Draft lecture – FIN 352 Professor Dow CSU-Northridge March 2012

 If markets are generally efficient, then…  Looking for undervalued assets is not a useful investing strategy.  Does it matter what you do?  MPT looks at the investing implications of market efficiency.  Assets are evaluated in terms of risk and expected return rather than price or intrinsic value.  The hard part is how to measure risk.

 An individual chooses what portfolio to have.  Portfolios are judged based on expected return and risk (as measured by standard deviation).  The risk of a single asset is the risk it adds to the portfolio.

 Market Efficiency  Previous Lecture  Portfolio Selection  We’ll learn the basic principles and calculations  Skip the more advanced calculations (see the book)  What is the bottom line for portfolio selection?

 Market Price of Risk  Quantifying the Risk-Return Tradeoff  Theory of Expected Returns ▪ CAPM (we’ll only cover the basics) ▪ Issues related to measuring uncertainty  How to Evaluate Investor Performance

 Markets are not necessarily efficient.  Uncertainty is not measured correctly.  Overly technical.  What is the alternative?

 Statistics Review  Expected Return  Standard Deviation  Covariance and Correlation  Normal Distribution ▪ Tail Probabilities

 The portfolio return equals the weighted average of the individual asset returns.  R P = w 1 R 1 + w 2 R 2  60% of your wealth is in stocks, 40% in bonds.  Stocks earned 7%, bonds earned 5%.  (0.6)(7%)+(0.4)5% = 6.2%

 The expected return to the portfolio is the weighted average of the expected returns to the individual assets.  E(R P ) = w 1 E(R 1 ) + w 2 E(R 2 )  60% of your wealth is in stocks, 40% in bonds. Stocks are expected to earned 12%, bonds are expected to earned 2%.  (0.6)(12%)+(0.4)2% = 8%

 Is the portfolio standard deviation the average of the individual standard deviations  NO!  Some of the changes will cancel out across securities.  This is diversification – combining different assets reduces risk.

 The correlation coefficient, Rho (  ), measures how movements in returns are related.   > 0  Returns tend to move in the same direction.   < 0  Returns tend to move in opposite directions.   = 0  Movements in returns are unrelated.

 The correlation coefficient, Rho (  ), determines the amount of diversification   = 1  Returns always move in same direction; no diversification   = -1  Returns always move in opposite direction; can eliminate risk completely.  0 <  < 1  Returns sometimes move in different directions; some diversification

 Negative correlations would be ideal.  Generally, security returns have positive correlations.  Why?  Correlations not equal to 1 so still opportunities for diversification.

  How much depends on which assets.  Can’t diversify away all risk.  Non-diversifiable, systematic or market risk  Reflects changes in the economy or in the willingness of investors to bear risk.

  Higher-risk assets offered higher return on average in the past.  Mixing assets classes will provide better diversification. Lower risk for the same expected return.  Holding more of the relatively high-risk assets will increase portfolio risk (and expected return).

 Fancy Version (discussed in book – optional, not required for class)  The Efficient Frontier  Market portfolio provides maximum diversification and is the best portfolio of risky assets.  You should hold the market portfolio and a risk- free asset; the share of each depending on your risk tolerance.

 Our basic investment strategy up to now:  Be diversified  Choose the mix of assets to match tolerance for risk.  This basic asset allocation approach is broadly consistent with MPT.  More complicated versions for sophisticated investors.

 MPT assumptions:  Markets are efficient (talked about previously)  We know the distribution of stock returns.  Portfolio risk is adequately described by the standard deviation. ▪ Returns are normally distributed. ▪ Individuals only care about standard deviations.  Assumptions don’t have to hold exactly, but should be reasonably good descriptions.

 History may not predict the future  Standard deviations may change ▪ Why?  Correlations may change ▪ Why?

 Distributions of returns may not be normal.  Asymmetric risk  Skewness  Downside risk  Fat tails  Greater risk of extreme event  Underestimate risk  Can investors take advantage of this?

 Cannot quantify important risks.  Risk vs. Uncertainty  Risk: We know the frequency (distribution of events)  Uncertainty: We don’t know how often events will occur. ▪ Examples?  What if we didn’t even know the event could occur?

[T]here are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know. - Donald Rumsfeld

 Black Swan Risk  What should an investor do?  Be conservative?  Be robust to shocks?  Gamble on the possibility of big changes?

 The market price of risk is the extra return you expect to get for holding an additional level of risk.  This is determined by the average of investors’ attitudes towards risk.  The market risk premium is defined as E(R m )- R f

 Can’t evaluate risk of a security in isolation.  How much risk does the security add to your portfolio?  Expected return to the security “should” be a function of this risk.

 Factor models.  Expected return is a function of various “factors”.  Economic factors  Business characteristics  Market returns

 Capital Asset Pricing Model (CAPM)  Risk consists of two parts  Business-specific risk ▪ Which can be diversified away  Market risk ▪ Which cannot be diversified away  If you hold a well-diversified portfolio, only the market risk matters.  Since only market risk matters, investors only need to be compensated for a security’s market risk.

 Beta (β) represents the amount of market risk.  How to measure β (the non-technical version).  On average, how much does the return to the asset change when the return to the market changes? ▪ If it changes an equal percentage, it has a β of 1. ▪ If it moves twice as much, it has a β of 2. ▪ If it’s movements are unrelated to the market, it has a β of 0. ▪ If it moves equally, but opposite of the market, it has a β of -1.  What determines β? 

 How much extra return do you get for a unit of risk? The market risk premium!  This gives us the CAPM equation  E(R i ) = R f + β i (E(R m ) - R f )  If the risk-free rate is 5%, the expected market return is 9% and the β of the security is 1.5, what return should it offer.  11%  What if the β was 0.5?

 How does CAPM perform?  Beta matters  But it’s not the only thing that matters  Multi-Factor Models

 Why evaluate performance?  Does an investment strategy work?  Did an money manager perform better than average?  Reasons for good performance  Risk  Skill  Luck

 Managers exceed expectations if they have higher return than they should given the risk.  Usual caveats about repeat performance  How to measure expectations? How to measure risk?

 Using a benchmark: Return compared with index portfolio of similar assets.  Use standard deviation as a measure of risk.  Sharpe Ratio = E(R i – R f )/σ  Downside risk.  Use a model to measure of risk.

 CAPM provides a measure of risk.  R i – R f = α i + β(R m -R f ) + u i  α measures excess return above that implied by the CAPM  α is sometimes used as a generic term to refer to the value-added produced by the investor.