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Assistant for Portfolio Managers, Slides of Investment Management and Portfolio Theory

Vanderbilt University (Vandy)Investment Management and Portfolio Theory

Assistant for Portfolio Managers by. Paul R. Cohen and Mark D. Lieberman. Computer ScienceDepartment. StanfordUniversity. Stanford, California94305 ...

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Stanford

Heuristic

Programming

Project

Memo

HPP-83-4

(Working

Paper)

January,

1983

Report

FOLIO:

Expert

Assistant

for

Portfolio

Managers

Paul

Cohen

and

Mark

Lieberman

Computer

Science

Department

Stanford

University

Stanford,

California

94305

Discover Slides of Investment Management and Portfolio Theory Vanderbilt University (Vandy)

Partial preview of the text

Download Assistant for Portfolio Managers and more Slides Investment Management and Portfolio Theory in PDF only on Docsity!

Stanford Heuristic Programming Project

Memo HPP-83-4 (Working^ Paper)

January, 1983

A Report on FOLIO: An Expert

Assistant for Portfolio Managers

by

Paul R. Cohen and Mark D. Lieberman

Computer Science Department

Stanford University

Stanford, California 94305

Abstract

FOLIO is an expert system to assist portfolio managers. It interviews a client and, on the basis of

expert knowledge, (^) determines the client's investment goals and (^) the portfolio that best (^) meets them.

For example, FOLIO may determine that one client requires a preponderance of tax-free investments

and a substantial hedge (^) against rising short-term interest rates, while another (^) is best served by a mix

of low-risk dividend-oriented stocks and intermediate-term bonds. FOLIO is a test bed for a theory of

heuristic reasoning about uncertainty (Cohen (^) and Grinberg, 1983), and its task has many (^) parallels to

established Al paradigms such as diagnosis in medicine and construction of a student model in ICAI

domains (Barr and Feigenbaum, 1982). FOLIO uses a (^) goal programming algorithm (Hillier (^) and

Lieberman, 1980) as a relaxation method for resolving the client's multiple goals into a portfolio that

fits them^ optimally.^ This^ paper^ discusses the motivations for building FOLIO; its task, design, and

operation; (^) and examples (^) of its recommendations.

Motivationsfor FOLIO

Modern portfolio (^) theory (Rudd and Clasing, 1982; (^) Sharpe, (^) 1981) is currently applied by large

institutions to problems of asset allocation for large clients, such as pension funds, as well as for

small, (^) individual clients. The central idea of (^) these applications is (^) to divide up (^) the client's assets

between several funds that have different characteristics. The relevant characteristics of the client

are the client's desired risk and return; given these, an optimum allocation of assets can be found with

a quadratic programming algorithm (Sharpe, 1970). Other characteristics of the client, besides those

associated with risk and return, can (^) enter into the problem but in practice are rarely considered. (^) This

may be because it is difficult to assess these factors accurately. The client's risk tolerance is

uncertain, (^) as is his or her tax status, (^) asset structure, and investment (^) goals. The information provided

by the client is often incomplete and inaccurate, and sometimes it is even contradictory. Thus, no

matter how^ sophisticated^ an^ asset allocation algorithm is, its recommendations are subject to the

same suspicion as the data on which they are based. Garbage in, garbage out.

Our goal in the FOLIO project has been (^) to develop an asset allocation program that is sensitive (^) to

the uncertainty implicit in client' data. Our research takes two paths: first, our work on an expert

system to interview a client and recommend a portfolio and, second, our development of a theory of

endorsers, (^) (Cohen and Grinberg, (^) 1983) to facilitate reasoning about the uncertainty that arises during

the interview. This paper discusses the expert system research.

We will digress briefly to discuss the theory of endorsers. The theory includes a representation of

states of certainty that supports sophisticated reasoning about uncertainty, and a body of heuristic

Dividend- oriented,^ lower risk (^) stocks
Growth-and-yield, lower (^) risk stocks
Growth-and-yield, (^) higher risk stocks
Commodity-sensitive,^ lower risk stocks
Commodity-sensitive,^ higher risk stocks
A mixture of maturities of (^) governmentand corporate bonds
A mixture of maturities of (^) municipal bonds
Discount bonds
Money-market funds (^) and other cash-equivalents

Figure 1 : The classes of securities used by FOLIO

securities, FOLIO requires only aggregate knowledge about the properties of the securities in each

fund; for example, it (^) knows the average riskiness and (^) rate of (^) return for the entire fund, (^) not for

individual securities within it. This has three important consequences. First, the program need not

know thousands of (^) stocks and bonds individually and intimately. Second, since (^) aggregate figures change more slowly (^) than those for individual securities, (^) FOLIO (^) can be kept current without

perpetually changing parameter values for large numbers of securities. Third, the responsibility for

security analysis rests with the investment advisor, not with FOLIO. This is consistent with the

investment philosophy of FOLIO'S consulting expert,^1 who holds that proper diversification over

securities within a class is less risky (preferable) to holding too few securities. The choice of which

securities to hold, say, from the class of high risk growth stocks, is judged to be less important than

the choice of that class for a client.

The Structure of (^) FOLIO FOLIO has three main components: a (^) set of (^) interview functions, a forward-chaining (^) production

system for inferring the client's goals, and a goal programming algorithm to maximize the fit of the

client's portfolio (^) to his (^) goals. The interview functions are very (^) simple, distinguished only by an editor

to allow the client to change his answers. It was decided that, since most clients are asked the same

questions, each should be asked all the questions at the beginning of the consultation. No effort has

been made to ask questions on a goal-directed, "as-needed" basis. After questions are answered,

and the answers edited, FOLIO derives several dozen numerical parameters and infers the client's

goals. But we defer (^) discussion of this stage (^) until we have described (^) what we mean by client goals

and how they are satisfied.

Mark Lieberman

Maximizingthe Fit to the Client's Goals

FOLIO uses a goal (^) programming algorithm to maximize the fit of a portfolio (^) to the goals (^) that the portfolio is (^) supposed to satisfy. Goal (^) programming is a kind of linear (^) programming in which the

objective function is made up of terms describing the deviations from the target values of each goal.

The (^) result is a solution that minimizes the (^) summed deviation from all the goals.

Fourteen goals, listed in Figure 2, received much discussion. Each goal is represented by five

parameters: a target value that is more desirable than any other; a penalty for exceeding the target

value, which is a monotonically nondecreasing function of the difference between the target value

and the actual value;^ a similar penalty for falling short of the target value; a lower bound, below which

the penalty becomes infinite; and (^) an upper bound, (^) above which (^) the penalty becomes infinite. These parameters are (^) described by four linear constraints on (^) each goal:

Where F. (^) is a (^) number that indicates whether (^) and to what extent fund i satisfies a given (^) goal, in this

case, gl.

Assuming that lowerbound B target B upperbound (which is always the case), if a

portfolio could be found such that diff" and diff +^ were equal to zero for every goal, that portfolio

would be a perfect fit to its goals. This rarely happens, however, so, instead, one might try to find a

portfolio that (^) minimizes the sum of cliff +^ and diff" for all goals g. In fact, (^) an additional

embellishment allows us to emphasize some goals over others: 2 We can multiply diff +^ and/or diff"

by a number that indicates the importance of achieving goalg, and try to minimize the following sum:

In fact, p+^ gj and p~^ gj are just the respective penalties for exceeding and falling short of the target

value for goal i. Equation 2 is minimized with a modified, two-phase simplex algorithm (Hillier and

Lieberman, 1980; Dantzig, 1963). Parts of the algorithm are written in Franz Lisp (FOLIO'S "native

language"), although the array pivoting procedures are Pascal "foreign functions." The algorithm

(^2) We (^) are grateful to (^) Professor William F. Sharpe, of (^) Stanford University, (^) for suggesting (^) this model for FOLIO

F 1 +F 2 +... +F g F lowerbound .j (1)

F 1 +F 2 +... +Fg B upperbound

F 1 + F 2+ ... +Fg F targetgl -difr g

F 1 + F 2+ ... + Fg B targetg1 + diff +g

<diff^ +^9 1 P^ V +^ < difr^ gi ^ P"fl ,)^ +■■^ ■^ +^ (difrgl4 " p-^ gu)^ (2)

Heuristic Rules^ for^ Inferring^ Goals FOLIO infers a client's (^) goals with heuristic rules. These are (^) represented in MRS (Genesereth and

Smith, 1982), a predicate-calculus-like language that allows for multiple ways to store and infer

propositions. MRS also has some default inference methods,^ such as forward- and backward-

chaining; and FOLIO uses the former. Figure 3 shows some examples of these rules inexpertly

translated into English.

In general, the conditions of (^) FOLIO's rules (^) test some aspect of the client's (^) assets structure, (^) risk status, or (^) tax bracket. Most conclusions specify one or more goal (^) statements. One of the rules in

Figure 3 has no conditions. FOLIO has eight such rules. Six of the rules set the target values for each

of six hedges to the maximum, one sets the target value for total rate of return to the maximum, and

one ensures that every client gets at least enough interest income to exploit the dividend-exclusion

clause in the federal income (^) tax.

The first of the rules in Figure 3 asks whether (^) the client needs a chunk of cash in less (^) than a year. If

so, it is the judgment of FOLIO's consulting expert that the necessary sum should be invested in a

fund that preserves capital (in practice, a money market fund). Note that, because a lower bound is

set in^ this^ example, the program will try (^) to guarantee that (^) at least (^) the needed amount is invested in

the client (^) needs a (^) relatively large sum of money in less than a year, THEN (^) set the lower bound for (^) the goal of "preserve capital" (^) to produce the needed (^) amount.

IF the client needs a relatively large sum of money in more than a year and

the client's risk-to-interest measure is greater than or (^) equal to 2.0, THEN (^) set the target (^) value for "dividends" to produce part of the needed (^) amount and set the^ target value for "interest" (^) to produce the (^) rest.

IF the client's (^) tax bracket is over 30%,

THEN set the upper bound on "interest" to produce the minimum needed income an<

set the (^) target value on "interest" (^) to zero.

ALWAYS (^) set the target (^) value on hedges against inflation (^) to its maximum.

IF a client is on a fixed (^) income THEN (^) set the penalty for (^) not achieving (^) the maximum hedge against inflation to be 500 Figu (^) re 3: A few of FOLIO's heuristic rules for inferring (^) goals

money market funds. 3 This rule is thus quite conservative: The client is virtually guaranteed that the

necessary amount of money will be protected against capital losses. The next rule is less conservative

and is not used unless the client is willing to accept some risk. It says that, if the sum in question is

needed in more than a year and the client is moderately risk tolerant, then some of the assets should

produce dividends, and the rest should produce income. FOLIO uses a simple method (not illustrated

in the English translation of the rule) (^) to determine (^) how much of each should be (^) produced: In this

case, the amount of assets that should be invested in dividend-producing positions should be

proportional to the client's tolerance of risk to principal. If the client will tolerate a lot of risk, then most

of the chunk of money that was mentioned in (^) the condition of the rule (^) will be (^) invested in stocks. If the

client is intolerant to risk, most of the money will be invested in bonds.

The third rule captures (^) the concept (^) that a person's portfolio should not generate (^) more interest than he (or she) (^) needs. Interest is taxed at income-tax rates, while (^) capital gains are taxed more favorably, thus, (^) the portfolio of a client in a (^) tax bracket (^) over 30% must never produce more (^) interest than is absolutely necessary, and should ideally (^) produce very little interest. (^) This is an appropriate time to

mention that FOLIO works with several different accounts simultaneously, if the client has more than

one (^) account. FOLIO (^) would recommend that a client's (^) portfolio produce interest in the (^) account that is

taxed the least;^ indeed, it encourages the client by its recommendations to seek as much interest as

possible in tax-free (^) and tax-deferred accounts. By similar reasoning, FOLIO (^) likes (^) to buy preferred or dividend-producing (^) stocks with the (^) assets in a corporate account, (^) to take advantage of the fact that U.S. corporate^ accounts only pay (^) tax on 15% of the dividends (^) they receive from (^) other corporations.

The fifth rule notes that a client on a fixed income is in special need of hedges against inflation. The

penalty for failing to achieve the maximum (^) possible is quite stiff.

The current version of FOLIO uses about 55 of these rules to infer one or more of the five

parameters of each of (^14) goals. Many rules conclude about all five parameters (^) of a goal. It is possible to have^ multiple^ values for a goal parameter; for example, the target (^) value for the "preserve-capital"

goal might be set to both 2.0% and 7.0% by different inference rules. Currently, such conflicts are

resolved by some 20 heuristic rules; for example, if there are multiple values for p +^ for a goal, the

(^3) In practice, (^) if contradictory (^) bounds are (^) set, the linear programming algorithm will (^) be unable to (^) find a feasible solution. For example, if we require (^) that 80% of a (^) client's assets produce (^) tax-free (^) interest, and (^) 60% producecapital gains, and (^) 40% produce taxable interest, the LP will (^) blow up^ because (^) 180% of the (^) client's assets are being (^) required (^) for three mutually (^) exclusive goals. Of course, it is perfectly^ permissible to want (^) 80% of the assets to produce (^) dividends and (^) 80% to produce capital gains, (^) because these aren't^ mutually^ exclusive.^ In^ general,^ FOLIO's rules (^) set target values and penalty (^) functions instead of (^) bounds to (^) avoid the problems (^) inherent in setting (^) inflexible bounds.

Dantzig, G.^ B. 1963 Linear programming (^) and extensions. Princeton University Press.

Princeton, NJ.

Duda, R. 0., Hart, P. E., and Nilsson, N. 1976. Subjective Bayesian Methods for Rule-Based

Inference Systems. Technical Note 124. Artificial Intelligence (^) Center, SRI International.

Genesereth, (^) M. R. and Smith, D. E. 1982. Meta-Level Architecture. (^) HPP Report 81-6. Department of Computer (^) Science. Stanford University. Stanford, CA.

Hillier, F. S., and Lieberman, G. J. 1980. Introduction to Operations Research. San Francisco,

CA.: Holden-Day, Inc.

Rudd, A. and Clasing, H. J. 1982. Modern Portfolio Theory. Homewood, Illinois: Dow Jones-Irwin.

Sharpe, (^) W. F. 1970. Portfolio theory and capital markets. New (^) York: McGraw-Hill

Sharpe, W. F. (^) 1981. Investments. (^) Englewood Cliffs, NJ.: Prentice-Hall.

Shortliffe, E. H. and Buchanan, B. G. 1975. A model of inexact reasoning in medicine

Mathematical Biosciences 23,^ 351-

f IX

List of^ Figures Figure 1: The classes of securities (^) used by FOLIO (^2) Figure 2: The goals that FOLIO (^) considers for each client (^4)