Portfolio MGMT CH 8: Asset Pricing Models

Developing the Capital Market Line PT. 2

*- CML is a special case of CAL when the Risky portfolio is the Market Portfolio* 1. The market portfolio includes all risky assets or anything that has value. - *But it is practically limited to assets that are tradable and investable.* 2. The "market" should contain as many tradable and investable assets as possible, including stocks, bonds, real estate assets, commodities, and so on - But is frequently defined narrowly because it is practical to do so 3. Typically, a local or regional stock market index is used as a proxy because of its visibility to local investors. -S&P500 used by analyst as benchmark for MKT performance in USA - it accounts for approximately 80% of the total equity market capitalization in the United States.

Exhibit 8.1

- *CML shows the risk-return relationship between E(Rp) and σp* - *This relationship holds for every combination of the risk-free asset with any collection of risky assets* -when the risky portfolio, M, is the market portfolio containing all risky assets held anywhere in the marketplace *this linear relationship is called the CML*

Systematic Risk

- *Only Systematic Risk remains in the Market Portfolio* - Variability in all Risky Assets caused by Macroeconomic conditions - *Measured by the SD of the market Portfolio* and it can change over time *SD = Total Risk = Systematic + Unsystematic - since MKT portfolio is diversified, unsystematic = 0

How to Measure Diversification

- All portfolios on the CML are perfectly positively correlated with each other and with the completely diversified market Portfolio M - That is, a completely diversified portfolio would have a correlation with the market portfolio of +1.00 - The reason is that complete risk diversification means the elimination of all the unsystematic or unique risk and the systematic risk correlates perfectly with the market portfolio

CML Recap of Important Stuff

- CML is a special case of CAL when the Risky portfolio is the Market Portfolio -Combining a Risk-Free Asset with a Risky Portfolio, M -Slope CML is the maximum risk premium compensation an investor can expect per unit of risk *(E(rm) - RFR)/ Om* -both return and risk increase in a linear fashion along the CML - All portfolios on CML are positively correlated - Represents a new EF that combines Markowitz EF of Risky Assets w/ the ability to invest in RFA

Capital Market Theory Overview

- CMT extends PT and develops a model for pricing risky assets - CAPM will allow you to find the Required Rate of Return for any asset

One can attain a higher expected return than is available by

- One can invest along the efficient frontier beyond point M, such as point D 1.With the risk-free asset, one can add leverage to the portfolio by . . . a. borrowing money at the risk-free rate (shorting the risk free asset) b. investing in the risky portfolio at point M to achieve a point like E

The CML and the Separation Theorem

- The CML leads all investors to invest in the M portfolio - Individual investors should differ in position on the CML depending on risk preferences -How an investor gets to a point on the CML is based on financing decisions - Risk averse investors will lend at the risk-free rate while investors preferring more risk might borrow funds at the RFR and invest in the market portfolio - *The investment decision of choosing the point on CML is separate from the financing decision of reaching there through either lending or borrowing*

Conceptual Development of the CAPM

- The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier - However, CML cannot be used to measure the expected return on an individual asset - *curiFor individual asset (or any portfolio), the relevant risk measure is the asset's covariance with the market portfolio* This is because investors have eliminated unsystematic risk - For an individual asset i, the relevant risk is Oi*Pi,m Pi,m = Correlation coefficient b/w asset and MKT

A Risk Measure for the CML

- The only important consideration is the asset's covariance with the market portfolio - Covariance with the market portfolio is the systematic risk of an asset -* Var (Rit)= Var (biRMt)+ Var(ε) where bi= slope coefficient for asset i ε = random error term*

Diversification and the Elimination of Unsystematic Risk

- The purpose of diversification is to reduce the standard deviation of the total portfolio - This assumes that imperfect correlations exist among securities - *As you add securities, you expect the average covariance for the portfolio to decline* - need 12-18 pre times - 40-50 now *The more the better*

Security Market Line (SML)

- a graphical form of the CAPM - shows the relationship between the expected or required rate of return and the systematic risk on a risky asset -The expected rate of return of a risk asset is determined by the RFR plus a risk premium for the individual asset - The risk premium is determined by the systematic risk of the asset (beta) and the prevailing market risk premium (RM-RFR)

Market Portfolio

- contains all risky assets held anywhere in the marketplace and receives the highest level of expected return (in excess of the risk-free rate) per unit of risk for any available portfolio of risky assets - *Maximizes investor's Risk Premium - *point of tangency between EF and CML* -completely diversified portfolio - *all unsystematic risk are diversified away*

Does a unique optimal risky portfolio exist?

- if we assume investors have homogeneous expectations regarding *Risk, Return, and Probability Dist.* Then they *should arrive at the same optimal portfolio* - assumption of identical expectations is referred to as homogeneity of expectations. -even if investors have different expectations, market prices are a proxy of what the marginal, informed investor expects. *This means that the market portfolio becomes the reference portfolio that other portfolios can be judged against. * *Different expectations = Different Optimal Portfolios* *Identical expectations = identical optimal portfolio*

Computing expected/required returns and Identifying Undervalued/ Overvalued Assets

-In equilibrium, all assets and all portfolios of assets should plot on the SML - Any security with an estimated return that plots above the SML is underpriced - Any security with an estimated return that plots below the SML is overpriced - must derive value estimates for assets that are consistently superior to the consensus market evaluation to earn better risk-adjusted rates of return than the average investor

Development of CMT

-major factor that allowed portfolio theory to develop into capital market theory is the concept of a risk-free asset

Assumptions of Capital Market Theory (8)

1. All investors are Markowitz efficient investors who want to *target points on the efficient frontier* 2. Investors can borrow or lend any amount of money at the risk-free rate of return, RF 3.All investors have homogeneous or similar expectations; that is, *they estimate identical probability distributions for future rates of return* 4.All investors have the same one-period time horizon 5. All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio *Think about a mutual fund or ETF* 6. There are no taxes or transaction costs involved in buying or selling assets 7. There is no inflation or any change in interest rates, or inflation is fully anticipated 8. Capital markets are in equilibrium, implying that *all investments are properly priced in line with their risk levels*

Developing the Capital Allocation Line (CAL)

1. Combination of the risk-free asset and a risky asset can *result in a better risk-return trade-off than an investment in a risky asset* - This is because the RF asset has zero correlation with the risky asset: - *Less Risk* 2. This combination is called the CAL *Graphically* combine RF and risky asset -CAL - superimpose utility curves on CAL - optimal risky or market portfolio

Recap of Lending and Borrowing at RFR

1. Lending - buying t bills - moves down CML -reduces risk 2. borrowing - selling t bills- moves up CML - increases risk

What is a risk free asset?

1. free of default risk 2. interest rate = Rf 3. expected Rf = Rf - this is constant per period 4. SD = 0 5. correlation b/w Rf asset and MKT return=0 6. Covariance = 0 7. Rf will be the y intercept (zero SD on the X axis)

One can reduce the Investment Risk by

1. lending money at the risk-free asset- *buying T bills* 2. Investing part of your wealth in M to points

Developing the Capital Market Line

Combining a Risk-Free Asset with a Risky Portfolio, M 1. Expected return: It is the weighted average of the two returns 2. Standard deviation: Applying the two-asset standard deviation formula, we will have *ER(p) = (Wrf*Rf) + ((1-Wrf)*E(rm) E(rm) = expected return of the market Wrf = weight of RF asset (1-Wrf) = Wportfolio = weight of RF asset subtracted from total