Risk-Free Asset, Estimating the SML

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Investment Analysis & Portfolio Management (FIN630)

Lesson # 37

ASSET PRICING MODEL Contd...

Introduction of the Risk-Free Asset:

The first assumption of CMT listed above is that investors can borrow and lend at the risk-

free rate. Although the introduction of a risk-free asset appears to be a simple step to take in

the evolution of portfolio and CMT, it is a very significant step. In-fact, it is the introduction

of a risk-free asset that allows us to develop CMT from portfolio theory.

With the introduction of risk-free asset, investors can now invest part of their wealth; in this

asset and the remainder in any of the risky portfolios in the Markowitz efficient set. Lt

allows Markowitz portfolio theory to be extended in such a way that the efficient frontier is

completely changed, which in turn leads to a general theory for pricing assets under

uncertainty.

A risk-free asset can be defined as one, with a certain-to-be-earned expected return and a

variance of return of zero. Since variance = 0, the nominal risk-free rate in each period will

be equal to its expected value. Furthermore, the covariance between the risk-free asset and

any risky asset i will be zero.

The true risk-free asset is best thought of as a Treasury Security, which has no risk of

default, with a maturity matching /the holding period of the investor. In this case, the

amount of money to be received at the end of, the holding period is known with certainty at

the beginning of the period. The Treasury bill typically is taken to be the risk-free asset, and

its rate of return is referred to here as RF.

Risk-Free Borrowing and Lending:

Assume; that the efficient frontier, has been derived by an investor. The arc AB delineates

the efficient set of portfolios of risky assets. We now introduce a risk-free asset with return

RF and σ = 0.

What if we extend this analysis to allow investors to borrow money? The investors no

longer restricted to his or, her wealth when investing in risky assets. Technically, we are

show selling the riskless asset. One way to accomplish this borrowing is to buy stocks on

margin, which has a current initial margin requirement of 50 percent. We will assume that

investors can also borrow at the risk-free rate RF. This assumption can be removed

without changing the basic arguments.

Borrowing additional investable funds and investing them together with the investor's own

wealth allows investors to seek higher, expected returns while assuming greater risk. These

borrowed funds can be used to lever the portfolio position beyond point M, the point of

tangency between the straight line emanating from RF and the efficient frontier AB.

Estimating the SML:

To implement the SML approach described here an investor needs estimates of the return on

the risk-free asset (RF), the expected return on the market index, and the beta for an

individual security. How difficult are these to obtain?

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The RF should, be the easiest of the three variables, to obtain. In estimating RF, the investor

can use as a proxy the return on Treasury bills for the coining period (e.g., a year).

Estimating the market return is more difficult, because the expected return for the market

index is not observable. Furthermore, several different market indexes could be used.

Estimates of the market return could be derived from a study of previous market returns.

Alternatively, probability estimates of market returns could be made, and the expected value

calculated. This would provide an estimate of both the expected return and the standard

deviation for the market.

Finally, it is necessary to estimate the betas for individual securities. This is a crucial part of

the CAPM estimation process. The estimates of RF and the expected return on the market

are the same for each security being evaluated. Only beta is unique, bringing together the

investor's expectations of returns for the stock with those for the market. Beta is the only

company-specific factor in the CAPM; therefore, risk is the only asset-specific forecast that

must be made in the CAPM.

Estimating Beta:

A less restrictive form of the single-index model is known as the market model. This model

is identical to the Single-index model except that the assumption of the error terms for

different securities being uncorrelated is not made.

The market model equation is the same as for the single-index model:

Ri = αi + βiRM + еi

Where;

= the return (TR) on security i

= the return (TR) on the market index:

αi

= the intercept term

βi

= the slope term

еi

= the random residual error;

The market model produces an estimate of return for any stock.

To estimate the market model, the TRs for stock i can be regressed on the corresponding

TRs, for the market index. Estimates will be obtained of αi (the constant return

on security i that is earned regardless of the level of market returns) and βi, (the slope

coefficient that indicates the expected increase in a security's return for a 1 -percent,

increase in market return). This is how the estimate of a stock's beta is often derived.

Arbitrage Pricing Theory:

An equilibrium theory of expected returns for securities involving few assumptions

about investor preferences

The CAPM is not the only model of security pricing. Another model that has received

attention is based on arbitrage pricing theory (APT) as developed by Ross and enhanced by

others. In recent years, APT has emerged as an alternative theory-of asset pricing to the

CAPM. Its appeal is that it is more general than the1 CAPM, with less restrictive

assumptions. However, like the CAPM, it has limitations, and like the CAPM, it is not the

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final word in asset pricing.

Similar to the CAPM, or any other asset-pricing model, APT posits a relationship between

expected return and risk. It does so, however, using different assumptions and procedures.

Very importantly, APT is not critically dependent on an underlying market portfolio as is

the CAPM, which predicts that only market risk influences expected returns. Instead, APT

recognizes that several types of risk may affect security returns.

APT is based on the law of one price, which states that two otherwise identical assets cannot

sell at different prices. APT assumes that asset returns are linearly related to a set of

indexes, where each index represents a factor that influences the return on an asset. Market

participants develop expectations about the sensitivities of assets to the factor. They buy and

sell securities so that, given, the law of one price, securities affected equal by the same

factors will have equal expected returns. This buying and selling is the arbitrage process,

which determines the prices of securities.

APT states that equilibrium market prices will adjust to eliminate any arbitrage

opportunities, which refer to situations where a zero investment portfolio can be

constructing that, will yield a risk-free profit. If arbitrage opportunities arise, a relatively

few investors can act to restore equilibrium.

Unlike the CAPM, APT does not assume:

A single-period investment horizon

The absence of taxes

Borrowing and lending at the rate RF

Investors select portfolios on the basis of expected return and variance

APT, like the CAPM, does assume:

Investors have homogeneous beliefs

Investors are risk-averse utility maximizers

Markets are perfect

Returns are generated by a factor model

Factor Model used to depict the behavior of security prices by identifying major factors in

the economy that affect large numbers of securities

A factor model is based on the view that there are underlying risk factor's that affect

realized and expected security returns. These risk factors represent broad economic forces

and hot company-specific characteristics, and by definition they represent the element of

surprise in the risk factor--the difference between the actual value for the factor and its

expected value.

The factors must possess three characteristics:

1. Each risk factor must have a pervasive influence on stock returns. Firm-specific

events are not APT risk factors.

2. These risk factors must influence expected return, which means they must have

nonzero prices. This issue must be determined empirically, by statistically analyzing

stock returns to see which factors pervasively affect returns.

3. At the beginning of each period, the risk factors must be unpredictable to the market

as a whole, this raises an important point. In our example above, we used in flatten

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and the economy's output as the two factors affecting portfolio returns. The rate of

inflation is not an APT risk factor, because it is at least partially predictable. In an

economy with reasonable growth where the quarterly rate of inflation has averaged 3

percent on an annual basis, we can reasonably assume that next quarter inflation rate

is not going to be 10 percent. On the other hand, unexpected inflation--the

difference between actual inflation, and expected inflation--is an APT risk factor.

By definition, it cannot be predicted, since it is unexpected.

What really matters are the deviations of the factors from their expected values. For

example, if the expected value of inflation is 5 percent and the actual rate of inflation for a

period is only 4 percent, this, 1-percent deviation will affect the actual return for the period.

Portfolio Management:

Portfolio management involves a series of decisions and actions that must be made by every

investor whether an individual or institution. Portfolios must be managed whether investors

follow a passive approach or ail active approach to selecting and holding their financial

assets. As we saw when we examined portfolio theory, the relationships among the various

investment alternatives that are held as a portfolio must be considered if an investor is to

hold an optimal portfolio, and achieve his or her investment objectives.

Portfolio management can be thought of as a process. Having the process clearly in mind is

very important, allowing investors to proceed in an orderly manner.

In this chapter, we outline the portfolio management process, making it clear that a logical

and orderly flow does exist. This process can be applied to each investor and by any

investment manager. Details may vary from client to client, but the process remains the

same.

Portfolio Management as a Process:

The portfolio management process has been described by Maginn and Tuttle in a book that

forms the basis for portfolio management as envisioned by the Association for Investment

Management and Research (AIMR), and advocated in its curriculum for the Chartered

Financial Analyst (CFA) designation. This is an important development because of its

contrast with the past, where portfolio management was treated on an ad hoc basis,

matching investors with portfolios on an individual basis. Portfolio management should be

structured so that any investment organization can carry it out in an effective and timely

manner without serious omissions.

Maginn and Tuttle emphasize that portfolio management is a process, integrating a set of

activities in a logical and orderly manner. Given the feedback loops and monitoring that is

included; the process is both continuous and systematic. It is a dynamic and flexible

concept, and extends to all portfolio investments, including real estate, gold, and other real

assets.

The portfolio management process extends to all types of investment organizations and

investment styles. In fact, Maginn and Tuttle specifically avoid advocating how the process

should be organized by money management companies or others, who should make the

decisions, and so forth. Each investment management organization, should decide for itself

how best to carry out its activities consistent with viewing portfolio management as a

process.

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Having structured portfolio management as a process, any portfolio manager can

execute the necessary decisions for an investor. The process provides a framework and a

control over the diverse activities involved, and allows every investor, an individual or

institution, to be accommodated in a systematic, orderly manner.

As outlined by Maginn and Tuttle, portfolio management is an ongoing process by

which:

1. Objectives, constraints, and preferences are identified for each investor. This leads

to the development of an explicit investment policy statement which is used to guide

the money management process.

2. Capital market expectations for the economy, industries and sectors, and individual

securities are considered arid quantified.

3. Strategies are developed arid implemented. This involves asset allocation, portfolio

optimization, and selection of securities.

4. Portfolio factors are monitored and responses are; made as investor objectives

and constraints and/or market expectations change.

5. The portfolio is rebalanced as necessary by repeating the asset allocation, portfolio

strategy, and security selection steps.

6. Portfolio performance is measured and evaluated to ensure attainment of the investor

objectives.

Individual Investors Vs Institutional Investors:

Significant differences exist among investors as to objectives, constraints, and preferences.

We are primarily interested here in the viewpoint of the individual investor, but the basic

investment management process applies to all investors, individuals, and institutions.

Furthermore, individuals are often the beneficiaries of the activities of institutional

investors, and an understanding of how institutional investors fit into the investment

management process is desirable.

A major difference between the two occurs with regard to time horizon, because

institutional investors are often thought of on a perpetual basis, but this concept has no

meaning when applied to individual investors. For individual investors, it is often useful to

think of a life-cycle approach, as people go from the beginning of their careers to

retirement. This approach is less useful for institutional investors, because they typically

maintain a relatively constant profile across time.

Kaiser has summarized the differences between individual investors and institutional

investors as follows:

1. Individuals define risk as ''losing money", whereas institutions use approach,

typically defining risk in terms of standard deviation.

2. Individuals can be characterized by their personalities, whereas for institutions, we

consider the investment characteristics of those with a beneficial interest in the

portfolios managed by the institutions.

3. Goals are a key part of what individual investing is all about, along with their assets,

whereas for institutions, we can be more precise as to their total package of assets

and liabilities.

4. Individuals have great freedom in what they can do with regard to investing whereas

institutions are subject to numerous legal and regulatory constraints.

5. Taxes often are a very important consideration for individual investors, whereas

many institutions, such as pension funds, are free of such considerations.

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The implications of all of this for the investment management process are as follows:

For individual investors: Because each individual's financial profile is different, an

investment policy for an individual investor must incorporate that investor's unique

factors. In effect, preferences are self-imposed constraints.

For institutional investors: Given the increased complexity in managing institu-

tional portfolios, it is critical to establish a well defined and effective policy. Such a

policy must clearly delineate the objectives being sought, the institutional investor's

risk tolerance, and the investment Constraints and preferences under which it must

operate.

The primary reason for establishing a long term investment policy for institutional investors

is two fold:

1. It prevents arbitrary revisions of a soundly designed investment policy.

2. It helps the portfolio manager to plan and execute on a long term basis and resist

short term pressures that could derail the plan.

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