6053 Lectures

Investment Analysis and Portfolio Management Portfolio Theory and its Limitations

Overview of Finance Finance

Corporate Finance Financing

Investment (in claims to real assets)

Investing (in real assets)

Financial Accounting

Management Accounting

2

Focus of the course  Less

of Investment Analysis and more of Portfolio Management  What is it which determines asset prices?  Selection of asset categories and individual assets in those categories, combining them into portfolios and managing those portfolios  Portfolio performance measurement  Managing equity portfolio risks through derivatives  Exposure to various methods and their limitations than knowledge of any magic bullet

3

Expectation from you  Attend

weekend, morning and evening classes  Read relevant chapters and articles before attending the class  Group (of 7 students) Formation by next Tuesday  Grading: – Class participation : 5% – 4 unannounced quizzes : 20% – Final Examination : 30% – Group Activities  Written solution of 3 cases : 15%  Portfolio Management : 30% 4

Key Issue: How is the value of investment determined? Evolution in Answer: Pre -’60s : Financial Statement Analysis Fundamental Analysis Technical Analysis ’60s – ’90s: Rational Expectation Paradigm Portfolio Theory Irrelevance Theorem 5

Continued….. Capital Asset Pricing Model Efficient Market Hypothesis Post – ’90s : Market Inefficiency Factor Model Market Microstructure Behavioural Finance 6

Investment Process  Determine

Investment Objective  Determine Investment Horizon  Decide which instruments to invest into  Decide how much should be invested in each  Manage the portfolio to achieve the objective

7

Portfolio Theory * Simultaneous choice of risky assets and determination of proportion of funds to invest in each of them * Efficient way to combine assets into portfolios so as to yield the highest return for a given level of standard deviation or the lowest standard deviation for a given level of return 8

Assumptions: Investors maximize one-period expected utility  Investors estimate the risk of the portfolio on the basis of the variability of expected returns  Investors decide solely on expected return and risk, i.e., their utility curves are a function of expected return and the expected variance of returns only 

9

Portfolio Choice of Risky Assets * In the absence of riskless asset: - tangency point between the investor’s indifference curve and the efficient frontier * In the presence of riskless asset: - tangency point between the straight line from the riskless return and the efficient frontier => Separation Theorem 10

Properties of Portfolio Theory  Combination

of two or more portfolios on the minimum variance set (MVS) will remain on minimum variance set  If beta-s of different securities are computed using a portfolio on the MVS, there will be a simple linear relationship between beta-s of different securities and their expected returns  All stocks have non-zero portfolio weights in nearly all portfolios in the MVS when shortsale is allowed 11

Limitations of Portfolio Theory  Too

many assets in the optimum portfolio  Too frequent and drastic change in the mix following small change in the expectations  Overuses estimated information and magnifies the impact of estimation errors  ‘Error Maximization’ often leads to poor returns in out-of-sample period  Portfolio weights often include significant position in illiquid stocks 12

Problem of Over-fitting of data  In

the absence of short-sale, the optimized portfolio is heavily weighted towards assets with high returns which are likely to contain positive estimation errors and as a result, the optimizer overstates the true efficiency of optimal portfolio  Input parameter errors result in optimized portfolio only approximating the true optimal portfolio - absence of knowledge as to the extent of approximation leads to rejection of MV optimizer 13

Optimizer from a different angle  Due

to variability in input estimates, many portfolios off the efficient frontier and other diversified portfolios are statistically as efficient as the ones on the efficient frontier  ‘Statistical equivalence’ of a large number of portfolios with the optimized portfolio indicates the essential statistical character of the MV optimization and reduce the need for frequent trade 14

Portfolio Optimization in Practice by Philippe Jorion  Underperformance

of the original point estimate of the optimizer can be gauged by the dispersion of optimal portfolios belonging to the same distribution  Effect of estimation error is more pronounced when restriction about short sale is removed as the statistically equivalent portfolios in the MVS are more dispersed  Both World and US bond indices are equivalent to optimal portfolio in terms of performance except in case of US bond index vs. optimal portfolio without short sale 15

Mean-Variance Optimization for practitioners of Asset Allocation  Restriction

on portfolio weights of different asset classes is often the outcome of lack of confidence in input numbers and a way of accommodating qualitative variables  Attraction of the optimizer towards high riskreturn assets often lead to imposition of constraints and that depresses the expected return  Cost of constraints in terms of foregone returns depend upon the constraint and the volatility of the portfolio 16

MV article contd. …..  If

higher volatility is suspected, constraint on portfolio weight goes to contain the overall portfolio volatility  However, in case of higher actual volatility the loss of returns in unconstrained portfolio will be worse  Simulation results show constrained portfolios have lower standard deviation over longer horizon, lower probability of loss of principal in case of higher actual volatility 17