FYP Briefing

Project #56 Is R&D a Priced Factor in APT Market Model for Capital Asset Pricing Model (CAPM) –R i = a i + b i R mt + ε i Where Ri = expected returns on asset i; Rmt = market returns E(ai) = 0 E( ε i) = 0 This is the single factor model originally developed by Markowitz in his portfolio theory and further detailed implementation by Sharpe. Implications: – Portfolios are formed based on mean variance efficiency – Risk is the only factor that is priced

Project #56 Is R&D a Priced Factor in APT Ross developed the APT R i = λ 0 + λ 1 b i1 + λ 2 b i λ k b ik where, R i = expected return on asset i, Λ k = priced risk factor k (also called systematic risk factor) b ik = sensitivity of asset i to factor k Λ 0 = risk free rate Relevant factors Change in GDP, interest rates, size of firm, market returns, etc. Implications Ability to build portfolios with exposure to specific risk by combinations of the right quantities of the relevant assets Some approximate pricing relationship should exist between different assets through their functional relationships with the priced factors

Project #56 Is R&D a Priced Factor in APT Why R&D? –Important driver of innovation and hence firm competitiveness –Higher competitiveness → Growth and Profitability → Increased stock return –Downside Uncertainty and hence higher risk Investors may not value the change in R&D investment Objective –Is ∆R&D a priced factor? –Possible reasons and implications Methodology –US stock data from CRSP and Compustat Database –Statistical Analysis Factor analysis Regression Portfolio formation –Data manipulation in EXCEL –Possible use of MATLAB

Project #57 Measuring Downside Risk for Investors of Different Risk Aversiveness Don’t mind this Avoid this

Project #57 Measuring Downside Risk for Investors of Different Risk Aversiveness Typical pricing model –Positive and negative deviations treated equally Real Life –Investors view positive and negative deviations differently –They have different utilities Conservativeness, wealth level –Utility function may be assymmetical between gain and loss

Project #57 Measuring Downside Risk for Investors of Different Risk Aversiveness Objective –Review the various downside risk measures –Understand the use of utility function and identify a feasible functional form for the research –Apply optimization techniques to maximize the utility of a portfolio on the downside measure to understand the characteristics of portfolio selected with each measure Methodology Development of Theoretical Framework Operations Research Techniques Manipulation of data with EXCEL Familiarity with MATLAB

Project #58 All Eggs in One Basket Conventional Wisdom –Efficient market hypothesis (Fama) –Prices are random walk E(R) = 0 –You cannot beat the market Buy the market (Index Fund) Alternative View –Stock-picking has value –You can beat the market

Project #58 All Eggs in One Basket Objective –Identify attributes of stocks that has ex-ante value in predicting performance –Use in-sample and out-of-sample test Methodology – Data from CRSP and Compustat database –Statistical techniques Portfolio analysis Regression –Manipulation of data in EXCEL

Project #59 Implied Growth Rate and Cost of Capital in Stock Prices Gordon dividend growth model for stock valuation High stock prices imply the following –High growth rate,g; or –Low cost of capital, r e Setting r e consistent with the CAPM model allows us to compute the g.

Project #59 Implied Growth Rate and Cost of Capital in Stock Prices Objective –To determine the growth rate, g, implied by the stock price, P for a cross-section of stocks and for the same stock over time –Test the reasonableness of g –Characterize the behavior of g with change in firm attributes Methodology –Data from CRSP and Compustat –Statistical tools –Data manipulation with EXCEL

Project # 60 Deviation of Intrinsic Value of Stock During the 1987 Stock Market Crash Intrinsic Value computed by the dividend growth model – fundamental valuation of stock Efficient market: rational investors will take advantage of mis-pricing and buy or sell to bring the price back in line

Project # 60 Deviation of Intrinsic Value of Stock During the 1987 Stock Market Crash Objective –To determine the level of mis-pricing and whether mis-pricing is significantly greater in the 1987 stock market crash Methodology –Data from CRSP and Compustat –Data manipulation in EXCEL –Statistical analysis

Project # 61 Optimization of Portfolio Returns with Risk and Time Horizon Constraints E(R i ) β RFR M 1 RMRM R i = a i + β i (R M - RFR)+ ε i Mean-variance optimization One period

Project # 61 Optimization of Portfolio Returns with Risk and Time Horizon Constraints Risk and Return versus length of holding period (Source: a) STOCKS Holding period (years) No. of holding periods No. of loss periods18720 No. of periods beating inflation b) BONDS Holding period (years) No. of holding periods No. of loss periods10200 No. of periods beating inflation c) T-BILLS Holding period (years) No. of holding periods No. of loss periods0000 No. of periods beating inflation

Project # 61 Optimization of Portfolio Returns with Risk and Time Horizon Constraints Objective –To create portfolios that minimize risk over the time horizon of the investors Methodology –Data from CRSP and Compustat –Data Manipulation with EXCEL –Operations Research Technique –May need to use MATLAB