Crux of Research Papers

8/12/2019 Crux of Research Papers

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Sharpe (1964)

Capital Assets Prices: A Theory of Market Equilibrium under Conditions of Risk

In equilibrium, capital asset prices have adjusted so that the investor, if he follows rational

procedures (primarily diversification), is able to attain any desired point along a capital market

line.

He may obtain a higher expected rate of return on his holdings only by incurring additional risk.

In effect, the market presents him with two prices: the price of time, or the pure interest rate

(shown by the intersection of the line with the horizontal axis) and the price of risk, the

additional expected return per unit of risk borne (the reciprocal of the slope of the line).

What is Expected Value?

Bernoul li (1937)Expected values are computed by multiplying each possible gain by the number of ways in

which i t can occur, and then dividing the sum of these products by the total number of

possible cases.

The determination of the value of an item must not be based on its price but rather on the utility

it yields. Price of the item is dependent only on the thing itself and is equal for everyone but

utility on the other hand is dependent on the particular state of the person making the estimate.

If the uti li ty of each possible prof it expectation is mul tipl ied by the number of ways in which

it can occur , and we then divide the sum of these products by the total number of possible

cases, a mean uti li ty [moral expectation] wil l be obtained, and the profi t wh ich corresponds to

this utility will equal the value of the risk in question.Moreover, it sheds considerable light on the relationship between the price of an asset and the

various components of its overall risk. For these reasons it warrants consideration as a model of

the determination of capital asset prices.

The Investor's Preference Function

Assume that an individual views the outcome of any investment in probabilistic terms; that is, he

thinks of the possible results in terms of some probability distribution. In assessing the

desirability of a particular investment, however, he is willing to act on the basis of only two


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parameters of this distribution-its expected value and standard deviation. This can be represented

by a total utility function of the form:

U = f (expected future wealth, standard deviation)

Investors are assumed to prefer a higher expected future wealth to a lower value (Rationality).

Moreover, they exhibit risk-aversion, choosing an investment offering a lower value of aw to one

with a greater level. These assumptions imply that indifference curves relating expected future

wealth and standard deviation will be upward-sloping.

Investment Opportunity Curve

The model of investor behavior considers the investors as choosing from the set of investment

opportunities which maximize his utility.

In order to derive conditions for equilibrium in the capital market we invoke two assumptions. First,

we assume a common pure rate of interest, with all investors able to borrow or lend funds on

equal terms. Second, we assume homogeneity of investor expectations.

Under these assumptions, given some set of capital asset prices, each investor will view his

alternatives in the same manner

THE PRICES OF CAPITAL ASSETS

We have argued that in equilibrium there will be a simple linear relationship between the

expected return and standard deviation of return for efficient combinations of risky assets. Thus

far nothing has been said about such a relationship for individual assets. Typically the expected

Return and standard deviation values associated with single assets will lie above the capital

market line, reflecting the inefficiency of undiversified holdings. Moreover, such points may be

scattered throughout the feasible region, with no consistent relation-ship between their expected

return and total risk. However, there will be a consistent relationship between their expected

returns and what might best be called systematic risk

Efficient Capital Markets: A Review of Theory and Empirical Work

Eugene F. Fama (1970)A market in which prices always fully reflect available information is called efficient market


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Portfolio Selection

Markowitz (1952)

This paper is concerned with the second stage. We first consider the rule that the investor does

(or should) maximize discounted expected, or anticipated, returns. This rule is rejected both as a

hypothesis to explain, and as a maximum to guide investment behavior. We next consider the

rule that the investor does (or should) consider expected return a desirable thing and variance of

return an undesirable thing.

One type of rule concerning choice of portfolio is that the investor does (or should) maximize the

discounted (or capitalized) value of future returns. Since the future is not known with certainty, it

must be "expected" or "anticipated' returns which we discount. Variations of this type of rule can

be suggested. Following Hicks, we could let "anticipated" returns include an allowance for risk.

Or, we could let the rate at which we capitalize the returns from particular securities vary with

risk.

The concepts "yield" and "risk" appear frequently in financial writings. Usually if the term

"yield" were replaced by "expected yield" or "expected return," and "risk" by "variance of

return," little change of apparent meaning would result.

Variance is a well-known measure of dispersion about the expected. If instead of variance the

investor was concerned with standard error, or with the coefficient of dispersion,

An Intertemporal Capital Asset Pricing Model

Robert C. Merton (1973)

Unlike a single-period maximizer who, by definition, does not consider events beyond the

present period, the intertemporal maximizer in selecting his portfolio takes into account the

relationship between current period returns and returns that will be available in the future.


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The capital asset pricing model is a static (single-period) model although it is generally treated as

if it holds intertemporally.

It is assumed that the capital market is structured as follows.

ASSUMPTION1: All assets have limited liability.

ASSUMPTION 2: There are no transactions costs, taxes, or problems with in-divisibilities of

assets.

ASSUMPTION3: There are sufficient number of investors with comparable wealth levels so that

each investor believes that he can buy and sell as much of an asset as he wants at the market

price.

ASSUMPTION 4: The capital market is always in equilibrium (i.e., there is no trading at non-

equilibrium prices).

ASSUMPTION5: There exists an exchange market for borrowing and lending at the same rate of

interest.

ASSUMPTION6: Short-sales of all assets, with full use of the proceeds, is allowed.

ASSUMPTION 7: Trading in assets takes place continually in time.

ASSUMPTIONS1 to 6 are the standard assumptions of a perfect market, and their merits have

been discussed extensively in the literature. Although Assumption 7 is not standard, it almost

follows directly from Assumption 2. If there are no costs to transacting and assets can be

exchanged on any scale, then investors would prefer to be able to revise their portfolios at any

time (whether they actually do so or not). In reality, transactions costs and indivisibilities do

exist, and one reason given for finite trading-interval (discrete-time) models is to give implicit, if

not explicit, recognition to these costs.


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An investor making a portfolio decision which is irrevocable ("frozen") for ten years, will choose

quite differently than the one who has the option (even at a cost) to revise his portfolio daily. The

essential issue is the market structure and not investors' tastes, and for well-developed capital

markets, the time interval between successive market openings is sufficiently small to make the

continuous-time assumption a good approximation.

Unlike a single-period maximizer who, by definition, does not consider events beyond the

present period, the intertemporal maximizer in selecting his portfolio takes into account the

relationship between current period returns and returns that will be available in the future. For

example, suppose that the current return on a particular asset is negatively correlated with

changes in yields ("capitalization" rates). Then, by holding this asset, the investor expects a

higher return on the asset if, ex post, yield opportunities next period are lower than were

expected.(CAPM is ex ant model based on probability or expectations rather actual

(ex-post)

ASSUMPTION 8: The vector set of stochastic processes describing the opportunity set and its

changes, is a time-homogeneous, Markov process.

ASSUMPTION 9: Only local changes in the state variables of the process are allowed.

ASSUMPTION 10: For each asset in the opportunity set at each point in time t, the expected rate

of return per unit time.

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