Chapter 16 Market efficiency and active portfolio management Fan Longzhen Types of market efficiency ? The weak-form of efficiency: price accurately reflect all information that can be derived by examining market trading data such as past prices, trading volume, short interest rate, etc. ? The semi-strong form of efficiency: prices accurately reflect all public available information, including past prices, fundamental data on the firm’s product line, quality of management, balance sheet composition, patents held, earning forecasts, accounting practice, etc. ? The strong-form of efficiency: prices accurately reflect all information that is known by any one, including inside information. Some words about market efficiency ? An inefficiency ought to be an exploitable opportunity. If there is nothing investors can properly exploit in a systematic way, then it is very hard to say that information is not being properly incorporated into stock prices;--- Richard Roll ? Financial markets are efficient because they don’t allow investors to earn above-average returns without taking above-average risk---Burton Malkiel ? The efficient markets theory holds that the trading by investors in a free and competitive market drives security prices to the true “fundamental” values. The market can better assess what a stock or a bond is worth than any individual investor.---Andrei Shleifer Information arrivals and price updates ? The efficient market theory states that security prices reflect all currently available information. ? One interesting empirical question is : how does the market adjust to the arrival of new information? ? Event study methodology is one such tool to measure the economic impact of events. Paths to efficient prices ? How does information get impounded in prices? ? If gathering information is costly, can price still perfectly reflect information? ? If market prices deviate from their fundamental values, what bring them back? ? How do prices derivate from their fundamental values in the first place? Limited of arbitrage ? Arbitrage plays a critical role in the analysis of securities markets, because its effect is to bring prices to fundamental values and to keep market to efficient. ? In practice, the arbitrageurs are of capital constrained, and their effectiveness in bring prices to fundamental values is limited. Mutual fund performance ? Equity funds: on average, active managers underperform index funds when both are measured after expenses, and those that do outperform in one-period are not typically the ones who outperform in the next. ? Fixed-income funds: on average, bond funds underperform passive fixed-income indexes by an amount roughly equal to expense, and there is no evidence that past performance can predict future performance. Anomalies ? The size effects ? The value effect ? The short-term momentum ? The long-term reversal ? The new issues puzzle ? The January effect… The bottom line ? The efficient market hypothesis is a useful framework for modeling financial markets. ? Like any model, the efficient market hypothesis is not a perfect description of reality; some prices are almost certainly “wrong”. ? However, it would be na?ve to think that prices are always wrong or that it is easy to exploit pricing errors. ? Instead of asking whether or not the market is efficient, the more relevant questions are: ? ---how efficient is the market? ? ---how does the market react to new information arrivals? And why? ? ---what are the mechanisms that bring market prices to fundamental values? Event studies ? Impact of “event” on security prices: ? Earning announcement; stock split; block trade; merger ? announcement; regulatory change. ? Need a model of “normal” or “expected” returns: ? constant mean; market model; multifactor models. ? Abnormal returns=Actual-Normal ? study abnormal returns: moments ? cumulative abnormal returns ? statistical inference. ? Event analysis ? For each security: ? estimation window event window post-event window ? Three “windows” in event time ? estimation window ? event window; ? post-event window. ? Event window: pre-event period; event date; post event period. 0 T 1 T 2 T 3 T Properties of individual stocks ? In the event time: ? Are these assumptions plausible? ? For each stock ? estimate on estimation window ? form residuals for event window ? use OLS τττ βα iiii eR +Λ+= ),0(~ 2 ii Ne σ ττ Λ 0,0],cov[ ≠≠=Λ ? korjiee kji τττ nii ,...,2,1, = ii βα , lT?? l? 0 l Event study--continued ∑ ∑ ?? ??= ?? ??= ? ?? = 1 2 1 )( ))(( ? l lT mm l lT mmii i RR RRRR τ τ τ ττ β miii RR βα ? ? ?= ∑ ?? ??= ? = 1 22 ? 2 1 ? l lT ii e T τ τ σ ∑ ?? ??= = 1 1 l lT ii R T R τ τ Prediction errors or residuals llRRe miiii ,..., ? ?? * ?=??= τβα τττ define ]'?,...?,?[? * , * 1, , ** ,. lili li i eeee +? ? ≡ ]',...,[ ,1, , * ,. lili li i RRRR +? ? ≡ ]',...,[ ,1,, * ,. lmlmlmm RRRR +?? ≡ ]'1[ * ,. * m RX r ≡ ]',[ iii βαγ ≡ Event study--continued ? Properties of prediction errors: 0)] ? ([] ? []?[ ** ,. *** ,. =??=?= iiiiii XeEXREeE γγγ *')'(* ]*')' ? )( ? (* *') ? (**')' ? ([]??[ 12 12 2 ,. * ,. * ,. * ,. * ,. * ,. XXXXI XX eXXeeeEeeE ili iiii iiiiiiiiii ? + += ??+ ????= σσ γγγγ γγγγ Two parts to variance of predictor error: . Variance of disturbances . Sampling error of i γ? i γ ? Event study--continued ? Prediction error for each observation: 0]?[ * = τi eE 2 1_ 2* 2* 2 * 1*22* ) )( )(1 1( ) 1 )'](1[1(]?[ it l lTk mmk mm i m mii RR RR T R XXReE σδ σ σ τ τ ττ = ? ? ++= ? ? ? ? ? ? += ∑ ? ??= ? 21 1_ 2* ** 2** ) )( ))(( 1 (]??[ 21 2 1 ττ σ ττ ττ ≠ ? ?? += ∑ ? ??= l lTk mmk mmmm iii RR RRRR T eeE Event study--continued ? Standardized prediction error: ? disturbance variance known: ? disturbance variance unknown: ? Cumulative prediction error: ? Disturbance variance known: ? )1,0(~ ? * N e ti i δσ τ 2 * ~ ? ? ?T ti i t e δσ τ 2*'1* ,. * ,. * )1)'(*'112(]?'var[ ?'? ii i l l i XXXXlel ele σ τ τ rr ? ?= ++= = ∑ )1,0(~)1*')'(*'112/( ? ' 21* ,. NXXXXlel ii σ rr ? ++ Event study--continued ? Disturbance variance unknown: ? Can test for impact of event using and ? Null hypothesis H: ? Alternative hypothesis K: 2 21* ,. ~)1*')'(*'112/( ? ' ? ? ++= Tiii tXXXXlel σω rr τi v τi w 0][ = τi vE 0][ > τi vE Aggregation over stocks and events ? Aggregate to increase power ? Sample of stocks for which event occurred; ? Multiple events possible for any one stock. ? Aggregation method 1: ? combine standardized prediction errors ? Null hypothesis: ? Recall and appeal to asymptotic ? ? Under H, apply CLT ? τ ν i llEH n i i ,...,0][: 1 ?== ∑ = τν τ 1 ~ ?Ti t τ ν ∑∑ == ? ? ? ? = n i i i n i i T T or T T n 11 4 2 4 2 ]var[ τ ν )1,0(~ ) 4 2 ( )( 2/1 1 N T T n z a n i i ? ? = ∑ = τ τ ν ν Aggregation over stocks and events---continued ? Similarly, apply CLT to ? Can also base test on ? under the null hypothesis H: ? Define s i 'ω )1,0(~ ) 4 2 ( )( 2/1 1 N T T n z a n i i ? ? = ∑ = ω ω τ s i ' 2 τ ν 2,1 2 ~ ?Ti F τ ν )4/()2(][ 2 ??= TTE iτ ν 4 2 2 ? ? = T T ii ττ νυ 6 )3(2 ][,1][ ? ? == T T VarE ii ττ υυ )1,0(~ ) 6 3 2( )( 2/1 1 N T T n n z a n i i ? ? ? = ∑ = τ τ υ υ Aggregation method 2 ? Form portfolio in event time: ? Can relax cross-sectional independence ? Example: constant mean model. ? But then ττττττ μμ ppp n i ipiii eRR n ReR +==+= ∑ = , 1 , 1 ∑ ?? ??= = 1 1 ? l lTk pp R T τ μ () ∑ ?? ??= ? ? = 1 2 2 ? 1 1 ? l lTk ppp R T μσ τ ) 1 1(]?[,0]?[ 22** T eEeE ppp +== σ ττ Aggregation method 2 ? Which implies: )1,0(~ ) 1 1( ? 2/1 * N T e p p +σ τ 1 2/1 * ~ ) 1 1(? ? ? + T p p t T e σ τ )1,0(~ ) )12( 12( ?'1 2/1 2 * ,. N T l l e p p + ++σ r 1 2/1 2 * ,. ~ ) )12( 12( ? ? '1 ? + ++ T p p t T l l e σ r Extensions ? Relax normality; ? Relax cross-sectional independence; ? Relax temporal independence; ? Allow for heteroskedasticity; ? Allow for event-date uncertainty ? Multi-factor models ?Etc. Example 1: earning announcements ? Quarterly earnings announcements for Dow Jones 30 ? January 1988 to December 1993 ? 600 announcements; ? three pieces of data: announcement date; ? announcement earnings and expected earnings. ? Three “types” of events: ? 1. Good news: unexpected earnings>2.5%; ? 2. Bad news: unexpected earning <-2.5% ? 3. No news: -2.5%<unexpected earnings<2.5% Example 1: earning announcements-- continued ? Daily returns used; ? 250-day estimation window; ? 41-day event window. Example 2: 10b-5 damages ? Company A seeks to acquire target B: ? Investment bank C intermediates ? C-insider trades before announcement; ? A sues C for inflating price of B. ? Issues: ? Do insider trades move prices in general? ? How large are damages in particular? ? General problem: event analysis ? Example 2: 10b-5 damages--continued ? Particular damages: market model with indicator variables: ? ? How large are these effects? ? suppose insider trades on n days ? total premium including insider: ? Total premium without insider: ittitiiit eDX ++Λ+= γβα ? ? ? = 0 1 t D If insider trade on date t otherwise 0 1 00 )exp( PXPPP T t itT ?=? ∑ = 00 1 00 * ) ? exp() ? exp( PnPPnXPPP iTi T t itT ??=??=? ∑ = γγ Example 2: 10b-5 damages--continued ? Damages= ? Litton acquires Itek at $48 per share: ? insider trading period: 12 Nov. 82 to 3 Jan. 83 ? insider trading days: 14 ? 4018856 shares outstanding ? initial stock price at $28.25. ? Therefore damages= * 0 * 0 )()( TTTT PPPPPP ?=??? 24.0 2 , )36.2()79.13( )66.0( , 016.0388.1 0007.0 = +++?= Λ ? R e tt R tItektItek D 37764331)] ? 14exp(1[401885648 =??×× γ Portfolio Management: active and Passive ? A purely passive portfolio strategy: ? (1) uses only index funds ? (2) weights these funds by fixed proportions that do not vary in response to perceived market conditions. ? An active portfolio strategy: ? (1) takes advantages of security analysis in selecting stocks, ? (2) and uses factors to time the market. Market timing in an efficient market ? An efficient market is not necessarily a static market with constant risk and return; ? In general, market condition changes over time, resulting in time-varying risk and return. That is true for almost all of the major assets we are interested in; ? Quite intuitively, such a time-varying investment condition induces an optimal portfolio strategy that is also time- varying; ? In this sense, an active portfolio management does not necessarily contradict with the market efficiency. ? In fact, under changing market conditions, the most efficient way is to use all available conditioning information, including the macroeconomic variables, to identify the market condition. Using conditioning information ? In order to obtain our best estimates of market condition, we use conditioning information. ? For example, let ? Be the conditional mean and variance of the next-period stock return, using all of the public information available at time t ? Our best effort in timing the market is to look for conditioning variables that are informative about ? And form our portfolio accordingly with ? ? Where is our time-t risk aversion. )var(,)( 1 2 1 tttttt IRIRE ++ == σμ t I tt σμ , 2 tt ft t A r y σ μ ? = t A Some conditioning information on expected returns ? Default spreads: differences in yields between defaultable bonds and treasury bonds with similar maturities; ? Term premiums: differences in yields between long- and short-term treasury bonds. This is a forward-looking variable predictive of future inflation, and is found to be important in forecasting real economic activity. ? Financial ratios: book-to-market, dividend yields, etc. variables that are important in fundamental valuation. Could be proxies for systematic valuation. Could be proxies for systematic risks that are higher when times are poor, and lower when time are good. Conditioning information on volatility ? The time-varying rates of information arrival cause the price adjustment to vary over time, resulting in changing volatility. ? The time-varying volatility of the market return is related to the time-varying volatility of a variety of economic variables, including inflation, money growth, industrial production. ? Stock market volatility increase with financial leverage: a decrease in stock price causes an increase in financial leverage, causing volatility to increase; ? Investors’ sudden changes of risk attitudes, changes in market liquidity, and temporary imbalance of supply and demand could all cause market volatility to change over time. ? Where is the best place to obtain an estimate of the future volatility? Market timing and option value ? What about the value of the superior market timing ability? Take the extreme case of perfect market timing: ? What is the fair price for such an ability that cannot be achieved by using the public information ? ? Mathematically, we can obtain the same intuition by observing ? In an efficient market, the value of the superior market time ability should be consistent with the option value of derivatives. ]), ~ max[1( 1 1 f tt T t rR ? = + Π t I f t f tt f tt rrRrR 111 ) ~ (), ~ max( ? + ?? +?= The Treynor-Black model: Mix security analysis with portfolio theory ? Suppose that you find several securities that appear to be mispriced relative to the pricing model of your choice, say the CAPM. ? According to the CAPM, the expected return of any security with is ? Where is the perceived abnormal return. ? You would like to exploit the “mis-pricing” in the subset A. For this, you form a portfolio A, consisting of the “mis- priced” securities. At the same time, you believe that the rest of the universe is fairly priced. k β fmkf CAPM k rrEr ?+= )((βμ k α continued ? The rest of the portfolio allocation problem then becomes a standard one: ? The objective is that of a mean-variance investor. ? The choice of assets: ? 1. The market portfolio with and ? 2. The portfolio of “mis-priced” securities A; ? 3. The riskfree asset. M μ M σ