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Principles of Finance

15.2 Risk and Return to Multiple Assets

Principles of Finance15.2 Risk and Return to Multiple Assets

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Table of contents
  1. Preface
  2. 1 Introduction to Finance
    1. Why It Matters
    2. 1.1 What Is Finance?
    3. 1.2 The Role of Finance in an Organization
    4. 1.3 Importance of Data and Technology
    5. 1.4 Careers in Finance
    6. 1.5 Markets and Participants
    7. 1.6 Microeconomic and Macroeconomic Matters
    8. 1.7 Financial Instruments
    9. 1.8 Concepts of Time and Value
    10. Summary
    11. Key Terms
    12. Multiple Choice
    13. Review Questions
    14. Video Activity
  3. 2 Corporate Structure and Governance
    1. Why It Matters
    2. 2.1 Business Structures
    3. 2.2 Relationship between Shareholders and Company Management
    4. 2.3 Role of the Board of Directors
    5. 2.4 Agency Issues: Shareholders and Corporate Boards
    6. 2.5 Interacting with Investors, Intermediaries, and Other Market Participants
    7. 2.6 Companies in Domestic and Global Markets
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Video Activity
  4. 3 Economic Foundations: Money and Rates
    1. Why It Matters
    2. 3.1 Microeconomics
    3. 3.2 Macroeconomics
    4. 3.3 Business Cycles and Economic Activity
    5. 3.4 Interest Rates
    6. 3.5 Foreign Exchange Rates
    7. 3.6 Sources and Characteristics of Economic Data
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  5. 4 Accrual Accounting Process
    1. Why It Matters
    2. 4.1 Cash versus Accrual Accounting
    3. 4.2 Economic Basis for Accrual Accounting
    4. 4.3 How Does a Company Recognize a Sale and an Expense?
    5. 4.4 When Should a Company Capitalize or Expense an Item?
    6. 4.5 What Is “Profit” versus “Loss” for the Company?
    7. Summary
    8. Key Terms
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  6. 5 Financial Statements
    1. Why It Matters
    2. 5.1 The Income Statement
    3. 5.2 The Balance Sheet
    4. 5.3 The Relationship between the Balance Sheet and the Income Statement
    5. 5.4 The Statement of Owner’s Equity
    6. 5.5 The Statement of Cash Flows
    7. 5.6 Operating Cash Flow and Free Cash Flow to the Firm (FCFF)
    8. 5.7 Common-Size Statements
    9. 5.8 Reporting Financial Activity
    10. Summary
    11. Key Terms
    12. CFA Institute
    13. Multiple Choice
    14. Review Questions
    15. Problems
    16. Video Activity
  7. 6 Measures of Financial Health
    1. Why It Matters
    2. 6.1 Ratios: Condensing Information into Smaller Pieces
    3. 6.2 Operating Efficiency Ratios
    4. 6.3 Liquidity Ratios
    5. 6.4 Solvency Ratios
    6. 6.5 Market Value Ratios
    7. 6.6 Profitability Ratios and the DuPont Method
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  8. 7 Time Value of Money I: Single Payment Value
    1. Why It Matters
    2. 7.1 Now versus Later Concepts
    3. 7.2 Time Value of Money (TVM) Basics
    4. 7.3 Methods for Solving Time Value of Money Problems
    5. 7.4 Applications of TVM in Finance
    6. Summary
    7. Key Terms
    8. CFA Institute
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  9. 8 Time Value of Money II: Equal Multiple Payments
    1. Why It Matters
    2. 8.1 Perpetuities
    3. 8.2 Annuities
    4. 8.3 Loan Amortization
    5. 8.4 Stated versus Effective Rates
    6. 8.5 Equal Payments with a Financial Calculator and Excel
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Problems
    12. Video Activity
  10. 9 Time Value of Money III: Unequal Multiple Payment Values
    1. Why It Matters
    2. 9.1 Timing of Cash Flows
    3. 9.2 Unequal Payments Using a Financial Calculator or Microsoft Excel
    4. Summary
    5. Key Terms
    6. CFA Institute
    7. Multiple Choice
    8. Review Questions
    9. Problems
    10. Video Activity
  11. 10 Bonds and Bond Valuation
    1. Why It Matters
    2. 10.1 Characteristics of Bonds
    3. 10.2 Bond Valuation
    4. 10.3 Using the Yield Curve
    5. 10.4 Risks of Interest Rates and Default
    6. 10.5 Using Spreadsheets to Solve Bond Problems
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  12. 11 Stocks and Stock Valuation
    1. Why It Matters
    2. 11.1 Multiple Approaches to Stock Valuation
    3. 11.2 Dividend Discount Models (DDMs)
    4. 11.3 Discounted Cash Flow (DCF) Model
    5. 11.4 Preferred Stock
    6. 11.5 Efficient Markets
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  13. 12 Historical Performance of US Markets
    1. Why It Matters
    2. 12.1 Overview of US Financial Markets
    3. 12.2 Historical Picture of Inflation
    4. 12.3 Historical Picture of Returns to Bonds
    5. 12.4 Historical Picture of Returns to Stocks
    6. Summary
    7. Key Terms
    8. Multiple Choice
    9. Review Questions
    10. Video Activity
  14. 13 Statistical Analysis in Finance
    1. Why It Matters
    2. 13.1 Measures of Center
    3. 13.2 Measures of Spread
    4. 13.3 Measures of Position
    5. 13.4 Statistical Distributions
    6. 13.5 Probability Distributions
    7. 13.6 Data Visualization and Graphical Displays
    8. 13.7 The R Statistical Analysis Tool
    9. Summary
    10. Key Terms
    11. CFA Institute
    12. Multiple Choice
    13. Review Questions
    14. Problems
    15. Video Activity
  15. 14 Regression Analysis in Finance
    1. Why It Matters
    2. 14.1 Correlation Analysis
    3. 14.2 Linear Regression Analysis
    4. 14.3 Best-Fit Linear Model
    5. 14.4 Regression Applications in Finance
    6. 14.5 Predictions and Prediction Intervals
    7. 14.6 Use of R Statistical Analysis Tool for Regression Analysis
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  16. 15 How to Think about Investing
    1. Why It Matters
    2. 15.1 Risk and Return to an Individual Asset
    3. 15.2 Risk and Return to Multiple Assets
    4. 15.3 The Capital Asset Pricing Model (CAPM)
    5. 15.4 Applications in Performance Measurement
    6. 15.5 Using Excel to Make Investment Decisions
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  17. 16 How Companies Think about Investing
    1. Why It Matters
    2. 16.1 Payback Period Method
    3. 16.2 Net Present Value (NPV) Method
    4. 16.3 Internal Rate of Return (IRR) Method
    5. 16.4 Alternative Methods
    6. 16.5 Choosing between Projects
    7. 16.6 Using Excel to Make Company Investment Decisions
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  18. 17 How Firms Raise Capital
    1. Why It Matters
    2. 17.1 The Concept of Capital Structure
    3. 17.2 The Costs of Debt and Equity Capital
    4. 17.3 Calculating the Weighted Average Cost of Capital
    5. 17.4 Capital Structure Choices
    6. 17.5 Optimal Capital Structure
    7. 17.6 Alternative Sources of Funds
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  19. 18 Financial Forecasting
    1. Why It Matters
    2. 18.1 The Importance of Forecasting
    3. 18.2 Forecasting Sales
    4. 18.3 Pro Forma Financials
    5. 18.4 Generating the Complete Forecast
    6. 18.5 Forecasting Cash Flow and Assessing the Value of Growth
    7. 18.6 Using Excel to Create the Long-Term Forecast
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  20. 19 The Importance of Trade Credit and Working Capital in Planning
    1. Why It Matters
    2. 19.1 What Is Working Capital?
    3. 19.2 What Is Trade Credit?
    4. 19.3 Cash Management
    5. 19.4 Receivables Management
    6. 19.5 Inventory Management
    7. 19.6 Using Excel to Create the Short-Term Plan
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Video Activity
  21. 20 Risk Management and the Financial Manager
    1. Why It Matters
    2. 20.1 The Importance of Risk Management
    3. 20.2 Commodity Price Risk
    4. 20.3 Exchange Rates and Risk
    5. 20.4 Interest Rate Risk
    6. Summary
    7. Key Terms
    8. CFA Institute
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  22. Index

Learning Outcomes

By the end of this section, you will be able to:

  • Explain the benefits of diversification.
  • Describe the relationship between risk and return for large portfolios.
  • Compare firm-specific and systematic risk.
  • Discuss how portfolio size impacts risk.

Diversification

So far, we have looked at the return and the volatility of an individual stock. Most investors, however, own shares of stock in multiple companies. This collection of stocks is known as a portfolio. Let’s explore why it is wise for investors to hold a portfolio of stocks rather than to pick just one favorite stock to own.

We saw that investors who owned DAL experienced an average annual return of 20.87% but also a large standard deviation of 51.16%. Investors who used all their funds to purchase DAL stock did exceptionally well during 2012–2014. But in 2020, those investors lost almost one-third of their money as COVID-19 caused a sharp reduction in air travel worldwide. To protect against these extreme outcomes, investors practice what is called diversification, or owning a variety of stocks in their portfolios.

Suppose, for example, you have saved $50,000 that you want to invest. If you purchased $50,000 of DAL stock, you would not be diversified. Your return would depend solely on the return on DAL stock. If, instead, you used $5,000 to purchase DAL stock and used the remaining $45,000 to purchase nine other stocks, you would be diversifying. Your return would depend not only on DAL’s return but also on the returns of the other nine stocks in your portfolio. Investors practice diversification to manage risk.

It is akin to the saying “Don’t put all of your eggs in one basket.” If you place all of your eggs in one basket and that basket breaks, all of your eggs will fall and crack. If you spread your eggs out across a number of baskets, it is unlikely that all of the baskets will break and all of your eggs will crack. One basket may break, and you will lose the eggs in that basket, but you will still have your other eggs. The same idea holds true for investing. If you own stock in a company that does poorly, perhaps even goes out of business, you will lose the money you placed in that particular investment. However, with a diversified portfolio, you do not lose all your money because your money is spread out across a number of different companies.

Table 15.7 shows the returns of investors who placed 50% of their money in DAL and the remaining 50% in LUV, XOM, or CVS. Notice that the standard deviation of returns is lower for the two-stock portfolios than for DAL as an individual investment.

    Two-Stock Portfolio
Year DAL DAL and LUV DAL and XOM DAL and CVS
2011 −35.79% −34.86% −8.56% −8.43%
2012 46.72% 33.38% 25.71% 33.50%
2013 132.61% 109.00% 76.36% 91.50%
2014 80.53% 103.50% 37.24% 58.83%
2015 4.05% 3.24% −4.37% 3.47%
2016 −1.35% 7.69% 9.27% −9.59%
2017 16.23% 24.32% 6.21% 5.24%
2018 −8.66% −18.47% −11.88% −7.85%
2019 20.38% 19.03% 13.81% 18.82%
2020 −30.77% −21.90% −33.49% −17.95%
Average 22.40% 22.49% 11.03% 16.75%
Std Dev 51.90% 49.11% 30.43% 35.10%
Table 15.7 Yearly Returns for DAL Versus a Two-Stock Portfolio Containing DAL and LUV, XOM, or CVS (data source: Yahoo! Finance)

As investors diversify their portfolios, the volatility of one particular stock becomes less important. XOM has good years with above-average returns and bad years with below-average (and even negative) returns, just like DAL. But the years in which those above-average and below-average returns occur are not always the same for the two companies. In 2014, for example, the return for DAL was greater than 80%, while the return for XOM was negative. On the other hand, in 2011, when DAL had a return of −35.15%, XOM had a positive return. When more than one stock is held, the gains in one stock can offset the losses in another stock, washing away some of the volatility.

When an investor holds only one stock, that one stock’s volatility contributes 100% to the portfolio’s volatility. When two stocks are held, the volatility of each stock contributes to the volatility of the portfolio. However, the volatility of the portfolio is not simply the average of the volatility of each stock held independently. How correlated the two stocks are, or how much they move together, will impact the volatility of the portfolio.

You will recall from our study of correlation in Regression Analysis in Finance that a correlation coefficient describes how two variables move relative to each other. A correlation coefficient of 1 means that there is a perfect, positive correlation between the two variables, while a correlation coefficient of −1 means that the two variables move exactly opposite of each other. Stocks that are in the same industry will tend to be more strongly correlated than stocks that are in much different industries. During the 2011–2020 time period, the correlation coefficient for DAL and LUV was 0.87, the correlation coefficient for DAL and XOM was 0.35, and the correlation coefficient for DAL and CVS was 0.79. Combining stocks that are not perfectly positively correlated in a portfolio decreases risk.

Notice that investors who owned DAL and LUV from 2011 to 2020 would have had a lower portfolio standard deviation, but not much lower, than investors who just owned DAL. Because the correlation coefficient is less than one, the standard deviation fell. However, because the two stocks are in the same industry and exposed to many of the same economic issues, the correlation coefficient is relatively high, and combining those two stocks provides only a small decrease in risk.

This is because, as airlines, DAL and LUV face many of the same market conditions. In years when the economy is strong, the weather is good, fuel prices are low, and people are traveling a lot, both companies will do well. When something such as bad weather conditions reduces the amount of air travel for several weeks, both companies are harmed. By holding LUV in addition to DAL, investors can reduce exposure to risk that is specific to DAL (perhaps a problem that DAL has with its reservation system), but they do not reduce exposure to the risk associated with the airline industry (perhaps rising jet fuel prices). DAL and LUV tend to experience positive returns in the same years and negative returns in the same years.

On the other hand, investors who added XOM to their portfolio saw a significantly lower standard deviation than those who held just DAL. In years when jet fuel prices rise, harming the profits of both DAL and LUV, XOM is likely to see high profits. Diversifying a portfolio across firms that are less correlated will reduce the standard deviation of the portfolio more.

Portfolio Size and Risk

As you add more stocks to a portfolio, the volatility, or standard deviation, of the portfolio decreases. The volatility of individual assets becomes less and less important. As we discussed earlier, the risk that is associated with events related to a particular company is called firm-specific risk, or unsystematic, risk. Examples of unsystematic risk would include a company facing a product liability lawsuit, a company inventing a new product, or accounting irregularities being detected. Holding a portfolio of stocks means that if one company you have invested in goes out of business because of poor management, you do not lose all your savings because some of your money is invested in other companies. Portfolio diversification protects you from being significantly impacted by unsystematic risk.

However, there is a level below which the portfolio risk does not drop, no matter how diversified the portfolio becomes. The risk that never goes away is known as systematic risk. Systematic risk is the risk of holding the market portfolio.

We have talked about reasons why a firm’s returns might be volatile; for example, the firm discovering a new technology or having a product liability lawsuit brought against it will impact that firm specifically. There are also events that broadly impact the stock market. Changes in the Federal Reserve Bank’s monetary policy and interest rates impact all companies. Geopolitical events, major storms, and pandemics can also impact the entire market. Investors in stocks cannot avoid this type of risk. This unavoidable risk is the systematic risk that investors in stocks have. This systematic risk cannot be eliminated through diversification.

In addition, as per research conducted by Meir Statman,4 the standard deviation of a portfolio drops quickly as the number of stocks in the portfolio increases from one to two or three (see Figure 2 illustration in this subsequent article by Statman for context). Increasing the size of the portfolio decreases the standard deviation, and thus the risk, of the portfolio. However, as the portfolio increases in size, the amount of risk reduced by adding one more stock to the portfolio will decrease. How many stocks does an investor need for a portfolio to be well-diversified? There is not an exact number that all financial managers agree on. A portfolio of 15 highly correlated stocks will offer less benefits of diversification than a portfolio of 10 stocks with lower correlation coefficients. A portfolio that consists of American Airlines, Spirit Airlines, United Airlines, Southwest Airlines, Delta Airlines, and Jet Blue, along with a few other stocks, is not very diversified because of the heavy concentration in the airline industry. The term diversified portfolio is a relative concept, but the average investor can create a reasonably diversified portfolio with approximately a dozen stocks.

Footnotes

  • 3Abigail Stevenson. “Jim Cramer Shares His #1 Rule for Investing.” Make It. CNBC, March 15, 2016. https://www.cnbc.com/2016/03/03/cramer-forget-sectors-a-better-way-to-diversify.html
  • 4Meir Statman. “How Many Stocks Make a Diversified Portfolio?” Journal of Financial and Quantitative Analysis 22, no. 3 (September 1987): 353–363. https://doi.org/10.2307/2330969
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