# 101127_APT

September 15, 2017 | Author: Anton NEyaskin | Category: Capital Asset Pricing Model, Market (Economics), Financial Economics, Money, Business Economics

#### Description

Empirical Validation of APT

Lecture 12 27 November 2010

APT: a solution to CAPM shortcomings z

Actual SML is flatted than predicted by CAPM

z

Factors other than β influence stock returns: –

Size of the firm (can be

measured by market capitalization) Firm’s perspectives (can be measured by book-to-market ratio) Momentum (average stock’s return over the past six months)

APT: a reminder z z z

Factor model + absence of arbitrage = APT Returns are determined by the sensitivity to a common set of factors The expected return of a security is determined by the following equation:

E (Ri ) = R f + β 1i λ1 + β 2i λ 2 + ... + β ki λ k –

Where λk = E(RPk) – Rf (risk premium of kth factor)

Estimating the factors z

Factor analysis –

z

Using macroeconomic variables to generate factors –

z

A statistical procedure aimed at finding factorreplicating portfolios

Macro variables are proxies for the factors

Using characteristic-sorted portfolios to estimate factors –

Portfolios of securities with some common characteristic are proxies for the factors

Factor analysis: intuition z

Consider 2 stocks whose returns follow a onefactor model: – –

z

From historical data, we can obtain their variances, and covariance between returns –

z

R1 = a1 + b1F + ε1 R2 = a2 + b2F + ε2

(σ1)2, (σ2)2, σ12

Therefore, we can find the factor properties, and the sensitivities of the two stock’s returns –

b1, b2, (σF)2

Factor analysis: intuition z

Once we’ve found the sensitivities of individual securities to the risk factor, we can construct a factor-replicating portfolio RP1 – –

z

RP1 = A + F Factor risk-premium = λ1 = E(RP1) – Rf = A – Rf

The same logic can be applies to a sample of N securities whose returns are described by a (N-1) factor model

Factor analysis: pros and cons z

z

RPs found in the process of factor analysis provide the best possible explanation of the covariance between the stocks’ returns estimated from historical data

Assumes covariances do not change over time Doesn’t name the economic variables to which factors are linked

Factor analysis: empirical findings z z

Roll & Ross (1980) tried to establish the # of factors Were forced to estimate factors on small number of stocks – –

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Results: – – –

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42 groups 30securities each In 88.1% of the groups there was at least 1 factor with non-zero risk premium In 57.1% - at least 2 factors In 33% - at least 3

Conclusions: –

At least 3 factors are important for APT, but probably no more than 4

Macroeconomic variables approach z

Identify the complete set of possible factor affecting the returns: changes (unanticipated) in – – – – – –

z

Limit the # of significant factors –

z

Unemployment Inflation Interest rates spreads Oil prices Credit spreads Etc. Usually no more than 5

Find out which factors are significant –

By regressing the stocks returns on different sets of factors

Macroeconomic variables approach: pros and cons z

z

Very intuitive Names the exact factors that determine the stocks returns

Potentially important factors may be difficult to quantify (e.g., political changes) ‘Factors’ are constructed as ‘unanticipated’ changes, which might be difficult to measure Multicollinearity issues

An example z z z z

Let the only factor affecting the returns be Fint, the news on interest rates Before the FOMC meeting, the market participants expect the FED not to change the base rate: E(Fint) = 0 After the meeting, B. Bernanke announces that the interest rate is raised by 25 b.p. => Fint = 0.25 > 0 What should the sensitivities to Fint be for: – – –

Fixed income securities? Stocks? Commodities?

Macroeconomic variables approach: empirical findings z

Chen, Roll & Ross (1986) –

Important factors: z z z

Less significant factors: z z

Changes in GDP growth rate Changes in default risk premium (spread b/w YTM on AAA and BBB rated bonds) Changes in the slope of the YC (spread b/w LT and ST bonds rates) Unexpected changes in the price level (difference b/w actual and expected inflation rates) Changes in expected inflation (T-bill yield)

Unimportant: z

The return on market index, when added to the regression, could not explain the expected returns

Macroeconomic variables approach: empirical findings z

Chan, Chen & Hsieh (1985); Jagannathan & Wang (1996) –

Identified default spread and labor income as systematic factors associated with positive riskpremiums Research on explaining the small firm effect z z z

Small cap stock returns appeared to be highly correlated with changes in the spread b/w BBB and default-free bonds The spread seems to be a fairly good predictor of future market returns Betas are higher when the spread is high

Characteristic-sorted portfolios approach z

Identify the possible characteristics: – – – –

z z

Size Forward-looking indicators (B/M) Backward-looking indicators (stock’s performance during the past 6-12 months) Etc.

Group portfolios of stocks that satisfy the above characteristics Calculate the risk premiums associated with the respective characteristic (risk factor)

Characteristic-sorted portfolios approach: pros and cons z

z

The approach is based NOT on cross-correlations between individual securities, but on the correlation with some common characteristic => does not require the constant correlation assumption Uses portfolios returns, which are highly unpredictable, but observable, to calculate factor risk premiums

Relationships found in historical data are not guaranteed to have explanatory power in the future

Characteristic-sorted portfolios approach: empirical findings z

Fama & French (1993) –

Suggested a 3-factor model composed of the following three zero-cost (self-financing) portfolios: z z z

Value-weighted index portfolio (long) + T-bills (short) High book-to-market stocks (long) + low book-to-market stocks (short) Small-firm stocks (long) + large-firm stocks (long)

Estimated risk-premiums for each factor (b/w 1963 and 1994) z

5.2%; 3.2%; 5.4%

Characteristic-sorted portfolios approach: empirical findings –

Estimated the factor sensitivities for stocks in different industry groups:

Characteristic-sorted portfolios approach: empirical findings 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% 0,7

0,8

0,9

1

1,1

1,2

1,3

APT vs. CAPM – 1 z

Desired portfolio: –

z

CAPM: two-fund separation theorem states that all investors will form their desired portfolios by combining only 2 assets – the risk-free asset and the market portfolio APT: in a complete market the desired portfolio can be formed by combining the factor-replicating portfolios and the risk-free asset

Securities pricing under both theories: –

Assets with identical risk exposures must bring identical returns => otherwise arbitrage is possible

APT vs. CAPM – 2 z

Sources of risk: – –

z

CAPM: fluctuations of the market portfolio returns APT: fluctuations in various risk factors (macroeconomic, financial, political, etc.)

Assumptions: APT is less restrictive – – –

It doesn’t require investors to have homogenous expectations CAPM – a pure theoretical framework APT – a practical framework

Assumptions (APT) z z z

In equilibrium there are no arbitrage opportunities Returns of risky assets can be described by a factor model Financial markets are frictionless – –

z

No transaction costs Perfect information, etc.

There is a large number of securities => investors hold well-diversified portfolios => specific risks are diversified away; the only source of risk arises from fluctuations in factors determining the return

APT vs. CAPM: Summary z

APT solves the major problem of CAPM –

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APT doesn’t name the particular factors that should be used to determine the expected returns –

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It does not require to determine the market portfolio

As opposed to CAPM, which specifies the particular source of risk

Both models state that only systematic (nondiversifiable) risk should be rewarded

A formal link b/w CAPM and APT z

Consider a one-factor model, where F if other than the return on the market portfolio –

z

Ri = ai + biF + εi

Assuming CAPM holds, and there is some correlation (ρ) b/w F and Market portfolio, the stock’s β can be calculated as following:

ρ β i = bi 2 σM

z

The case can be extrapolated to the case of a multi-factor model

Brealey, Myers: Principles of Corporate Finance, Seventh Edition –

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Chapter 8.4

Grinblatt, Titman: Financial Markets and Corporate Strategy, Second Edition –

Chapter 6