1. Principles of Investing FIN 330
CHAPTER 8
MODERN PORTFOLIO THEORY
CAPITAL ASSET PRICING THEORY
Dr David P Echevarria
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2. STUDENT LEARNING OBJECTIVES
What is Modern Portfolio Theory (MPT)
What does MPT tell us about managing risk and diversification?
How do we measure investment risk?
What is the Capital Asset Pricing Model?
How does CAPM describe the efficient frontier?
Dr David P Echevarria
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3. Some Background on MPT
Prior to MPT there was no real quantitative method for constructing portfolios or measuring their investment efficiency.
Harry Markowitz developed the idea of mean and variance efficient portfolios. The locus of which would later be identified as the Efficient Frontier.
Mean and Variance Efficiency = the best rate of return for a given level of risk. All assets meeting this criteria fall on the efficient frontier.

4. Assumptions of MPT
1. Risk of a portfolio is based on the variability of returns from the said portfolio.
2. Investors are risk averse.
3. The investor's utility function is convex and increasing, due to risk aversion and consumption preference.
4. Analysis is based on single period model of investment.
5. An investor either maximizes portfolio return for a given level of risk or maximizes return for the minimum risk.
6. An investor is rational in nature.

5. Investment RISK
The probability of losing some or all of your investment
Risk is a function of the dispersion of possible future outcomes
Expected Value: probability of a particular outcome times the magnitude
Risk is measured as the standard deviation of expected outcomes
Dr David P Echevarria
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6. Modern Portfolio Theory (H. Markowitz)
The expected return of a portfolio is a weighted average of the expected returns of each of the securities in the portfolio
E(Rp) = S Xi Ri
The weights (Xi) are equal to the percentage of the portfolio’s value which is invested in each security and Ri is the [expected] return for each asset i in the portfolio.
Dr David P Echevarria
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7. Modern Portfolio Theory
The riskiness of a portfolio is more complex; it is the square root of the sum of the weighted (X2i) times the variances (s2) of each security and the correlation (r - rho) between the 2 securities in a 2-Asset Portfolio.
sp = (X2i s2i + X2j s2j + 2 Xi Xj ri,j si sj)1/2
2 Sources of Risk: Variance and Covariance
Dr David P Echevarria
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8. Modern Portfolio Theory
sp = (X2i s2i + X2j s2j + 2 Xi Xj ri,j si sj)1/2
The correlation coefficient (ri,j) can be positive (+1), zero, or negative (-1)
If the average correlation of securities in the portfolio is positive – the riskiness of the portfolio will be larger.
If the average correlation of securities in the portfolio is negative – the riskiness of the portfolio is smaller: the third term will be negative
Dr David P Echevarria
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9. Example of Efficient Frontier 2-Asset Portfolio
Two assets are positively correlated but r is less than 1
Minimum Variance Investment Portfolio
Dr David P Echevarria
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10. Modern Portfolio Theory
D. Correlation: Range from +1 to 0 to -1
When the holding period returns of two securities move in the same direction, by the same amount at the same time, the pair is perfectly positively correlated: rho = 1
When the holding period returns of two securities are totally unrelated to each other, the pair is uncorrelated; rho = 0
When they move in opposite directions, the pair are negatively correlated: rho = -1
Dr David P Echevarria
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11. Modern Portfolio Theory
MPT Efficient Portfolios
Mean & Variance Efficient portfolios form a curvilinear frontier
Assets that are efficiently price will fall on the frontier as will all efficient portfolios.
Assets lying below or above the efficient Frontier are not mean-variance efficient.
Assets below the EF are said to be overpriced. Assets above the EF are said to be underpriced.
Dr David P Echevarria
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12. Modern Portfolio Theory
The risk of a portfolio is the weighted average of the risk of each security in the portfolio, and the correlations between each pair of securities in the portfolio
Some textbooks use the covariance terms in the third term: si,j = ri,j si sj
sp = (X2i s2i + X2j s2j + 2 Xi Xj sj,j)1/2
Dr David P Echevarria
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13. Risk Reduction: Benefits of Diversification
Portfolio diversification
Diversification can increase the risk/return tradeoff if the average correlation coefficient between individual securities in the portfolio is less than 1.0
The benefits of diversification increase as the correlation coefficient gets smaller
Dr David P Echevarria
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14. Risk Reduction: Benefits of Diversification
B. Diversification across securities
As the number of securities in a portfolio increases the portfolio risk decreases and approaches the risk of the total market
Market risk is inherent from business cycles, inflation, interest rates, and economic factors
Firm-specific risk is tied to the company’s labor contracts, new product development and other company related factors
Dr David P Echevarria
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15. Risk Reduction: Benefits of Diversification
Forms of Diversification
Mathematical: Increasing the number of stocks reduces the portfolio risk
Diversification across time
Dollar cost averaging
Dr David P Echevarria
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16. Risk Reduction: Benefits of Diversification
4. Naive Diversification
Naive diversification occurs when investors select stocks at random, and purchase and equal dollar amount of each security
When N becomes large enough, naive diversification averages out the firm-specific (unsystematic) risk of the stocks in the portfolio, so that only the market (or systematic) risk remains
Dr David P Echevarria
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17. Capital Asset Pricing Model (CAPM)
Equation that defines the risk/return relationship
The CAPM assumes two assets: the risk-free asset and the risky market portfolio
The two asset CAPM world results in a linear efficient frontier: Capital Market Line (CML)
Dr David P Echevarria
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18. Capital Asset Pricing Model (CAPM)
The risk aversion characteristic of the investor will determine how much is invested in the risk-free asset and how much is invested in the risky market portfolio
The standard deviation of the risk-free asset is zero.
Based on the idea that investors accept a higher risk only for a higher return
Dr David P Echevarria
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19. Capital Asset Pricing Model (CAPM)
Assumptions of the CAPM
Investors have cost-free and equal access to information leading to homogenous expectations
Frictionless capital markets
No transaction costs or taxes (perfect)
Securities infinitely divisible (complete)
Investors are rewarded for systematic risk (b)
Non-systematic risk is diversified away.
Dr David P Echevarria
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20. Capital Asset Pricing Model (CAPM)
B. Assumptions of the CAPM (cont.)
Investors are rational and seek to maximize their expected utility functions
All investment is for the same time period
All investors can borrow or lend at the risk-free rate
Dr David P Echevarria
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21. The Capital Market Line (CML)
Expected Portfolio Return:
E(Rp) = (X) E(Rp) + (1 - X) RF
Where: X = % of Wealth Invested
Portfolio Risk: sP = S Xi si
Where: Xi = proportion invested in asset i, si = the standard deviation (riskiness) of asset i
CML is locus of all combinations of the risk-free asset and the risky market portfolio.
The CML is also termed the Borrowing-Lending line.
Dr David P Echevarria
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22. The Capital Market Line (CML)
The Market Portfolio
The Market Portfolio (point M) must be the only risky portfolio chosen by all risk-averse investors. Because it is demanded by all investors, it must contain all the securities and other traded assets
Portfolio M’s risk = Market risk
Dr David P Echevarria
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23. The Capital Market Line (CML)
Measuring Relative Risk (Beta b)
Relative risk contribution of security i
Known as beta, b , it measures security risk, or volatility relative to the market portfolio
Beta greater than 1.0 is riskier than the market
Beta less than 1.0 is less risky than the market
Dr David P Echevarria
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24. The Capital Market Line (CML)
The value of beta implies something about returns relative to the market portfolio
The choice of a proxy affects beta: e.g. S&P 500, Wilshire 5000, Russell 1000, etc.
Dr David P Echevarria
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25. The Capital Market Line (CML)
Types of CAPM Risk
Systematic or non-diversifiable risk: Beta is the measure of systematic risk
Non Systematic or diversifiable risk
Risk due to firm specific attributes
Become irrelevant in a well-diversified portfolio
Decisions made by total risk (standard deviations) instead of beta ignore the systematic risk and diversifiable risk components of total risk
Dr David P Echevarria
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26. The Capital Market Line (CML)
F. The Security Market Line (SML)
The SML addresses the risk-return characteristics for individual securities
The slope of the SML is equal to the stock’s beta coefficient.
Dr David P Echevarria
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27. HOMEWORK
Dr David P Echevarria
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