Capital Market Theory

Question 1

Common Risk

Answer 1

Risk that is perfectly correlated • Risk that affects all securities

Question 2

Independent Risk

Answer 2

Risk that is uncorrelated • Risk that affects a particular security

Question 3

How to Identify Inefficient Portfolios

Answer 3

In an inefficient portfolio, it is possible to find another portfolio that is better in terms of both expected return and volatility.

Question 4

How to Identify Efficient Portfolios

Answer 4

In an efficient portfolio there is no way to reduce the volatility of the portfolio without lowering its expected return.

Question 5

Volatility Versus Expected Return for Portfolios of Intel and Coca-Cola Stock，which portfolio would you recommend?

Answer 5

• Efficient Portfolios with Two Stocks

– Consider investing 100% in Coca-Cola stock. As shown in on the previous slide, other portfolios—such as the portfolio with 20% in Intel stock and 80% in Coca-Cola stock— make the investor better off in two ways: It has a higher expected return, and it has lower volatility. As a result, investing solely in Coca-Cola stock is inefficient.

Question 6

The Effect of Correlation

Answer 6

• Correlation has no effect on the expected return of a portfolio. However, the volatility of the portfolio will differ depending on the correlation.
• The lower the correlation, the lower the volatility we can obtain. As the correlation decreases, the volatility of the portfolio falls.
• The curve showing the portfolios will bend to the left to a greater degree as shown on the next slide.

Question 7

Volatility and Expected Return:

Effect on Volatility and Expected Return of Changing the Correlation between Intel and Coca-Cola Stock, draw the picture.

Answer 7

Effect on Volatility and Expected Return of Changing the Correlation between Intel and Coca-Cola Stock

Question 8

Draw the picture of Efficient Portfolio: Only 2 risky assets are available

Answer 8

A rational investor only would select an efficient portfolio from the efficient frontier

Question 9

What is “Long Position”多头、看涨?

Answer 9

A positive investment in a security

Question 10

What is “Short Position” 空头、看空？

Answer 10

– A negative investment in a security

– In a short sale, you sell a stock that you do not own and then buy that stock back in the future.

– Short selling is an advantageous strategy if you expect a stock price to decline in the future.

Question 11

Suppose you have $20,000 in cash to invest. You short sell $10,000 worth of cola stock and invest the proceeds you get from the short sell, plus your $20,000 in Intel. What is the expected return and volatility of your portfolio?

Answer 11

Question 12

Efficient Portfolios with Many Stocks:

Consider adding Bore Industries to the two stock portfolio:

Answer 12

Although Bore has a lower return and the same volatility as Coca-Cola, it still may be beneficial to add Bore to the portfolio for the diversification benefits.

Question 13

3 risky assets are available, what is the picture?

Answer 13

• Adding another investment (example: commodities with expected return and volatility of 15% each) offers additionally more feasible portfolios (opportunity set)
• A new efficient frontier results (it is more efficient compared to the 2 asset case)

Question 14

According to the picture below, is many risky assets are available, what is the picture?

Answer 14

With many risky assets available, then the opportunity set and efficient frontier looks like the following:

Question 15

1. What is Firm Specific News？
2. What is Market-Wide News？
3. What is Independent Risks？
4. What is Common Risks？

Answer 15

1. Firm Specific News：Good or bad news about an individual company
2. Firm Specific News：News that affects all stocks, such as news about the economy
3. Independent Risks：Due to firm-specific news

– Also known as: » Firm-Specific Risk » Idiosyncratic Risk » Unique Risk » Unsystematic Risk » Diversifiable Risk

4. Common Risks： Due to market-wide news

– Also known as: » Systematic Risk » Undiversifiable Risk » Market Risk

– When many stocks are combined in a large portfolio, the firm-specific risks for each stock

will average out and be diversified.

– The systematic risk, however, will affect all firms and will not be diversified.

Question 16

Firm-Specific Versus Systematic Risk：

Consider two types of firms:

• Type S firms are affected only by systematic risk. There is a 50% chance the economy will be strong and type S stocks will earn a return of 40%; There is a 50% change the economy will be weak and their return will be –20%. Because all these firms face the same systematic risk, holding a large portfolio of type S firms will not diversify the risk.
• Type I firms are affected only by firm-specific risks. Their returns are equally likely to be 35% or –25%, based on factors specific to each firm’s local market. Because these risks are firm specific, if we hold a portfolio of the stocks of many types I firms, the risk is diversified.

What is the volatility of the average return of ten type S firms? What is the volatility of the average return of ten type I firms?

Answer 16

Actual firms are affected by both market-wide risks and firm-specific risks. When firms carry both types of risk, only the unsystematic risk will be diversified when many firm’s stocks are combined into a portfolio. The volatility will therefore decline until only the systematic risk remains.

Question 17

Risk Premium

Answer 17

The risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk.

– If the diversifiable risk of stocks were compensated with an additional risk premium, then investors could buy the stocks, earn the additional premium, and simultaneously diversify and eliminate the risk.

– By doing so, investors could earn an additional premium without taking on additional risk. This opportunity to earn something for nothing would quickly be exploited and eliminated. Because investors can eliminate firm-specific risk “for free” by diversifying their portfolios, they will not require or earn a reward or risk premium for holding it.

The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk

– This implies that a stock’s volatility, which is a measure of total risk (that is, systematic risk plus diversifiable risk), is not especially useful in determining the risk premium that investors will earn.​

Question 18

Standard deviation

Answer 18

Standard deviation as a measure of volatility is not an appropriate measure of risk for an individual security. There should be no clear relationship between volatility and average returns for individual securities. Consequently, to estimate a security’s expected return, we need to find a measure of a security’s systematic risk.

Question 19

Diversifiable VS Systematic risk

Answer 19

Question 20

What is Beta(β)？

Answer 20

• Sensitivity to Systematic Risk: Beta (β)
– The expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio.

• Beta differs from volatility. Volatility measures total risk (systematic plus unsystematic risk), while beta is a measure of only systematic risk.

Question 21

• Estimating Beta
• Interpreting Beta (β)

Answer 21

– A security’s beta is related to how sensitive its underlying revenues and cash flows are to general economic conditions. Stocks in cyclical industries are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries.

Question 22

Estimating the Risk Premium

Answer 22

– Market risk premium

• The market risk premium is the reward investors expect to earn for holding a portfolio with a beta of 1.

• Adjusting for Beta
– Estimating a Traded Security’s Cost of Capital of an investment from Its Beta

Question 23

Expected Return and Beta

Answer 23

Question 24

• Problem

– Assume the economy has a 60% chance of the market return will 15% next year and a

40% chance the market return will be 5% next year.

– Assume the risk-free rate is 6%.

– If Microsoft’s beta is 1.18, what is its expected return next year?

Answer 24

Question 25

Identifying the Tangent Portfolio

Answer 25

**• Combinations of the risk-free asset and the tangent portfolio provide the best risk and return tradeoff available to an investor.** – This means that the tangent portfolio is efficient and that all efficient portfolios are combinations of the risk-free investment and the tangent portfolio. Every investor should invest in the tangent portfolio independent of his or her taste for risk. **• An investor’s preferences will determine only how much to invest in the tangent portfolio versus the risk-free investment.** – Conservative investors will invest a small amount in the tangent portfolio. – Aggressive investors will invest more in the tangent portfolio. – Both types of investors will choose to hold the same portfolio of risky assets, the tangent portfolio, which is the efficient portfolio.

Question 26

Optimal Portfolio Choice

Answer 26

Question 27

Portfolio Improvement: Beta and the Required Return – Assume there is a portfolio of risky securities, P. To determine whether P has the highest possible slope, consider whether its slope could be raised by adding more of some investment i to the portfolio. – The contribution of investment i to the volatility of the portfolio depends on the risk that i has in common with the portfolio, which is measured by i’s volatility multiplied by its correlation with P.

Answer 27

• Portfolio Improvement: Beta and the Required Return –Increasing the amount invested in i will increase the slope of portfolio P if its expected return E[Ri] exceeds the required return r_i , which is given by:公式 – Required Return of i • The expected return that is necessary to compensate for the risk investment i will contribute to the portfolio.

Question 28

Required Return of a new Investment

Answer 28

Question 29

Expected Returns and the Efficient Portfolio

Answer 29

– A portfolio is efficient if and only if the expected return of every available security equals its required return.

Question 30

The Capital Asset Pricing Model

Answer 30

* The Capital Asset Pricing Model (CAPM) allows us to identify the efficient portfolio of risky assets without having any knowledge of the expected return of each security. * Instead, the CAPM uses the optimal choices investors make to identify the efficient portfolio as the market portfolio, the portfolio of all stocks and securities in the market. * The market portfolio is the efficient portfolio. * The risk premium for any security is proportional to its beta with the market.

Question 32

The CAPM Assumptions

Answer 32

– Assumption 1• Investors can buy and sell all securities at competitive market prices (without incurring taxes or transactions costs) and can borrow and lend at the risk-free interest rate. – Assumption 2• Investors hold only efficient portfolios of traded securities—portfolios that yield the maximum expected return for a given level of volatility. – Assumption 3：Investors have **homogeneous expectations** regarding the volatilities, correlations, and expected returns of securities. * Homogeneous Expectations-- All investors have the same estimates concerning future investments and returns.

Question 33

The Capital Market Line：Optimal Investing

Answer 33

• When the CAPM assumptions hold, an optimal portfolio is a combination of the risk- free investment and the market portfolio. – When the tangent line goes through the market portfolio, it is called the **capital market line (CML).** • The expected return and volatility of a capital market line portfolio are:​公式

Question 34

Determining the Risk Premium

Answer 34

Question 35

Computing the expected return for a stock

Answer 35

Question 36

The Security Market Line

Answer 36

• There is a linear relationship between a stock’s beta and its expected return (See figure on next slide). The security market line (SML) is graphed as the line through the risk-free investment and the market. – According to the CAPM, if the expected return and beta for individual securities are plotted, they should all fall along the SML.

Question 37

The Capital Market Line and the Security Market Line, panel (a)

Answer 37

(a) The CML depicts portfolios combining the risk-free investment and the efficient portfolio, and shows the highest expected return that we can attain for each level of volatility. According to the CAPM, the market portfolio is on the CML and all other stocks and portfolios contain diversifiable risk and lie to the right of the CML, as illustrated for Exxon Mobil (XOM).

Question 38

The Capital Market Line and the Security Market Line, panel (b)

Answer 38

(b) The SML shows the expected return for each security as a function of its beta with the market. According to the CAPM, the market portfolio is efficient, so all stocks and portfolios should lie on the SML.

Question 39

Beta of a Portfolio

Answer 39

– The beta of a portfolio is the weighted average beta of the securities in the portfolio.