Northern Virginia Community College

HOW MUCH FINANCIAL RISK SHOULD YOU TAKE?

Mark D. D'Antonio

Nova Southeastern University

FORT LAUDERDALE, FLORIDA, U.S.A.

Abstract

A successful retirement investment program is subjective. Investors find the variety of choices and strategies confusing and difficult. This case helps investors to gain an understanding of diversification and asset allocation. Modern Portfolio Theory provides a base for the case study and Fuzzy Cognitive Mapping is used as a means to facilitate understanding and to empower investors to understand and reduce risks and increase returns. Students can benefit from a real case study based on decisions on asset allocation. As students work their way through complex problems, they must learn finance theory and fuzzy logic to determine intangible concepts.

KEYWORDS: Asset allocation, portfolio risk, modern portfolio theory, diversification, fuzzy cognitive map, defined benefit plan, defined contribution plan, efficient frontier, capital asset pricing model, portfolio drift, capital market line, correlation, optimization and satisficing

ASSET ALLOCATION decisions AND COMPETITIVE ADVANTAGE:

Case Study Scenario CASE OBJECTIVES

The purpose of this case is to construct a clear visual model of how individual risk factors (such as age, income etc.) contribute to a personal risk aversion profile. The case will further illustrate how the overall personal risk assessment can be mapped to a comprehensive plan to maximize return and minimize risk all within the parameters identified by individual investors. This case uses Fuzzy Cognitive Maps (FCM) with the seminal theory of Modern Portfolio Theory (MPT) [Markowitz, 1952]. The use of MPT provides the strategic purpose of optimizing an investment plan for the individual while FCMs provide a clearer understanding of causality and the methodology leading to a particular investor allocation. In conducting a case study for such an allocation, a number of financial theories are introduced and reinforced. A work group (or classroom) can take a team approach in the evaluation of various criteria of investors including demographics and investor sentiment toward risk. The team may then determine the appropriate asset allocation for each individual. The teaching objectives are:

• The evaluation of the relationship between risk and return
• The development of an understanding in regards to the determinants of asset allocation.

CASE FRAMEWORK

Since the implementation of the Individual Retirement Account (IRA) and the introduction of the many variants of retirement vehicles, such as the 401(k) and the 403(b), the individual investor has a much greater need for understanding and information.Many employment issues are affected by the changing of trends in society and their profound effects on retirement planning. Past thinking indicates the idea that employees are afforded stability and predictability on the job. An organization may employ the worker for life and implement and manage health and pension programs on the employee's behalf. Today, there is a new psychological and social contract that involves less paternalism and more self-reliance. Workers are taking more responsibility for many facets of their jobs and careers [Cascio & Aguinis 2005]. This trend has recently taken a more international direction.

This case introduces and discusses the aspect of risk and return as described by MPT. This case links the intricacies of finance theory with the asset allocation needs of the individual through the use of a FCM. Fuzzy cognitive mapping is a manner of representing causality between objects that have uncertain relationships. This causality is often represented in a percentage or by degree. Thus "fuzzy" representations can represent relationships that manifest partial causality [Kostco, 1985}. This case introduces a foundation for a more comprehensive approach to risk management and asset allocation. The case will reconcile the "fuzzy" needs of the individual with established financial theory.

THE SCENARIO

Aegis Home Inspections Inc. (AHI) is a rapidly growing small company that provides home inspection services in the Washington D.C. Metropolitan area. A recent real estate boom in the area has made business very strong and the company has aggressively added more employees and has expanded from home inspection to pest inspection. The company employs 300 inspectors and earned $18 million in revenue. Rose Wilson is the founder and President of AHI and is committed to future growth. Wilson is considering expansion into the pest treatment and home appraisal business. With such big changes in business scope AHI will need to attract and maintain a talented and well-trained workforce. Wilson is dedicated to maintaining this diverse workforce by offering a modern and competitive compensation and benefit package.

Ms. Wilson called a senior staff meeting to discuss the many changes happening in the company. She spoke to operational managers about the logistical changes and to financial managers about the finances of these changes. She also approached Mark Wolfe, Vice President of Human Resources for AHI. Wilson told Mark that a modern retirement plan would be required and that she wanted the plan to be a major attraction for prospective employees. In addition the president said that she wanted a pilot test of a defined contribution system in 30 days for the next strategy meeting. Wilson stated a number of critical success factors that she regarded as important:

• She wanted employees to be knowledgeable and involved concerning their own finances
• She wanted employee retirement assets to be properly allocated
• She wanted employees to be excited about the plan and expected it to be a means of improving organizational commitment among workers
• She wanted the plan to provide a competitive advantage for AHI in attracting talented employees
• She said he wanted the plan to be intuitive and easy to understand and inspirational to employees
• She said that she wanted employees to be well informed and to have many options regarding retirement savings
• Finally she wanted the plan to be similar to the other plans offered in the workplace today.

GETTING STARTED

After the meeting Wolfe reflected on what was being requested. He felt that the goals were noble and necessary but he was apprehensive because he was not an expert on investments or asset allocation. Wolfe genuinely wanted to help and did not want to let the boss down so he went home that Friday afternoon and thought over the weekend on how to tackle this problem. On Monday morning he started doing research on how such a savings plan could be developed. In a few hours he had learned a lot. Wolfe had used the Internet to search for general information on asset allocation and retirement savings. At this point Mark started to make a list of terms that he could refer to with a definition or explanation for each term. He planned to keep this list as a guide for himself and ultimately his employees. The final list is displayed in Appendix A.

Mark learned that in a world where the responsibility for retirement assets has shifted from the employer (defined benefit plans) to the employee (defined contribution plans) greater knowledge and proper planning for the investor is paramount and investors were often nave [McClatchey and VandenHul, 2005]. This customer driven focus for investment knowledge and information required a new need for a more profound understanding of human factors as they relate to asset allocation. Mark realized that there was a lot he did not know and he decided to take a ride to the nearby bookstore at lunch to look at some books on asset allocation.

THE BOOKSTORE

He quickly found the business section and was looking for suitable books when a small child raced past him. The child was laughing in a playful manner as if she were trying to escape from someone. A minute later Mark heard the voice of an adult calling out "Pam, where are you?" The voice sounded familiar, and when Mark heard it again he recognized his friend Gary from his MBA program 4 years ago.

The two men shook hands as the child laughed, circling and pointing at them. Gary was impressed when he heard that Mark was a vice president of AHI. Gary explained that he was an investment advisor for a large brokerage firm. Gary said that after being married he and his wife moved to North Carolina and started a family. They were back in the area to visit family and friends. After a few laughs Mark realized that he had someone in front of him that could help with his questions. The two men sat in the caf with a coffee in front of each of them while Pam nibbled at a cookie and drank her milk. Mark explained the task he had regarding the new retirement savings plan. Gary listened and nodded while Mark explained what the problem was. Finally, Gary spoke explaining that he agreed that the world had changed and that employees needed to get much more involved in their own retirement affairs. Gary said that there was a great deal of research concerning asset allocation. He stated that much research dealt with the ideas of asset correlation, risk and investment category selection focused on portfolios of assets rather than individual securities. The theory was known as Modern Portfolio Theory (MPT) [Markowitz, 1952]. Gary simplified the ideas of risk and return by stating that they were two sides of the same coin [Springett, 2004]. He said that for each degree of risk there was a maximum return. Thus the investor that has a good idea of his or her own risk tolerance could more accurately find a portfolio with an asset allocation that maximizes return for that level of risk. Gary stated that this risk/return relationship was the essence of MPT and this analysis of risk is more important than ever because of the larger role that an individual plays with defined contribution plans. Mark retorted that this was consistent with readings he had seen earlier that morning. Employers and employees had a changing social contract leading to a change in thought and a greater amount of employee participation [Stefanic, 2003]. Gary continued by explaining that since the early days of asset allocation, investors have tried to pick the right investments in the right asset classes to reap the best returns. Gary also said that much research in asset allocation found that up to 90% of gains in a portfolio are achieved not by stock selection but by keeping true to proper asset allocation [Ferri, 2006].

Mark was amazed by this and sat with his mouth open. The silence was broken by the sound of a cookie hitting the floor followed by a carton of milk. The men both found themselves mopping up milk and cookies on the caf floor while other readers stared at them over the top of books. After standing in line and purchasing a new snack for Pam Mark and Gary sat to continue their talk. Mark asked how this could be. Specifically, Mark was amazed that asset allocation was so important. He began to be relieved because this seemed so simple. Just find the right portfolio mix and invest in it. But Mark asked how this could be so. He said, "Why does a certain mix of stocks, bonds or other asset categories perform better than any category individually?" Gary attempted to explain but it was clear that Mark did not understand so Gary picked up a dry napkin from the table and started to make a sketch of the relationship between risk and return. This is shown in Figure 1 below.

FIGURE 1 - GARY'S SKETCH

Gary's illustration showed risk on the horizontal axis and return on the vertical axis. Gary explained that it illustrated two very important concepts. One was the Capital Market Line that showed the tradeoff between risk and return and the most efficient portfolio based on a risk free rate. Gary explained that Capital Market Line also showed that to earn a greater return an investor needed to increase the risk. The second concept was the efficient frontier. The efficient frontier was a line of portfolios that showed the highest return for a particular portfolio with various mixes of assets that are not perfectly correlated at a certain level of risk. Thus there were many other portfolios below the efficient frontier that did not return a risk adjusted return as high as the portfolios on the line.

Gary said that imperfect correlation between asset classes such as stocks and bonds refers to the idea that when one asset class is increasing in value (like stocks) another asset class (such as bonds) is increasing, stable or even decreasing in value. Thus when one asset class is doing well another imperfectly correlated asset class tends to perform differently. Gary indicated that the negative correlation was not perfect and even changed from time to time but that a balanced portfolio returned better risk adjusted results over time. This was because the mix of multiple asset classes had far greater return for the level of risk than any asset class did by itself. Both men heard a noise and saw Pam, arms extended, pretending to be an airplane flying around the caf with different sets of eyes looking up at her as she flew by each table. The two men laughed.

Mark pondered what Gary had said but then squinted. Gary asked what was wrong. Mark then said if this were true that the allocation would change over time then the portfolio would no longer be in balance. Gary smiled and said this was correct. He went on to say that a portfolio needed to be adjusted over time because of two factors changing. One was the need of the investor due to age or other factors and the other was portfolio drift. He called this need to periodically rebalance, dynamic portfolio reallocation.

PORTFOLIO DRIFT AND REALLOCATION

Gary pointed at the napkin with his pen and then and drew another picture similar to the first. It is shown in Figure 2.

FIGURE 2 - GARY'S SECOND SKETCH

In Figure 2 Gary added 100% portfolios at each end of the efficient frontier. Thus the risk and the return for the 100% portfolios were clearly visible on the diagram. It was also clear that on other portfolios with different percentages of stocks and bonds the risk was lower and the return was higher. Gary stated that this was a benefit of the imperfect correlation between the asset classes. Gary said an allocation of 50% stocks and 50% bonds may change to 60% and 40% after asset class values change. Since these asset classes are not perfectly correlated one can benefit by rebalancing the portfolio.

Essentially the idea of "selling high and buying low" leads to higher returns and risk is mitigated through diversification. Mark finally understood. As one asset class increased in value part of that asset class was sold off and the under performing asset class was purchased. This truly was "selling high and buying low." After all, as Gary explained, the investment world was cyclical and asset classes move in and out of favor. If an investor sticks to his or her allocation plan and periodically rebalances they can take profits on highly priced assets when selling and purchase another asset class while they are lower in value. Gary added that the interval used to do this could vary. Some investors used a time period such as every six months to adjust allocation. Other investors waited for a certain percent change in the asset classes before a reallocation.

Mark smiled as if he knew the secret to a great mystery. He nodded at Gary and Gary smiled back. Mark said that he understood how portfolio theory worked with mixtures of asset classes periodically rebalanced to take advantage of imperfect correlation and mitigation of risk. Mark then said, "Gary I understand! All I need now is the correct percentage for the asset classes for my employees." The smile disappeared from Gary's face and Mark seemed to see the folly of his statement just as quick. Gary grabbed the pen and created Table 1.

TABLE 1 - PORTFOLIO DRIFT AND DYNAMIC ASSET REALLOCATION

Dynamic asset reallocation Start - A=40%, B=40%, C=20%
Asset	Starting	Ending	Adjusted	Allocation
Class	1-Jan-06	31-Dec-06	1-Jan-07	Variance Amt
A	$88,000.00	$96,800.00	$113,520.00	-$16,720.00
B	$88,000.00	$140,800.00	$113,520.00	$27,280.00
C	$44,000.00	$46,200.00	$56,760.00	-$10,560.00
Total	$220,000.00	$283,800.00	$283,800.00

Table 1 showed a starting portfolio of three asset classes on 1 Jan 2006. It then showed a hypothetical change in the asset values in each class over a one-year period on 31 Dec 2006. The table also showed how far off the initial allocation the portfolio had drifted. The table showed the allocation values needed to be back in balance with the original allocation on 1 Jan 2007. The final column showed the variance or amount that the allocation had drifted. Gary then told mark that the allocation percentages for each asset class would be different for each employee. Mark said "Gary, I guess I forgot that each employee is different and that their allocation will also be different." Gary nodded in approval. Mark thought for a minute and turned to Gary with a sour look on his face. Gary said, "What's wrong now?"Mark then stated that he thought that he had the whole problem figured out but that there was a whole new dimension regarding allocation for each employee.

At this moment there was a loud noise and it was Pam. A moment before she was rocking back and forth on a chair next to her father when it suddenly flipped backward throwing the small child into a pile of Teddy bears just behind the table. Fortunately the child was unhurt and she quickly leaped up and picked up the chair. All eyes in the caf were again upon the child and Gary noticed this as well. Pam quickly jumped back on the chair positioning for another backward leap. Gary stood and grabbed his daughter quickly and Mark picked up the empty cups and deposited them in the trash. Gary, Mark and Pam walked out of the store and into the parking lot.

INDIVIDUAL ALLOCATION

Mark was pondering the problem of how any employee might allocate. The image of Gary's drawing was in his head and he had the crumpled napkin in his pocket. He knew that portfolios along the frontier returned the best returns for that level of risk but how did any employee determine what point on the line they should be? He asked Gary as the three walked up to a blue minivan in the parking lot. Gary opened the door and strapped Pam into a child seat. He then said that all investors are not the same. Gary stated that there were many factors that could determine the allocation of investors and that this made asset allocation a "fuzzy" problem. Gary suggested that Mark do some research on the topic and consult his employees for factors that might affect their allocation. Gary also mentioned Fuzzy Cognitive Maps (FCM). Mark remembered that he and Gary had used FCMs in their MBA strategy class to evaluate management policy decisions and he realized that a simplified version of the maps might be useful in determining something so individual as personal asset allocation. Gary and Mark shook hands and the two men exchanged business cards. Mark waved to Pam as the blue van moved away from him in the crowded parking lot.

Mark drove back to the office slowly pondering all of the progress he had made during his trip to the bookstore. He now had a good understanding of portfolio management, correlation and even rebalancing. However, he did not understand the factors that affect allocation or even what they should be. When he got back to the office he closed his door and searched the Internet for examples of factors involved in asset allocation. He was proud of his efforts because in short order he found several demographic factors that needed consideration. Mark learned that every individual had a personal risk profile that had to do with factors such as their age, gender and their own attitude towards taking risks. Mark understood that when similar classes of investors (by age, gender etc) are different in terms of personal risk aversion (individual tolerance for risk) their allocation would be different. Hence some factors that are linked to determining risk aversion for asset allocation are very clear such as age, income and net worth. Others such as special circumstances, risk aversion and outside influences can be characterized as "fuzzy." Thus asset allocation is a truly personal decision and varies between individuals. Mark realized that organizational characteristics, personal characteristics and work experience affect the degree of personal risk an individual is likely to accept in a portfolio. Thus the risk disposition of the individual is a very important consideration. Ultimately the personal preference and other factors that make up the risk profile should match the actual degree of risk in the portfolio.

OPTIMIZATION

Mark felt his head hurting from all of this thought. He realized that busy home inspectors were not likely to give all of this much thought and he would have to find a way to present this to them in a clearer and less time consuming manner. Mark knew, from his conversation with Gary, that having a focused investment strategy is one way to help mitigate the increased complexity and confusion connected with risk and return. Mark thought that perhaps fuzzy cognitive mapping could help to link understanding and strategy to execution while improving investor knowledge and focus. Mark had a page of notes in front of him from his research on asset allocation and a crumpled napkin from the bookstore. He had a reasonably good base on the seminal theory of risk and return. Mark wanted a plan that empowered his employees to optimize their portfolio based on their individual situations. He drew a little chart to remind himself of the goal that his boss mentioned. He wanted to build a retirement savings plan that was not adequate but exemplary. He wanted AHI employees to move from a mode of investment satisficing towards a more optimal configuration based on their individual parameters. Mark knew that it was not reasonable to assume that any model could precisely identify the optimal requirements of each investor. He was more concerned with moving investors away from a "one size fits all" configuration and toward a more optimal choice. He drew the following strategy diagram (Figure 3).

FIGURE 3 - AHI INVESTMENT STRATEGY

FUZZY FACTORS

It was time for Mark to commit what he learned on paper to help employees to develop an understanding of the "fuzzy" factors involved in personal risk assessment. Mark decided to draw his own fuzzy cognitive map that outlined the factors he felt were in asset allocation. He looked at the notes he had taken during his research and he began to draw boxes on a clean sheet of paper. He added more boxes and then drew lines connecting the boxes. After many crossed out boxes and misconnected lines he arrived with a diagram that he believed summarized the individual risk profile. Mark did not try to determine the nuances of causality for each of these potential factors. He simply made a diagram showing factors that had an effect on the personal risk tolerance. This Fuzzy Cognitive Map is labeled as Figure 4.

FIGURE 4 - FUZZY COGNITIVE MAP OF PERSONAL RISK PROFILE

SAMPLE EMPLOYEES

Mark then decided that perhaps the best way of determining what factors should be considered is to try a little sample employee allocation exercise. He decided to use the 10 employees that worked for him in the Human Resources department to do a quick study of how a risk profile system might work using some of the variables displayed in the fuzzy map he had drawn. First, Mark created Table 2 with imaginary names and demographics. This information would be provided to his 10 employees as an exercise on how to determine asset allocation.

TABLE 2 - EMPLOYEE DEMOGRAPHICS

Number	Name	Gender	Income	Age	Net Worth	Risk Profile
1	Mike Smith	M	$75,000.00	45	$300,000.00	High
2	Ben Johnson	M	$35,000.00	56	$400,000.00	Very High
3	Fran Klien	F	$90,000.00	44	$600,000.00	Medium
4	William Grouper	M	$85,000.00	43	$500,000.00	High
5	Mary Quinn	F	$120,000.00	40	$250,000.00	Low
6	Sam Willard	M	$25,000.00	24	$10,000.00	Low
7	Karen Queen	F	$110,000.00	54	$3,000,000.00	Medium
8	Dan Ziggler	M	$112,000.00	34	$1,500,000.00	High
9	Anna Lowe	F	$25,000.00	25	$50,000.00	Medium
10	Mike Younger	M	$102,000.00	63	$1,100,000.00	Medium
11	Sally Ringer	F	$75,000.00	34	$800,000.00	High

His research revealed that the risk profile of an individual is typically defined with the use of a questionnaire. Mark created his own risk assessment questionnaire and filled it out for himself (questionnaire shown in Appendix B). For the purpose of this test Mark filled in the risk profile cells of Table 2 with risk profiles of low, medium, high or very high. He arrived at these assignments randomly but based on his additional research Mark knew that questionnaires are often used to the risk assessment profile of an investor. A series of questions is asked that allows a respondent to indicate the amount of risk that he or she would be willing to accept. Mark determined that questionnaires could be purchased and used by AHI and the risk assessment of each employee could easily be determined.

Mark intended for his Human Resource employees to use the information in Table 2 to complete Table 3. The lower portion of Table 3 included rules that Mark wrote so that Table 3 could be completed. Mark tested Table 3 by using these rules and the information in Table 2 for the first sample employee, Mike Smith.

TABLE 3 - EMPLOYEE CATEGORIES

				Age		Risk
Number	Name	Gender	Income	Score	Net Worth	Profile
1	Mike Smith	M	Medium	30	Medium	High
2	Ben Johnson	M				Very High
3	Fran Klien	F				Medium
4	William Grouper	M				High
5	Mary Quinn	F				Low
6	Sam Willard	M				Low
7	Karen Queen	F				Medium
8	Dan Ziggler	M				High
9	Anna Lowe	F				Medium
10	Mike Younger	M				Medium
11	Sally Ringer	F				High

Rules for Table 3

If Income is < $50,000 then Income Category = Low

If Income is = or > $50,000 and < $100,000 then Income Category = Medium

If Income is equal or greater than $100,000 then Income Category = High

Age score = (Mandatory retirement age of 65 - employee age) X 1.5

See example Mike Smith (65-45) X 1.5 = 30 in Table 2

If Net worth is < $300,000 then Net worth category = Low

If Net worth is = or > $300,000 and < $1,000,000 then Net worth category = Medium

If Net worth is = or > $1,000,000 then Net worth category = High

EMPLOYEE SCORING

Mark then needed to create a table converting the categories in Table 3 into scores. He designed another similar table that converted the category information into scores. Again Mark completed the first sample employee, Mike Smith, and was pleased with his result.

Mark gave a completed Table 2 and blank copies of Table 3 and Table 4 to his ten Human Resources employees at his weekly staff meeting. He asked them to complete Tables 3 and 4 by the next weekly meeting. The Human Resource department was eager to help since they were curious about what Mark was doing and were wondering why Ms. Wilson was so interested. Before long the employees had ten identical completed copies with calculations on them for Tables 3 and 4. It seemed that Mark now had a method to determine a personal risk score based on a number of fuzzy factors. But Mark knew he had another problem. Now that he had the risk scores how could he get the correct allocation for each employee and which asset classes should he offer?

TABLE 4 - EMPLOYEE SCORING

				Age		Risk Aversion	Personal risk
Number	Name	Gender	Income	Score	Net Worth	Score	Score (sum)
1	Mike Smith	M	5	30	5	5	45
2	Ben Johnson	M
3	Fran Klien	F
4	William Grouper	M
5	Mary Quinn	F
6	Sam Willard	M
7	Karen Queen	F
8	Dan Ziggler	M
9	Anna Lowe	F
10	Mike Younger	M
11	Sally Ringer	F

Rules for Table 4

If Income is Low the point value = 0, If Income is medium the point value = 5

If Income is high the point value = 10

Copy Age score from Table 3 to Table 4 (round upward if not an integer)

If Net Worth is Low value = 0, If Net Worth is medium the point value = 5

If Net Worth is high the point value = 10

If Table 2 risk profile = Low then Risk aversion score = 20

If Table 2 risk profile = Medium then Risk aversion score = 10

If Table 2 risk profile = High then Risk aversion score = 5

If Table 2 risk profile = Very High then Risk aversion score = 0

Mark had some decisions to make. When Wilson passed Mark in the hallway she asked Mark how the project was going. Mark exclaimed, "Fine Ms. Wilson, I am researching and testing ideas on asset allocation." Ms. Wilson seemed impressed and nodded. Mark was more motivated than ever to keep moving. But he had a lot of questions. How many investments should he offer and what kind of asset classes should they be?He was troubled because he did not know what to do next.

Mark then decided to call his friend Gary again. He asked Gary, "What asset classes should I offer in the new retirement plan?" Gary laughed in a reassuring tone. He then said, "Mark, I thought you might want to talk about this so I had given it a little thought." Gary then explained that Mark should consider modeling the pilot plan of off another widely known, respected and successful plan. Gary asked Mark if he knew anyone local that he could speak to about his or her plan. Gary added, "Perhaps a teacher or Federal employee?" Mark thanked Gary again for his help and promised to meet again soon.

THE SAMPLE PLAN

Mark had an idea right away. His father in law, Steve Wilson, was a Federal employee and always bragged about how the Federal employee retirement plan was making so much money. He was quite a talker and enjoyed discussing anything. Mark knew the plan was not difficult to understand and decided to call Steve. Mark fumbled through his desk for the phone number and dialed.

Steve was a cheerful man that was pleasant to speak with and when he heard what Mark wanted to talk about he was more than happy to discuss the plan. Mark asked Steve what options the government plan offered. Steve immediately answered with five simple asset classes: money market fund, international fund, large stock index, small stock index and a bond fund. Steve said that the Human Resources department of his agency encouraged employees to study the web site to explore the differences between them and then consider their own risk tolerance before allocating their contributions into any of them. Mark was excited because this was the information he sought. He scribbled notes as he switched the phone from ear to ear being sure not to miss a word. Steve said that employees were encouraged to consider their own risk tolerance but were also given a table of suggested allocations based on their age. Steve went on to say that the mixture of the five asset classes got progressively conservative as the employee got older and closer to retirement. This was the understanding that Mark had based on his conversations with Gary and from his own research. Mark Quickly drew a small table of allocation that showed the five asset classes. This is shown in Table 5.

TABLE 5 - ALLOCATION PERCENTAGES

Percentage of Asset Classes
Money		Large	International	Small
Market	Bonds	Stocks	Stocks	Stocks	Total (%)
					100

Steve jabbered on about standard deviations and portfolio risk and the like as Mark drew his table. Finally Mark stopped Steve when he heard the term Lifecycle funds. Mark asked him to explain. Steve said that the government had introduced Lifecycle funds so that employees were relieved from the need to rebalance the portfolio as they aged or as their risk profile changed. These Lifecycle funds were simply composed of the five funds mentioned earlier and they simply changed the percentages of each based on the retirement date of the employee. Steve said he enjoyed moving his own money around too much to turn control over to the Lifecycle funds. However, Mark saw the future value in this because he knew that many employees were to busy or not interested in periodic reallocation. He would file this information away for the future plan.

Steve continued talking about "outpacing the index" and the addition of a Real Estate Investment Trust (REIT) to future government plans. Mark knew that additional asset categories could be helpful if they were not perfectly correlated with the other asset classes. For the purpose of his pilot study he would stick with the five categories Steve had shared. Mark thanked Steve for his help and said goodbye.

RISK SCORE AND ALLOCATION

Mark had only to determine how much each employee should allocate to each asset class in his imaginary retirement plan from Table 5. Mark looked at the personal risk scores from the Table 4 results he and his employees had completed. Using Table 4 and 5 and after working all afternoon Mark came up with a guide for allocation that had portfolio choices and percentages based on employee scoring. This is shown in Table 6.

TABLE 6 - ASSET ALLOCATION BASED ON RISK SCORE

Personal	Portfolio Choices (percentage)
Risk	Money		Large	International	Small	Total
Score	Market	Bonds	Stocks	Stocks	Stocks	Points %
0 to 10	65	30	5	0	0	100
11 to 20	51	37	8	2	2	100
21 to 29	43	36	11	5	5	100
30 to 39	36	34	14	8	8	100
40 to 49	28	33	17	11	11	100
50 to 59	20	32	20	14	14	100
60 to 69	12	31	23	17	17	100
70 to 79	6	27	26	20	21	100
80 to 89	2	23	28	23	24	100
90 to 100	1	16	30	26	27	100

Mark based Table 6 on a personal risk score that he could calculate based on the demographic information in earlier tables. Both Gary and Steve had also mentioned to him that other organizations based their suggested allocations on a similar figure. Mark scratched both his head and the paper numerous times. There were pieces of crumpled up paper all over the floor. He saw a few of his employees giggle as they walked by his office. Suddenly, they all straightened up. Shortly afterward Ms. Wilson came by and stuck her head into Mark's office. Wilson noticed the balled up papers on the floor and remarked, "I see things are being worked out, I will check with you later."

FINAL ALLOCATION

Table 6 enabled Mark to take the data from Table 4 earlier and create a recommended allocation plan for any employee with any score. This was exactly what he wanted. The next morning Mark sat down at his desk to put the final parts of his plan together. He took the Personal risk score from Table 4 and the portfolio choice percentages from Table 6 and created a final allocation table. This is shown as Table 7.

TABLE 7 - FINAL ALLOCATION RESULTS

Final Allocation results	Percentage of
		Money		Large	International	Small
Number	Name	Market	Bonds	Stocks	Stocks	Stocks	Total (%)
1	Mike Smith	28	33	17	11	11	100
2	Ben Johnson
3	Fran Klien
4	William Grouper
5	Mary Quinn
6	Sam Willard
7	Karen Queen
8	Dan Ziggler
9	Anna Lowe
10	Mike Younger
11	Sally Ringer

Mark used the risk aversion score for Mike Smith in Table 4 to fill in the allocation for Mike Smith in Table 7. During the weekly status meeting he explained what he had accomplished and he decided to again test the remaining allocation results by assigning each member of his department to complete Table 7 using the data they had compiled in Table 4 earlier and the allocation information in Table 6. During the meeting the following week Mark found that all of the employees had reached the same conclusions on the tables as they had earlier.

Mark knew that he was successful at designing a pilot study for the status meeting for Wilson. He was proud of his effort and he walked into the conference room with a presentation explaining the new retirement package. As he shook Wilson's hand he was sure he would be asked to move forward. He would be asked to find an appropriate firm to design and administer the plan. The preliminary research had been an education but there was much more to do.

CONCLUDING COMMENTS

Selection of an investment plan from a large and confusing list of choices can be daunting. Investors have tended to be "satisfied" with limited choices and a very low understanding of the risk/return tradeoff. Simply put, there are no absolute answers that can be "mass produced" for all investors. A "fuzzy" approach with input from a well-informed and empowered saver can potentially offer a better solution.A number of client preferences may create a number of possible allocations. Basically, under a "fuzzy" system there are a large number of variables that are very dynamic and have multiple solutions for any particular client.

Ultimately the amount of risk undertaken by an individual should vary based on a number of factors. Some of these factors are based on simple demographics such as age and gender. Other factors include more "fuzzy" criteria such as the individual risk aversion of the investor. Once a risk profile is established and a level of risk is determined the correct portfolio can be designed to achieve the best return for that level of risk. This case study is designed to identify the process of matching returns with the correct risk level with the use of fuzzy cognitive maps.

INSTRUCTIONS

1. As a group:Calculate numeric risk scores for employees using Table 2 information to calculate table 3 figures. Groups should calculate risk scores for each individual in Table 2 and complete Table 3 using Income, Age and net worth as demographic factors. Use the notes under table 3 to make calculations (Mark Smith is an example).

1. As a Group: Use completed Table 3 values and notes under Table 3 to complete Table 4 (Mark Smith is an example).

1. As a Group: Match the risk score calculated from Table 4 with the Allocations in Table 6 and use these to complete Table 7.

1. As a group: Which two employees have the most conservative portfolios (least risky)? Does this make sense for these employees? Why?

1. As a group: Which two employees have the most aggressive portfolios (most risky)? Does this make sense for these employees? Why?

APPENDIX A - DEFINITION OF TERMS

• Actual portfolio risk - The actual risk taken by the investor as a consequence of the investments selected. It is usually measured by the standard deviation or beta.
• Annuity - A sum of money that is payable at an interval (monthly, annually) agreed upon by contract between an individual and another entity.
• Asset allocation - The arrangement and weighting of asset classes in order to properly diversify the funds within an individual account.
• Asset Class- A Category of investments or assets (e.g. Stocks, real estate, bonds, cash or international stocks).Same class assets generally behave the same in markets, exhibit similar characteristics and are subject to the same regulations.
• Capital Market Line -Aline used to illustrate the rates of return forefficient portfolios depending on the risk-free rate of return and the level of risk for a particular portfolio.
• Correlation - In finance,a statistical measure of how two securities move in relation to each other. Correlations are used in advanced portfolio management.
• Defined benefit plan - A traditional pension plan that allows employees and employers to make contributions. The plan typically would provide a guaranteed benefit to each employee at retirement time. The payments of the plan are based on the years of service and grade of the retiring employee. Typically a defined benefit plan would be administered by the employer or by someone designated by the employer.
• Defined contribution plan - A plan that allows both employees and employers to contribute. A defined contribution plan has no guaranteed payout at distribution time. The individual balance of each employee can follow the employee through their career and is typically converted into an annuity at retirement time. The amount of money distributed varies according to the amount of money in the plan, actuarial data and the prevailing rates of investments available at the time of retirement.
• Dynamic Asset Reallocation - Investorsallocate their account values to a specific selection of investment alternatives that are reallocated or adjusted to reflect changing market conditions.
• Efficient Frontier- The line along the upper edge of all possible asset combinations (portfolios). The combinations on this line represent the portfolios that have the lowest risk for a given level of return. Also for a given amount of risk, the portfolio on the efficient frontier has the combination offering the best return.
• Individual risk profile - The assessment of risk that a participant can tolerate. It is generally calculated by questions answered by the participant on a questionnaire. It may also include other factors such as age and income.
• Investor - refers to an individual that participates in a retirement or savings plan
• Lifecycle fund - A fund that combines a mixture of various asset classes in a certain percentage so that the holder of the fund is properly allocated based upon a certain retirement year. The allocation automatically changes to get more conservative as retirement approaches.
• Personal Risk Profile - A measure or score of the level of risk that any individual should take. The number is based on a number of demographic factors such as age and income and it is also partially based on more fuzzy factors such as the individual aversion toward risk.
• Portfolio Drift - The phenomena that over time, the asset weightings of an investment portfolio may fall out of balance with an investor's objectives due to different appreciation levels for different asset classes.
• REIT - Real Estate Investment Trust -A security selling like a stock on exchanges and invests in real estate directly. It purchases properties or mortgages. A REIT has special tax considerations and usually offers high yields. Because of their structure they are also liquid. Finally, traditionally a REIT has not been perfectly correlated to other asset classes in the markets.

APPENDIX B - Sample Risk Aversion Questionnaire

Questionnaire - Individual Risk Profile -Please respond to the following 9 questions using the following scale.

1 - Strongly disagree 2 - Disagree 3 - Somewhat disagree 4 - No opinion

5 - Somewhat agree 6 - Agree 7 - Strongly agree

1) I am comfortable taking on high levels of risk in pursuit of higher

returns in my retirement plan over time. __________

2) If my investments declined in value 10% or more, I would move

assets to an investment that I would not expect to lose money. __________

3) I prefer that my account grow with the highest possible returns, even

though different choices may grow more consistently and at a lower rate. __________

4) In order to make some money in my account I am willing to take some risk. __________

5) I am more concerned with preserving the value of my account than in

maximizing growth. __________

6) I prefer to take a less aggressive approach to investing in my account. __________

7) In my account, choice A has the possibility for much higher gains than

Choice B. Choice A also has the possibility for much higher losses than Choice B.

I would prefer Choice B. __________

8) I am more concerned with investments that return high levels of

growth than with those that have steady income. __________

9) Seeking higher long-term returns is important to me, so I am willing

to accept substantial and dramatic short term declines in value of my account

in order to achieve my goals. __________

References

Cascio, W.F., Aguinis, H. Applied Psychology in Human Resource Management (6^th edition).

(2005, Pearson Prentice Hall).

Ferri, R. All About Asset Allocation. (2006, McGraw-Hill Companies, Inc.).

Kostco, B. Fuzzy Cognitive Maps. Baylor Business Review,1985, pp. 26-32.

Markowitz, H. Portfolio Selection. The Journal of Finance,1952, pp. 77-91.

McClatchey, C., VandenHul, S. The efficacy of optimization modeling as a retirement strategy

in the presence of estimation error. Financial Services Review, 2005, pp. 269-285.

Springett, A. The Pension Strategy. (2004, Insomniac Press).

Stefancic, A. Retirement Plan Trends: Where are we all headed? Benefits Quarterly,2003, pp. 7.

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