Phoebe Martin

Chloe Bidos

Richard Hardy

Kenny Bayeroju Can the Market Portfolio be specified & tested? Definitions Methods of Specification Problems with Specification Criticisms of Specification Testing the efficiency of the market portfolio Market Portfolio: portfolio that includes all the available risky capital assets

Weights the assets by their relative market value (Levy & Post, 2005) Use proxy – Standard & Poor Stock Market Index 500 (US)

"Index funds created to approximate market portfolio" (Sigman, 2005)

Benchmarks – Fama/French

Efficient market assumption –implies that the “composition of the portfolios of every investor is the same as that of the market portfolio” (Perez, Granero, Segovia, Rambaud, 2004) Erroneous market portfolio specifications lead to false arguments of asset riskiness - due to 'failure to capture average return of investors' (Rosenberg)

Ambiguity of market portfolio makes riskiness of assets difficult to analyse (Rosenberg)

Roll, 1977 – used empirical research to analyse riskiness of assets, found dependent upon choice of portfolio & market portfolio Tests should show that ER on high beta assets are lower than the equation suggests (possibly have negative alpha’s)

Also, return on low beta assets are higher than the equation suggests (positive alpha’s)

Expected return on a security can represented by two-factor model To test the efficiency of the market portfolio we use the indexes as a proxy.

The indexes are regressed against the historical data of mutual funds, producing the table below. Testing: measuring statistical significance and efficiency of the market portfolio Specification: identifying accurately and clearly the meaning of the market portfolio & considering its theoretical and pragmatic composition Ibbotson & Fall (1979) Study:

32 years (1947-78), 5 different classes:

•Index 1 – Common Stock

•Index 2 – index 1 + fixed income corporate issues

•Index 3 – index 2 + real estate

•Index 4 – index 3 + US government issues

•Index 5 – index 4 + municipal bonds

•Index 6 – index 5 minus common stock To construct market proxies: use historical rates of return & relative market values of all relevant classes of capital market assets

BUT

May seem optimal market portfolio (Brown & Brown, 1987) but Ibbotson & Fall argued against this; there may be omitted variable bias - specification issues

Karl Sigman (2005): Market Portfolio in CAPM should be computable under an efficient market but must have symmetric stocks info

To specify/identify market portfolio – need to ‘control for selected macroeconomic fundamentals’

BUT some unobservable characteristics “The market portfolio represents the value of all the assets in the economy […that is...] the total value of the economy” (Clark & Kassimatis, 2011) "World market portfolio is the sum of all individual assets in the world" (Clark & Kassimatis, 2011) Shortcomings of world market portfolio – data constraints, difficult to construct on frequent basis "Several studies included market portfolio as an additional pricing factor alongside macroeconomic factors" (Aretz, Batram, Pope, 2005)

Use Hicks model (1987) of discounted macroeconomic cash flows to calculate the value of the economy

“International market portfolio” can be used in CAPM & Fama-French multifactor model (1998) – to explain asset returns BUT not efficient, is significant Alternative Specifications Roll, 1978 – believes that market portfolio cannot be truly estimated using CAPM, found could “never observe the true market portfolio” (Brown & Brown, 1987)

Different estimations could give exactly opposite results “Inefficient market proxy could lead to invalid inference” (Brown & Brown, 1987) CAPM The CAPM is a model that describes the relationship between risk and expected return and is used in the pricing of risky securities

CAPM:

adapt into Jensen’s performance measure:

Beta measures risk relative to the estimated market portfolio

- coefficient closest to 1, closest to true market portfolio Introduction to Specification

Definitions

Specification methods

Alternative methods of specification

Problems with Specification

CAPM

Introduction to Testing Testing the Market Indexes used in Brown & Brown paper (1989)

Testing validity of CAPM using Times series regression (Black, Jensen & Scholes, 1972)

Analysis

We assume that alpha on every asset is zero

This model does not provide an adequate description for the relationship between risk and return for securities

Mille & Scholes (1972) indicates that model does not provide a complete description of the structure of security returns In particular, alpha’s on individual assets depend in a systematic way on their beta’s:

1. High beta assets tend to have negative alpha’s

2. Low beta assets tend to have positive alpha’s Conduct time series tests instead, showing that the usual form of the model does not provide an accurate description of the structure of security returns. The results we see show that the expected excess return on an asset is not strictly proportional to beta

Enough evidence for us to reject the traditional equation Times Series Test We would prefer to use data on a large number of securities in an efficient manner instead of single securities

Grouped data solves problem

10 groups, top 10% to bottom 10%, high beta to low beta

Used 5 previous years before start and calculated the beginning beta (January 1926 to December 1930) Tests from January 1931 to January 1965. Obtaining 35 years of monthly returns on ten portfolios

Alpha’s different, Beta's different

Although some T values of alpha’s not significant Jensen’s performance measure Jensen’s performance measure is given by alpha

Measures the constant return the portfolio generates above or below the risk premium The alphas for indexes 1 and 2 are both insignificant. The alphas for indexes 3, 4 and 5 are negative and significant at the 95% level. This represents the lower expected return, which is due to the reduction in risk when real estate is added to the portfolio. The Beta values Here beta measures the risk relative to the market portfolio, so should be 1

The beta values for indexes 1 and 2 are close to 1

Evidently, Index 2 best represents the market portfolio Conclusions Questions? Testing Validity of CAPM Two-Factor Model Many different market portfolio specifications

Tested market portfolio proxy by regressing against historical data

Tested for models' statistical significance

Betas from CAPM & Times series test differ

Cannot be generically specified BUT its proxies can be tested

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# Financial Presentation - Market Portfolio

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