Capital Allocation, Asset Allocation and the Efficient Market Hypothesis Part A Otto Khatamov

1. Client needs: Investment policy statement Focus: Investor’s short-term and long-term needs, expectations 2. Portfolio manager: Examine current and projected financial, economic, political, and social conditions Focus: Short-term and intermediate-term expected conditions to use in constructing a specific portfolio 3. Portfolio manager: Implement the plan by constructing the portfolio Focus: Meet the investor’s needs at minimum risk levels 4. Client/Portfolio manager: Feedback loop Monitor and update investor needs, environmental conditions, evaluate portfolio performance

SeriesGeometric AverageArithmetic averageStandard Deviation Small-Company Stocks 11.64%17.74%39.30% Large-Company Stocks 10.01%12.04%20.55% Long-Term Government Bonds 5.38%5.68%8.24% US Treasury Bills3.78%3.82%3.18% Source: BKM Chapter 5 – Sources: Returns on T-bills, large and small stocks – CRSP, T-bonds - RSP for returns and Lehman Brothers long-term and intermediate indexes for 1996 and later returns.  What are the sources of differences in risk, returns and risk premiums?

 Types of risks:  Business risk/Financial risk/Liquidity risk – i.e. BA decides to buy 20 new planes.  Industry risk – i.e. Subprime crisis  Country risk/Exchange rate risk – i.e. Iceland Krona, recession in the economy  Investors may held a portfolio of different assets  What happens to the risk of a portfolio as we add more assets?  Risk that can be eliminated by diversification is called unsystematic risk whereas risk that remains is called systematic risk.

The concept of diversification: An example of Systematic vs Unsystematic risk Debt Mutual FundEquity Mutual Fund Expected return, E(r)8%13% Standard deviation, σ12%20% Correlation, p D,E 1

The concept of diversification: Systematic vs Unsystematic risk Unsystematic risk Systematic risk No of Shares Standard Deviation  Why not continue to add stocks / assets to our portfolios?

The Efficient set with the market portfolio and a risk-free asset σ RpRp RfRf M (Market Portfolio) E(R m ) σΜσΜ

“How to allocate the capital between the market and the risk free asset?”  … That decision has been shown to account for an astonishing 94% of the differences in total returns achieved by institutionally managed pension funds. There is no reason to believe that the same relationship does not also hold true for individual investors… (J. Bogle, Chairman of the Vanguard group of investment companies).

Capital Allocation between the risk free asset and the market portfolio “How to allocate the capital between the market and the risk free asset?”  Feasible risk return combinations: Let assume we have decided the proportion of investment asset, w 1 to be allocated in the market portfolio and w 2 in the risk free.  What is the expected return and the variance of the portfolio?

Capital Allocation between the risk free asset and the market portfolio σ RpRp RfRf M 0 1 E(R m ) σmσm

Capital Allocation between the risk free asset and the market portfolio: The role of risk tolerance…  How to choose the complete portfolio from among the feasible risk return combinations? Let assume y = w 1, the portion of money to be allocated in the market portfolio and 1-y = w 2 the portion of money to be allocated in the risk free.  The purpose is to maximise our utility by choosing the best allocation to the risky asset, y.

Capital Allocation between the risk free asset and the market portfolio: The role of risk tolerance…

 Utility as a function of allocation to the market portfolio (y) …  Complete portfolio using an indifference curve …

Capital allocation line: In practice…  It is impossible to invest in the market portfolio o Limits to diversification benefits Transaction costs Private information o Some assets are not traded Human capital  Invest in an optimal risky portfolio o How to create the optimal risky portfolio?  How to determine the assets to include in the risky portfolio o Efficient Market Hypothesis Passive strategy Active strategy

 Let assume we can invest in two risky funds, bonds and stocks and the risk free asset Graphical representation of the feasible risk return combinations… Debt Mutual FundEquity Mutual FundRisk Free Asset Expected return, E(r)8%13%5% Standard deviation, σ12%20%0 Correlation, p D,E 0.3

 The mathematics of optimal risky portfolio using two risky assets

 Back to the example… Debt Mutual Fund Equity Mutual Fund Risk Free Asset Expected return, E(r) 8%13%5% Standard deviation, σ 12%20%0 Correlation, p D,E 0.3

 Markowitz portfolio selection problem: Generalized portfolio construction to the case of many risky securities and a risk free asset Standard Deviation Expected Returns Risky Assets

 Markowitz portfolio selection problem: Feasible risk-return combinations

Standard Deviation Expected Returns Risky Assets Efficient Frontier Minimum-variance Frontier Minimum Variance

 Markowitz portfolio selection problem: Find the optimal risky portfolio

Standard Deviation Expected Returns Risky Assets Efficient Frontier Minimum-variance Frontier Minimum Variance Optimal risky portfolio CAL

 Markowitz portfolio selection problem: Find the complete portfolio Standard Deviation Expected Returns Risky Assets Efficient Frontier Minimum-variance Frontier Minimum Variance Optimal risky portfolio CAL

o Specify the characteristics of all securities Expected returns, variances, correlations o Asset allocation to find the optimal risky portfolio Create the efficient frontier Find the weights that maximise the Sharpe ratio (CAL) Using these weights calculate the expected return and the variance of the optimal portfolio o Capital allocation between the optimal risky portfolio and the risk free asset Maximise the Utility of the investor and find the y * (i.e. portion of money to be allocated in the optimal risky portfolio) Calculate the portion of money to be allocated in the risk free portfolio and the expected return and the variance of the complete portfolio

Capital allocation line: In practice…  It is impossible to invest in the market portfolio o Limits to diversification benefits Transaction costs Private information o Some assets are not traded Human capital  Invest in an optimal risky portfolio o How to allocate the proportion of assets to create the optimal risky portfolio?  How to determine the assets to include in the risky portfolio o Efficient Market Hypothesis o Passive strategy o Active strategy

 Kendal (1953) identify no predictable patterns in stock prices – stock prices evolve randomly  Irrational market (Market psychology)  Rational market  Example…

 Suppose that stock prices are predictable – XYZ stock price will rise in three days by 10%.  Action (Immediately reflect good news): ◦ If you do not hold XYZ stock – Buy XYZ ◦ If you hold XYZ stock – Do not sell XYZ  A forecast about future performance leads to changes in current performance  Stock prices reflect all available stock information

 Why are price changes random? ◦ Prices react to information (If it could be predicted, then the prediction would be part of today’s stock price) ◦ Thus, flow of new information (cannot be predicted) is random ◦ Therefore, price changes are random  Random price changes indicate a rational market…

 Why should stock prices fully and accurately reflect all available information? ◦ Information may be costly to uncover and analyze thus need the appropriate reward  Intensive competition among market participants assures prices reflect all information

 Forms of the EMH: ◦ Weak (Prices will reflect all information that can be derived from trading historical data such past prices and trading volume) ◦ Semi-strong (Prices will reflect all publicly available information regarding the prospects of the firm) ◦ Strong (Prices would reflect all information relevant to the firms’ prospects, even inside information)

 Active or Passive Management? ◦ Passive Management (Proponents of EMH – stock prices are at fair levels)  Index Funds (well-diversified portfolios) ◦ Active Management  Security analysis (Technical and Fundamental analysis)  Timing  What would happen to market efficiency if all investors follow a passive strategy?

 Active or Passive Management? The empirical evidence… Source: Fund data provided by Morningstar; index data provided by Thomson Financial – The Active – Passive debate: Bear Market Performance, 2008, C Philips, Vanguard.

 Active or Passive Management? The empirical evidence… ◦ Mutual fund risk adjusted performance  Malkiel, 1995, Returns from Investing in Mutual Funds , Journal of Finance ◦ Superior analysts (SAT, MBA)  Chevalier and Ellison, 1999, Are Some Mutual Fund Managers Better than Others? Cross Sectional Patterns in Behavior and Performance, Journal of Finance ◦ Informed vs Uninformed investors  Barber, Lie, Liu and Odean, 2008, Just how Much do Investors Lose by Trading?, Review of Financial Studies

Bodie, Kane and Marcus, Chapter