Asset Pricing

Asset Pricing

1. Portfolio Theory: The returns of individual stocks tend to be riskier than large, well-diversified portfolios. Markowitz, 1952

2. CAPM: Sharpe, Litner and Treynar in 1960s

   • Assumptions
     • All investors are small relative to market, price-takers
     • One period model
     • All investments are equally available, model does not include alternative investments
     • No taxes
     • No transaction costs
     • Borrowing at risk free rate
     • Homogenous assumptions - everyone has same mean-variance optimisation problem
   • CAPM in practice: How to measure
     • Forecasting Beta
       • Use historic data and run regression
         • Based on EMH: equity market determines required returns
       • Look up on Bloomberg
         • 2 year - weekly or 5 year - monthly
       • Evidence suggest that betas regress to average of 1. Blume, 1973
     • Forecasting risk free rate
       • Yield of long-term treasury bonds
       • For shorter investments, shorter maturity bonds might be more appropriate
       • No credit but default risk on t-bill
     • Forecasting market premium
       • S&P500 adequate market: Sufficient analyst covering
   • Evidence on CAPM: Testable Hypotheses
     • Only risk measured by beta affects returns
       • Historically true
       • Anomalies
         • Firm Size: Small firms generate higher returns. Banz, 1981
         • Market-to-book ratio: Small generates higher returns. Statman, 1980; Rosenberg et al, 1985
         • P/E ratio: Small generates higher returns. Basu, 1997
         • Dividend yield: high generates higher returns.
         • Momentum: Buy stock with high past-6 months returns. XXX
         • Calendar effects
         • Daniel & Titman, 1997: Portfolios of mispriced stocks
         • Either: Investors systematically ignoring profitable opportunities OR: Positive-alpha strategies contain risks not caputred by CAPM
     • Expected returns increase linearly with beta
       • Empirical SML is flatter than CAPM predicts. Black et al 1972
       • More recent estimations suggest it is flatter still. XXX
       • Securities should have zero alpha. But large variance make it impossible to say alpha categorically zero
     • Market portfolio is mean variance efficient
     • CAPM Supporters say tests are bad, rather than theory
       • Real Betas are not observed: based on historical values and delevered by today's leverage ratio
       • Expected returns are not observed: actual returns need not equal expected returns for irrational investors or concern about certain event
       • The market proxy is not correct: investors hold assets other than the ones used for CAPM, e.g. houses
       • Data snooping: given enough characteristics, we can find some that by chance are related to estimation error of regression
       • Anomalies can be explained by disaster. Gabaix, 2002
       • CAPM has never actually been tested
         • Fama & French, 2004. Use specific proxy for market portfolio, efficient from set of portfolios
         • Roll, 1970. True market portfolio cannot be measured, all hypotheses around CAPM arise from mean variance efficiency
           • Says one lacking assumption is that market portfolio must be identifiable
   • Consumption-based CAPM
     • ICAPM: Takes into account consumption over multiple periods. Merton, 1973
     • Rather than using mean-variance preferences, this links asset returns to consumption
       • Investors as consumers that optimise their portfolio against a consumption tracking portfolio
         • Risk of securities is measured with regard to covariance with aggregate consumption
           • E(Rm) - Rf = A Cov(Rm,Rc): equity risk premium is driven by A (risk aversion) and covariance of market relative to consumption-tracking portfolio (Cov(Rm,Rc) can be assumed as Var(Rc) as return on market assumed equivalent to consumption tracking portfolio
       • Investors value the flow of consumption associated with wealth
     • Equity Risk Premium Puzzle. Mehra and Prescott, 1985
       • Look at covariance of market with actual consumption
       • Disparity between returns on bonds and stock is so great that it implies an implausibly high level of investor risk aversion (approx 6% too high 1889-1978). XXX
         • Maybe covariance not correctly measured
         • Maybe actual risk aversion is higher
         • Maybe risk premium incorrect as period too short, sample size too small
         • Hypothesis: Actual returns higher than expected returns in second half of 20th century. Fama & French
           • Goetzmann & Ibbotson, 2005: Prior to 1792 only 3.66%
           • Suggestion that US is outlier, however ERP high everywhere. Mehra & Prescott, 2008
         • Survivorship bias in stock markets
         • Behavioural Finance: Irrational investor behaviour, less averse, keen to maintain attained level of consumption
           • Investors engage in narrow framing, seeing individual investment for inherent risk rather than market
       • Maybe measuring consumption wrong, e.g. extrapolation from GDP survey and smoothing
         • Savov, 2011. Garbage production as measure of consumption, manages to reduce relative risk significantly, yet small ERP remains
   • First model to specify what drives returns: BETA
   • Single-factor model

3. Arbitrage Pricing Theory: Multifactor model Ross, 1976

   • Intuition: If you have n factors, n securities can replicate any factor profile. Price of n+1st security must be determined by previous n securities. In practice # of factors << # of securities
   • E(Ri) = Rf + Summation(BETAijLAMBDAj) LAMBDA is risk premium on each factor, BETA it's sensitivity
   • No reliance on mean-variance analysis
   • Crucial Assumptions
     • Arbitrage impossible in market equilibrium
     • Securities' returns functions of (macro) factors
     • Large number of traded assets
   • Limitations
     • Lack of theoretical foundations for choice of factors
     • Have all factors been considered?
   • Self-Financing Portfolio: Going long on some, short on others, weight sums to zero
     • Small-Minus-Big: Firm size
     • High-Minus-Low: Book-to-market ratio
     • One-Year Momentum: PR1YR
     • E.g. Fama-French-Carhart model: Mkt, SMB, HML, PR1YR
       • Extensively used in event studies
       • Also used in risk measurement of actively managed mutual funds
     • Fama-French: Market Return, SMB, HML
       • Jagannathan & Wang, 2006: 4th quarter consumption, FF SMB and HML linked to consumption beta, e.g. smaller firms associated with higher betas/consumption risk

4. Excess Volatility Puzzle. Shiller, 1981: shifts in dividends and discount rates far less volatile than actual share prices and LeRoy & Porter 1981

   • Consumption is far less volatile than wealth
   • Barro, 2006: Both ERP and EVP solved by disasters
     • Defined as falls in GDP per capita > 15%, almost all OECD countries experienced one in 20th century
     • Gabaix, 2012: Suggest that disaster can also solve Daniel & Titman, 1997, anomalies
   • Shiller, 2003: Forward feedback model. Speculative prives rise, encouraging a fad until bubble
     • Bubbles tend to form if people are conditioned to expect bubbles
     • Kahneman & Tversky, 1974: Judgements are made closest to previous pattern without attention to whether new events will follow past pattern
     • Smart investors amy reinforce feedback loop to make money. De Long et al, 1990