复旦大学：《投资学讲义》（英文版） Chapter 15 the equity market

Chapter 15 the equity market (cross-Section patterns and time-series patterns Fan longzhen

Chapter 15 the equity market (cross-section patterns and time-series patterns) Fan Longzhen

Introduction In this class we again look at the stock return data but with a very different view point Previously we examined the data through the eyes of CAPM. We had a noble intension although it didnt work very weI Now we are going to get our handsdirty", and plunge right into the data, without a formal model In particular, we will look at some well-established patterns--size, value, and momentum-that have been successful in explaining the cross-sectional stock returns

Introduction • In this class, we again look at the stock return data, but with a very different view point; • Previously, we examined the data through the “eyes” of CAPM. We had a noble intension, although it didn’t work very well; • Now we are going to get our hands “dirty”, and plunge right into the data, without a formal model; • In particular, we will look at some well-established patterns---size,value, and momentum—that have been successful in explaining the cross-sectional stock returns

Cross-section vs time-series For a publicly traded firm i, the following information can be readily obtained ---the stock price P at any time t; the cash dividend Di- paid between t-1 and t At any time t, we can calculate the realized stock return for firm i ---percentage returns R P+D -- --log-returns =In(P+ D)-In P Cross-section of stock returns: R,, i=1,2,,N Time series of stock returns: rit=12.T

Cross-section vs time-series • For a publicly traded firm i, the following information can be readily obtained: • ---the stock price at any time t; • ---the cash dividend paid between t-1 and t; • At any time t, we can calculate the realized stock return for firm i: • ---percentage returns: • ---log-returns: • Cross-section of stock returns: • Time series of stock returns: i Pt i Dt−1 i t i t i t i i t t P P D P R 1 1 − + − − = i t i t i t i rt P D P 1 = ln( + ) − ln − R i N i t , = 1,2,..., r t T i t , = 1,2

Multifactor-regressions For each asset 1, we use a multi-factor time-series regression to quantify the assets tendency to move with multiple risk factors h=a+B(-r)+/F+e2 1. Systematic factors rIsk premium M=E( E: risk premium 2=E(F) 2 idiosyncratic factors no risk premium E(e,=0 3. Factor loadings beta(i): sensitivity to market risk sensitivity to the factor ris

Multifactor-regressions • For each asset i, we use a multi-factor time-series regression to quantify the asset’s tendency to move with multiple risk factors: • 1. Systematic factors: • : risk premium • ：risk premium • 2 idiosyncratic factors: • : no risk premium • 3. Factor loadings: • beta(i): sensitivity to market risk; • : sensitivity to the factor risk. i i t t f t M i i t f t i tr − r = α + β ( r − r ) + f F + e M tr ( ) f t M t Mλ = E r − r Ft ( )t F λ = E F i t e ( ) = 0 i t E e i f

The pricing relation Given the risk premia of the systematic factors, the determinants of expected returnS: E( -r)=B 2M+f a What are the additional systematic factors?

The pricing relation • Given the risk premia of the systematic factors, the determinants of expected returns: • What are the additional systematic factors? F i M i f t i t E ( r − r ) = β λ + f λ

Size: Small or big We sort the socks by their market capitalization share price* number of shares outstanding

Size: small or big • We sort the socks by their market capitalization: share price* number of shares outstanding

Value or growth We can sort the croSs-section of stocks by their book-to-market ratios growth stocks firm with low book-to-market ratios Value stocks firms with high book-to-market ratios

Value or growth • We can sort the cross-section of stocks by their book-to-market ratios: growth stocks:firm with low book-to-market ratios; • Value stocks:firms with high book-to-market ratios

Other factors Price-to-earining ratios, The market skewness fcator ---Havey and Siddique(jF, 2000)report that systematic skewness is economicall important and commands an average risk premium of 3.6% per year

Other factors • Price-to-earining ratios, • The market skewness fcator • ---Havey and Siddique(JF,2000) report that systematic skewness is economically important and commands an average risk premium of 3.6% per year

Time-series behavior For the time -series behavior of stock returns we focus in particular on the time-varying nature of expected return and volatility We are interested in building dynamic models that explicitly incorporate conditioning information to best describe the behavior of future stock returns

Time-series behavior • For the time-series behavior of stock returns, we focus in particular on the time-varying nature of expected return and volatility; • We are interested in building dynamic models that explicitly incorporate conditioning information to best describe the behavior of future stock returns

Conditional information Let y be the price of a single family house, let X be the zipcode, X=45005235000 ·450000 X=200433 65000 E(E(YX))=E(Y)

Conditional information • Let Y be the price of a single family house, let X be the zipcode; • 450000 X=450052 35000 X=200433 65000 E ( E ( Y X )) = E ( Y )