing multiple uncertainties, EVPI may help prioritize
which ones are most worthy of further research
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To do for next session(
Review Solution Set 7
To be posted on website shortly
Prepare Exercise Set 8
Topic: Risk preferences
Exercise 8.1: may be a bit tricky, take a look but don’t spend time
(will be revisited in Session 10)
Case “Measuring Your Risk Attitude”:
- the ASSESS program can be installed on your PC
- Measure your risk tolerance using both the CE method and PE
method. No need to turn in a report, just be prepared to show
and debrief the findings from your experiment
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