Principles of Finance with Excel, 2 nd edition Instructor materials Chapter 10 Portfolio returns and the efficient frontier

This chapter  Mean and standard deviation for portfolio of two assets  Portfolio risk and return  Minimum variance portfolio  The efficient frontier  Mean-variance calculations for three- asset portfolios 2

Excel in Chapter 10  Average, Varp, Stdevp  Regression  Sophisticated graphing  Solver 3

4 Fidelity Funds: Diversification reduces risk and volalitility

Simple example: Coin flip 5 Flip two coins  Each coin:  Heads: You earn 20%  Tails: You lose 8%

A coin flip is like buying a stock  The return is random (risky)  Flipping two coins is like buying two stocks—an investment portfolio  Message: The portfolio return depends on  The returns/standard deviation of the individual coins  The correlation between the coins 6

Case 1: Single flip 7 A single coin flip has average return 6% and standard deviation 14%.

Case 2: Flip 2 uncorrelated coins 8 Flipping two coins where there is no correlation between them: average return 6% and standard deviation 9.90%. Message: correlation = 0 reduces risk

Case 3: Flip 2 completely correlated coins 9 Flipping two coins with correlation 1 between them: average return 6% and standard deviation 14%. Message: Correlation = 1 means that one coin’s results fully predict the second coin’s results. NO RISK REDUCTION.

Case 4: Flip 2 completely negatively correlated coins 10 Flipping two coins with correlation -1 between them: average return 6% and standard deviation 0%. Message: Correlation = -1 means that one coin’s results fully offset the second coin’s results. RISK = 0!

Case 5: Partial correlation 11 Flipping two coins with correlation between -1 and +1: average return 6%. Less standard deviation. Message: When returns are partially correlated, we can offset some but not all of the risk. Like in stocks …

Coin flip messages  If the correlation between asset returns is +1, then diversification will not reduce portfolio risk.  If the correlation between asset returns is −1, then we can create a risk-free asset—an asset with no uncertainty about its returns (a bank savings account is an example)—using a portfolio of the two assets.  In the real-world asset returns are almost never fully correlated. When asset returns are partially, but not completely, correlated (meaning that the correlation is between −1 and +1), diversification can lower risk, although it cannot completely eliminate it. 12

Kellogg (K) and Exxon (XOM) 13

Regress XOM on K 14

Portfolio: 50% K and 50% XOM 15

Portfolio: 75% K and 25% XOM 16

Recall the formulas from Chapter 9 17

Implementing the formulas 18

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Easier if you know Data Table (Chapter 27) 20 The pink/purple area below is the Data Table.

Some portfolios are obviously not optimal 21

Some choices are more interesting! 22

The minimum variance portfolio 23 The book gives two ways of locating the minimum variance portfolio:  Trial and error  A formula

Min. variance portfolio: the formula 24

The Efficient Frontier 25

The meaning of the efficient frontier  The efficient frontier is all the interesting portfolio choices  All the choices represent a tradeoff between expected return and risk  On the efficient frontier Higher expected return  Higher risk 26

Effect of correlation on efficient frontier 27

Correlation = When the correlation between the stocks is -1, there is a way to completely offset the risk and get a s = 0% portfolio. [Of course this rarely exists: Most stocks are positively correlated.]

Correlation = +1 29