Investments Hoorcollege 1. Refresher slides: Basic terms investment portfolio: collection of investment assets Securities: invest in specific items across different asset classes, e.g. deposits, bonds, shares risk-return trade off: determines choice of securities: how risk averse are you? Formula: Realized return( Dividend yield + Capital gain rate): the return that actually occurs over a particular time period Dividend Yield= Capital Gain rate= Average annual return: Rt= the realized return of a security of a security in year t, for the years 1 trough T Variance and Volatility of Returns: Common risk: -Risk that is perfectly correlated -Risk that affects all securities Independent risk: -Risk that is uncorrelated -Risk that affects a particular security Diversification -the averaging out of independent risks in a large portfolio Risk premium: risk premium with diversifiable risk is zero Risk premium of security is determined by its systematic risk and does not depend on its diversifiable risk Portfolio: -efficient: portfolio with only systematic risk. There is now way to reduce the volatility of the portfolio without lowering its expected return -Market: An efficient portfolio that contains all shares and securities in the market Expected return of a portfolio: X= the weight of the securities in the portfolio. Risk in a Portfolio: - combining stocks follows in a reduce risk trough diversification -the amount of reduced risk depends on the degree to which the stocks face common risks and that their prices move together Covariance: The expected product of the deviation of two returns from their means, if they move together If the covariance is positive, the two returns tend to move together If the covariance is negative, the two returns tend to move in opposite directions Correlation: a measure of the common risk shared by stocks that does not depend on their volatility Variance for a two security portfolio: Variance for of a large portfolio: is the weighted average covariance of each stock with the portfolio. Investing in risk free securities and a risky portfolio: expected return: Standard deviation: Highest possible expected return for any level of volatility highest Sharpe ratio. A investor preference will determine how much to invest in a tangent portfolio(combination of risk-free asset with a portfolio on the efficient frontier with highest Sharpe ratio) vs a risk-free investment The CAPM -equilibrium model that underlies modern financial theory, derived using principles of diversification with simplified assumptions Assumptions CAPM Results in: The risk premium of the Market portfolio M = -the optimal investment in the risky portfolio for the individual investor Mutual Fund Theorem( Optimale portefolio van : risicovrije assets and one good diverdified market index mutual fund) -the allocation between the mutual fund and the risk-free asset depends on individual investor’s risk aversion -Expected returns on individual securities -reward-to-risk ratio for asset I of individuals= -Market portfolio: Combine the two returns when the equilibrium of the two is equal Bond Yield to maturity: interest rate that makes the present value of the bond’s payments equal to its price Options: -Financial: a contract that gives its owner the right ( not a obligation) to purchase or sell an asset at a fixed price as some future date -Call option: gives its owner the right to buy an asset -Put Option: gives owner the right to sell an asset -Option Writer: = the seller of an option Contract. Hoorcollege Week 1 future returns (1 asset) - quantifying risk (1 asset) Variance: Portfolio risk-return: 2- asset- Correlation ( one bond and one equity) Return(rp): Corr= 1 Corr=-1 Hoorcollege 3 Investments. We use a Heuristic = a Rule of thumb -to do expectations and predictions Heuristic of today: 1/N -Allocate resources equally to each of N alternatives -Better than the portfolio optimization model: they often overfit often perform worse -1/N heuristic does not estimate any parameter cannot overfit Other heuristic ( bad one) = Imitate the most successful -follow the most successful person excessive risk taking Three models (stories of today, how we see the world in stocks) SIM= Single index Model -With large n, Large estimation error Large data requirements We want to simplify the estimation Important assumption Cov(ei,rm)=0 Return asset i: variance asset I compared to the market= -High Beta companies luxury products -When n becomes large, sigma^2 becomes negligible , this follows in another formula of a variance is the diversifiable risk Covariance between 2 assets: Regression Single Index Model Coefficient is the coefficitent of Amazon. But you have to substract the 1 of the market index 1.5326 -1 = 0.5326 minus the standard error it is to low. Amazon moves with the market index Parameters needed for the SIM: CAPM predictions 1. Everyone rational all investors hold the same portfolio : the market portfolio =market portfolio = tangency portfolio = the capital market line 2. Reward-to-risk ratio of the market and of individual securities are the same - Fair risk premium of a stock is (SML): - Required (total) return: Investors: Investor who views the beta of an individual security as the security’s proper measure of risk: passive trader Investor who views the standard deviation of an individual securitya a proper measure of risk = entrepreneurs, put everything in one stock ATP Approach = Arbitrage Pricing Theory (APT) -predicts a SML linking expected returns to risk - relies on three key assumptions - securities return can be described by a risk factor model - There are sufficient securities to diversify away firm-specific risk - Markets do not allow for the persistence of an arbitrage opportunities -When a market is well-functioning, arbitrage opportunities should quickly disappear no-arbitrage equilibrium Arbitrage en equilibrium -Arbitrage: investor makes riskless profit wit zero net investment -LOOP(law of one price): If two assets are equivalent, they should have the same market price Portfolio with two stocks: not so well diversified F= extra-market risk factor with unanticipated economy wide changes Well-diversified portfolio: The single stock is the lose end. Multifactor APT: -several sources of systematic extra-market risk: negative yield curve, inflation, regulation. -APT can be generalized to accommodate these multiple sources of risk Overview of implementation of factors: FAMA-French (FF) three factor Model SMB(Small minus Big): the return of a zero-cost, long-short. Portfolio of small stocks (Long) in excess of the return on a portfolio of a large stocks (Short) HML (High minus low): High book-to-market ratio stocks (LONG) in excess of the return of low book-tomarket ratio stocks (Short) Efficient Market Hypothesis (EMH) -prices of securities fully reflect available information -several forms of market efficiency: - weak form: using only past prices: All past information is immediately reflected in the price hypothesis: Momentum effect: tendency of recent pas winners(losers) to out (under)perform in the short run Follow the upward or downward trend. --? Patterns in stock returns. reversal effect: - Semistrong form: using al publicly available information if pike of new information holds: it is correct if new information slowly increase after the announcement: the semistrong form does not hold -PEAD, January effect - Strong form: using a public and private information -pre announcement runups there is already info before the event happened. -Market efficiency, means allocational efficiency Event studies in international finance research. -measure impact of an event of interest on stock returns -CAR(abnormal return)= difference between the stock’s actual return and the stock’s expected return in the absence of the event -due to announcements. (unanticipated events) look at world index. 1. Choose a topic based on events: publication of a COVID-19 vaccine 2. Get news date of event(s): date of announcement counts! Sources of news: LexisNexis’ Nexis Uni (see here: https://libguides.vu.nl/nexis-uni) FactSet (see here: https://libguides.vu.nl/finding-data/factset) Refinitiv SDC Platinum (for M&A: https://libguides.vu.nl/finding-data/sdc-platinum) Search/scrape biggest news outlets yourself online 3. Finding stock, return & firm data - control variables 4. 5. Define event and estimation window: as narrow possible around the first news of the event - closing price day before news (t-1) - until closing price of t+1, to be sure that news after market hours or in other time zones are included 6. The actual analysis == AR= real return – estimated return Estimated return= 7. Univariate analyses calculate t-value 1 event day: Calculate t-value > event days: Multiple firms and event days: 8. Multivariate analysis Ordinary least squares regression 9. Explaining anomalies: 10. Superior returns are truly abonormal: Why does mispricing exist in the first place How can mispricing survive
