RISK: EXPONENTIAL SMOOTHING FORECASTING AND VALUE OF INFORMATION Risk: The Value of Information Scenario: Using the same situation from the Module 3 SLP, recall that you are deciding among three investments. You have heard of an expert who has a highly re

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RISK: EXPONENTIAL SMOOTHING FORECASTING AND VALUE OF INFORMATION

Risk: The Value of Information

Scenario: Using the same situation from the Module 3 SLP, recall that you are deciding among three investments. You have heard of an expert who has a highly reliable “track record” in the correct identification of favorable vs. unfavorable market conditions. You are now considering whether to consult this “expert.” Therefore, you need to determine whether it would be worth paying the expert’s fee to get his prediction. You recognize that you need to do further analysis to determine the value of the information that the expert might provide.

In order to simplify the analysis, you have decided to look at two possible outcomes for each alternative (instead of three). You are interested in whether the market will be

Favorable

Unfavorable

, so you have collapsed the Medium and Low outcomes. Here are the three alternatives with their respective payoffs and probabilities.

Option A: Real estate development. This is a risky opportunity with the possibility of a high payoff, but also with no payoff at all. You have reviewed all of the possible data for the outcomes in the next 10 years and these are your estimates of the Net Present Value (NPV) of the payoffs and probabilities:

High/Favorable NPV: $7.5 million, Pr = 0.5

Unfavorable NPV: $2.0 million, Pr = 0.5

Option B: Retail franchise for

Just Hats

, a boutique-type store selling fashion hats for men and women. This also is a risky opportunity but less so than Option A. It has the potential for less risk of failure, but also a lower payoff. You have reviewed all of the possible data for the outcomes in the next 10 years and these are your estimates of the NPV of the payoffs and probabilities.

High/Favorable NPV: $4.5 million, Pr =

0.75

Unfavorable NPV: $2.5 million, Pr =

0.25

Option C: High Yield Municipal Bonds. This option has low risk and is assumed to be a Certainty. So there is only one outcome with probability of 1.0:

NPV: $2.25 million, Pr = 1.0

You have contacted the expert and received a letter stating his track record which you have checked out using several resources. Here is his stated track record:

True State of the Market

Expert Prediction

Favorable
Unfavorable

Predicts “Favorable”

.9
.3

Predicts “Unfavorable”

.1
.7

You realize that this situation is a bit complicated since it requires the expert to analyze and predict the state of two different markets: the real estate market and the retail hat market. You think through the issues of probabilities and how to calculate the joint probabilities of both markets going up, both going down, or one up and the other down. Based on your original estimates of success, here are your calculations of the single probabilities and joint probabilities of the markets.

Probabilities

Favorable
Unfavorable

Real Estate

0.50

B: Just Hats

0.75
0.25

Joint Probabilities

A Fav, B Fav (A+, B+)

0.375

A Unf, B Unf (A-, B-)

0.125

A Fav, B Unf (A+, B-)

0.125

A Unf, B Fav (A-, B+)

0.375

Finally, after a great deal of analysis and calculation, you have determined the Posterior probabilities of Favorable and Unfavorable Markets for the Real Estate business and the boutique hat business.

Real Estate
Just Hats
F
U
F
U

0.45

says “F/F”

0.75
0.25

0.90

0.10

0.15

says “F/U”

0.75
0.25

0.30

0.70

0.30

says “U/F”

0.125

0.875

0.90
0.10
0.10

says “U/U”

0.125
0.875
0.30
0.70

For example, this table says that there is 45% chance that the expert will predict Favorable for both markets (F/F), and when he makes this prediction, there is a 75% chance that the Real Estate market will be favorable and 25% chance that it won’t, and also a 90% chance that the Hat market will be Favorable and 10% chance it won’t.

You have developed a Decision Tree showing the original collapsed solution and also showing an expanded Decision Tree for evaluating the value of the expert’s information. You need to enter the probabilities into this tree to see if the expert’s information will increase the overall expected value of your decision. Download the Excel file with the incomplete Decision Tree: Decision Tree for BUS520 SLP 4 (see Attached)

Assignment

Complete the information in the Decision Tree in the Excel file. Determine the Expected NPV of the decision if you were to consult the Expert. Does use of the Expert increase the value of your analysis? If so, by how much?

Write a report to your private investment company and explain your analysis and your recommendation. Provide clear rationale/ justification for your decision.

Upload both your written report and Excel file with the Decision Tree analysis to the SLP 4 Dropbox.

SLP Assignment Expectations

Analysis

Accurate and complete analysis in Excel.

Required:

Length requirements: 3 pages minimum (not including Cover and Reference pages). NOTE: You must submit 3 pages of written discussion and analysis. This means that you should avoid use of tables and charts as “space fillers.”
Provide a brief introduction to/background of the problem.
Written analysis that supports Excel analysis and provides thorough discussion of assumptions, rationale, and logic used.
Complete, meaningful, and accurate recommendation(s).

Note: Please add heading for each section of the work, APA Format, Use Reference from peer-review.

4 attachments

Example

>>>

Want high value

8 8
26
26

24.2 0.6 Want avg value

0 0

																	Value Measure	U-Value
	Market Behavior
	Product choices				0				Want high value			Market behavior
						50				Expert			High value			Avg Value
			High V, High C			Says “wants high value”	0.					8			0.08
			Says “wants avg value”	0.15		0.92
					26			0.6						Want avg value
						10
		0.4
			Avg V, avg C
			24.2
											35
Consult the expert

Example (2)

Value Measure U-Value

Market Behavior

0.4 0.6
Product choices 0.4 Want high value Market behavior
50 50 Expert High value Avg Value
High V, High C Says “wants high value”

Says “wants avg value”

26 26 0.6 Want avg value

10 10 Expert

Says “wants high value”

Says “wants avg value”

0.4 Want high value

8 8

Avg V, avg C Market behavior
Expert High value Avg Value
24.2 24.2 0.6 Want avg value Says “wants high value”

35 35 Says “wants avg value”

100%

Want high value

50 50

>>> High V, High C

37.276168

45.04

Want avg value

10 10

45.04 45.04 0.876 Want high value
8 8
Avg V, avg C

11.348 0.124 Want avg value

35 35

>>>

37.276168 37.276168

Want high value

50 50

High V, High C

13.92

Want avg value

10 10

32.354 0.098 Want high value

8 8

>>> Avg V, avg C
32.354 32.354 0.902 Want avg value
35 35

85%	8%
15%	92%
38.8%	34.0%	4.8%
61.2%	6.0%	55.2%
			100.0%
Conditiional
87.6%	12.4%		100%
9.8%	90.2%
	0.876
			37.276168
			45.04			0.12
				0.3	Says “want High V
	11.348
Consider
	Consult Expert
	0.098
	13.92		0.902
0.612	Says “wants Avg V
			32.354

Practice Problem

Value Measure U-Value

25 Expert Left

0.92 0.12

0.08

23.5 0.3 Right

0.7 Left

24.5 20 20
>>>

24.5 24.5 0.3 Right

35 35

	0.7			Left	Future Behavior
			25			Right
Alternative 1			Says “Left”
Says “Right”		0.88
23.5
							20
		24.5
Alternative 2

Consult the Expert???
You do it. Then check your results.

Practice Problem-Solution

Value Measure U-Value

0.7 0.3
0.7 Left Future Behavior
25 25 Expert Left Right
Alternative 1 Says “Left” 0.92 0.12
Says “Right” 0.08 0.88

23.5 23.5 0.3 Right

20 20 Expert

Says “Left”

Says “Right”

0.7 Left 100.0%
20 20

100.0%

Alternative 2

100.0%

24.5 24.5 0.3 Right
35 35

25 25

>>> Alternative 1

27.1798

24.735

20 20

Says “Left”

24.735 24.735 0.947 Outcome 1

20 20

Alternative 2

20.795 0.053 Outcome 2

35 35
>>> Consult Expert

27.1798 27.1798

Outcome 1

25 25

Alternative 1

20.875

Outcome 2

20 20

Says “Right”

32.375 0.175 Outcome 1

20 20

>>> Alternative 2
32.375 32.375 0.825 Outcome 2

35 35

68.0%	0.644	0.036
32.0%	0.056	0.264
94.7%	5.3%
17.5%	82.5%
	0.947			Outcome 1
			27.1798
			24.735	0.053	Outcome 2
0.68
	20.795
	0.175
	20.875		0.825
0.32
			32.375

EV with Expert info is $27.18
EV w/o Expert info is $24.50
Increased value. Is it worth consulting him?

Sheet3

Deciding to use an

Expert

: the Value of Information

Wouldn’t it be nice if you could find an expert that could predict the future with

100%

accuracy? (Imagine how rich this expert would be.) All you would have to do is pay this expert and he would tell you whether the future will go one way or the other, and then you would know what to do. Your decision would be easy. But that is a fantasy. Some experts are good at predicting the future and we can find out what their track record is.

For example, suppose you are in the last stages of product development of two similar product designs, a new smart phone. One smart phone has many new advanced features but will be very costly to produce and sell with a high price. The other smart phone has only a few new features and would be considered to be only average in its value and have only an average price on the market. We need to decide which one of these two smart phone options we are going to finish and take to market, but only one. We estimate the two possible future states of the market demand: the market will generally want a High Value, High Price smart phone (Pr =

0.4

), or an Average Value, Average Price smart phone (Pr =

0.6

). This is the decision tree for this decision including the payoffs.

You know an Expert that you can consult who has a good track record of predicting the future in these situations. This is the track record:

Market behavior

Expert

High value

Avg Value

Says “wants high value”

0.85

0.08

Says “wants avg value”

0.15

0.92

When the Market actually is demanding High Value, the expert is correct (predicts “High value”)

85%

of the time, and is wrong (predicts “Avg. value)

15%

of the time. When the Market is actually demanding Avg. value, the expert is correct (predicts “Avg. value)

92%

of the time, and is wrong (predicts “High value”) 15% of the time. We can also state these using conditional probability statements:

Pr( Expert Says “wants high value” | Market demand is High value) = 85%

Pr( Expert Says “wants avg value” | Market demand is High value) = 15%

Pr( Expert Says “wants high value” | Market demand is Avg value) =

Pr( Expert Says “wants avg value” | Market demand is Avg value) = 92%

We are showing these probability statements because in a moment you will be asked to read an article that explains Bayes’ Theorem, which uses this kind of probability statements.

Here is the modified decision tree if you were to consider consulting an Expert. Note that you have not yet consulted the expert, but are only considering it.

In this scenario, with the consideration of consulting an expert, you do not know what he/she will say, and therefore these are unknown future states. He could say the market “wants High V” or “wants Avg V”. We need to determine these probabilities. And note that the probabilities of which actual future market will occur will be different depending on the expert’s prediction.

We need to use Bayes’ theorem to help us determine these new probabilities. Go to this website page which provides an easy to understand explanation of Bayes’ theorem using a medical example, testing for cancer.

http://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

Now that you have an understanding of Bayes’ Theorem and “flipping” the probabilities, here are the calculations for the smart phone example.

Market behavior

Expert

High value

Avg Value

Says “wants high value”

Says “wants avg value”

0.4	0.6
85%	8%
15%	92%

This is the expert’s track record. Multiply the probabilities (your estimates) of actual market behavior (0.4, and 0.6) down the column to get conditional probabilities.

Expert

Says “wants high value”

Says “wants avg value”

38.8%	34.0%	4.8%
61.2%	6.0%	55.2%
100.0%

Then you add across to get the probabilities of what the expert might say:

Pr(Expert Says “wants high value”) = 38.8%

Pr( Expert Says “wants avg value”) = 61.2%

And added together these equal 100%, since the expert must say one or the other.

Now calculate the conditional probabilities of the future states given what the expert says:

Market behavior

Expert

High value

Avg Value

Says “wants high value”

Says “wants avg value”

100%

Conditional
87.6%	12.4%	100%
9.8%	90.2%

For example, in the top row: 0.34 / 0.388 = 0.876, and 0.048 / 0.388 = 0.124.

Now we can enter these probabilities into the decision tree and determine what the EVM payoff is for consulting the expert. If this EVM is higher than the EVM for not consulting the expert, then there is value in the information provided by the expert.

Finally, we need to decide if the value of this information is enough for us to pay for it. If this value is more than what the expert charges, then we should consult the expert.

Watch the video to see how this is done in Excel and what the EVM is for consulting the expert.

>Orig. Collapsed Solution

-Value

avorable

7.5

>>>

.75

0.5

2 2

High/

orable

4.5

4.75
4.75 4 4

UNFAVORABLE

2.5

2.25

										Value Measure	U
							0	High/	F
				7.5
A-		Real Estate
			4	4.75	UNFAVORABLE
0.75			Fav
				4.5
B-		Just Hats
0.25
				2.5
10 year	Bond
						2.25

Expanded Solution No Probabilit

Value Measure U-Value
0.5 Favorable
7.5 7.5

>>> A-Real Estate

4.75 4.75 0.5

orable

2 2
0.75 Favorable
4.5 4.5

B-Just Hats

4 4 0.25 Unfavorable
2.5 2.5

10 year Bond

2.25 2.25
0 Favorable

7.5 7.5

Real Estate
0 0 0 Unfav

2 2

0 Favorable

4.5 4.5

Just Hats

2.25 2.25

4.75 0 0 0

4.75 2.5 2.5

Real Estate Just Hats

>>> Bond

Prediction F U F U

2.25 2.25

says “F/F”

0.750 0.250

0.30

0.900 0.100

0 Fav 0.10

0.125 0.875

0.700

7.5 7.5
Real Estate

0 0 0 Unf

2 2

0 Fav
0

4.5 4.5

Just Hats
2.25 2.25
0 0 0 Unf
2.5 2.5

>>> Bond

2.25 2.25

0 Fav

0 0 7.5 7.5

Real Estate

0 0 0 Unf
2 2

0 Fav

4.5 4.5

Just Hats
2.25 2.25
0 0 0 Unf
2.5 2.5

>>> Bond
2.25 2.25

0 Fav
7.5 7.5
Real Estate

0 0 0 Unf
2 2

0 Fav

4.5 4.5

Just Hats
2.25 2.25
0 0 0 Unf
2.5 2.5

>>> Bond
2.25 2.25

							Unf
Exp	says “F/F”
Unfav.
Posterior Probabilities of Market States
Expert’s	Prediction
Prob.
0.45		0.750		0.250		0.900		0.10
0.15	says “F/U”		0.30		0.700
says “U/F”		0.125		0.875
says “U/U”	0.300
Exp says “U/U”
Consult Expert
Exp says “F/U”
Exp says “U/F”

Use the probabilities from the Table below and fill in this decision tree. The cells that need probability values are highlighted in green.
Once you have correctly updated the d-tree with the probabilities, you will be able to see the Expected NPV of this analysis with the Expert’s predictions.
Keep in mind that you have not consulted the Expert yet, you are simply performing an analysis based on his track record and your prior estimates of the probabilities of Favorable or Unfavorable markets. You want to see if consulting this expert will provide additional value to your decision.
Be sure to write your report and include the results of this analysis. Upload your report and this Excel file to SLP4 Dropbox.

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