# Investment Statistics - Value of Information

Scenario: Using the same situation from SLP 3, recall that you are deciding between three investments. You have heard of an Expert who has a "track record" of high confidence in correctly identifying when market conditions are favorable or not. You are now considering whether to consult this "expert" and if it would be worth paying his fee to get his prediction. So you are going to do further analysis to determine the value of this information that the expert might provide.

In order to simply the analysis a bit, 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 or Unfavorable, so you have collapsed the Medium and Low outcomes. Here are the three alternatives with the adjusted NPV outcome 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 of the cash flow and probabilities.

High/Favorable NPV: $5 million, Pr = 0.5

Unfavorable NPV: $1.2 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 Net Present Value of the cash flow and probabilities.

High/Favorable NPV: $3.4 million, Pr = 0.75

Unfavorable NPV: $2 million, Pr = 0.25

Note that this option requires less investment, so there is $0.2 million available, which will be invested in the same bonds as Option C. The NPV of this investment in this option (B) is $0.4 million. This has been added to NPV for the Favorable and Unfavorable outcomes of the boutique.

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: $1.5 million, Pr = 1.0

You have contacted the Expert and received a letter stating his track record which you have checked out by 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. Base on your original estimates of success, here are your calculations of the single probabilities and joint probabilities of the markets.

Probabilities Favorable Unfavorable

A: Real Estate 0.50 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 calculations, 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. SLP 4-Decision Tree.xlsx

Requirement

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 this increase the value of your analysis? By how much?

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

Expectations

Analysis

• Accurate and complete analysis in Excel.

Required:

• Length requirements = 2-3 pages minimum (not including Cover and Reference pages)

• Provide a brief introduction/ background of the problem.

• Complete and accurate Excel analysis.

• Written analysis that supports Excel analysis, and provides thorough discussion of assumptions, rationale, and logic used.

Complete, meaningful, and accurate recommendation(s).

https://brainmass.com/statistics/descriptive-statistics/investment-statistics-value-information-619038

#### Solution Preview

Hello,

Please see attached and let me know if you have any question.

Statistics - Value of Information

Introduction

There are three basic options for investment and the choice of the most prudent investment has to be based on the business sense, profitability, and ease of implementation as regards capital investment that comes with the options. In order to arrive at the most appropriate option, the involvement of expert opinion will be important to get a clearer perception of what would be the most appropriate and viable option for investment (Thorp, 2010). The three options are a real estate development investment, a retail franchise for Just Huts, and a high yield municipal bond investment.

Summary of the Investment Options

The first option, real estate development, is a risky opportunity with the possibility of a high payoff, but also with no payoff at all. The following are the critical investment attributes that define this option:

High/Favorable NPV: $5 million, Pr = 0.5

Unfavorable NPV: $1.2 million, Pr = 0.5

The second option, Retail franchise for Just Hats, a boutique store selling fashion hats for menandwomen. This also is a risky opportunity but ...

#### Solution Summary

Using the same situation from SLP 3, recall that you are deciding between three investments. You have heard of an Expert who has a "track record" of high confidence in correctly identifying when market conditions are favorable or not. You are now considering whether to consult this "expert" and if it would be worth paying his fee to get his prediction.