Capital Markets, Asset Pricing, and Efficient Markets

Topic 4: Theory of Capital Markets / Asset Pricing Model / Efficient Market

Learning Outcomes

• Explain the Capital Asset Pricing Model (CAPM), Securities Market Line (SML), and other asset pricing models.
• Apply CAPM and SML in real scenarios.
• Understand the Efficient Market Hypothesis (EMH).

Return, Risk, and the Security Market Line

Dollar Returns

• The gain or loss from an investment is called the return on your investment.
• Return usually has two components:
  • Income component: Cash received directly while owning the investment (e.g., dividends).
  • Capital gain/loss: Change in the value of the asset.
• Example: Video Concept Company stock
  • Beginning of year price: $37 per share.
  • Bought 100 shares for a total outlay of $3,700.
  • Dividend: $1.85 per share.
  • Total dividend income: 1.85 \times 100 = $185

Dollar Returns (Continued)

• Value of stock rises to $40.33 per share by year-end; 100 shares are worth $4,033.
• Capital gain: ($40.33 - $37) \times 100 = $333
• Total dollar return: Dividend + Capital gain
• Example: Total dollar return = 185 + $333 = $518
• If sold at year-end, total cash would be initial investment + total return.

Percentage Returns

• Let $P<em>t$ be the stock price at the beginning of the year, and $D</em>{t+1}$ be the dividend paid during the year.
• Dividend yield: D{t+1} / Pt = $1.85 / $37 = 0.05, or 5%.
• Capital gains yield: (P{t+1} - Pt) / P_t = ($40.33 - $37) / $37 = $3.33 / $37 = 0.09, or 9%.
• For every dollar invested, get 5 cents in dividends and 9 cents in capital gains, totaling 14 cents on the dollar, or 14%.

Calculating Returns

Capital Asset Pricing Model (CAPM)

• CAPM measures the relationship between expected return and risk of investing in a security.
• Used to analyze securities and price them given the expected rate of return and cost of capital.
• Assumes investors hold fully diversified portfolios.
• Investors want a return on investment based on its systematic risk alone (beta).
• Minimum return required by investors (no risk) is called the risk-free rate of return.
• CAPM Equation:
  $R = r<em>f + \beta(r</em>m - r_f)$

The Capital Asset Pricing Model

• CAPM is the equation of the SML, showing the relationship between expected return and beta.
• Let $E(R<em>i)$ and $\beta</em>i$ stand for the expected return and beta, respectively, on any asset in the market.
• CAPM shows that the expected return for a particular asset depends on three things:
  1. Pure time value of money: Risk-free rate, $R_f$, is the reward for waiting for your money without taking risk.
  2. Reward for bearing systematic risk: Market risk premium, $E(R<em>M) - R</em>f$, is the reward for bearing an average amount of systematic risk.
  3. Amount of systematic risk: $\beta_i$, is the amount of systematic risk present in a particular asset or portfolio, relative to that in an average asset.

Security Market Line (SML)

• The security market line (SML) is a visual representation of the CAPM.
• Theoretical representation of the expected returns of assets based on systematic, non-diversifiable risk.
• Positively sloped, straight line displaying the relationship between expected return and beta.
• Market portfolio: A portfolio made up of all assets in the market, with expected return $E(R_M)$.
• All assets in the market must plot on the SML, so must a market portfolio made up of those assets.
• The market portfolio is representative of all assets in the market, so it must have average systematic risk (beta of 1).
• The slope of the SML is the market risk premium: $E(R<em>M) - R</em>f$
• SML Equation: $r<em>f + \beta(r</em>m - r_f)$

CML vs SML

The SML and the Cost of Capital: A Preview

• SML tells us the reward for bearing risk in financial markets.
• Benefit shareholders by finding investments with expected returns superior to what financial markets offer for the same risk (positive NPV).
• To determine if an investment has a positive NPV, compare its expected return to what the financial market offers for the same beta.
• Appropriate discount rate on a new project is the minimum expected rate of return an investment must offer to be attractive (cost of capital).
• An investment is attractive if its expected return exceeds that of investments with the same risk in financial markets; effectively using the internal rate of return (IRR) criterion.

Risk and Return

• CAPM: Theory of the relationship between risk and return; the expected risk premium on any security equals its beta times the market risk premium.
  • Market risk premium = $r<em>m - r</em>f$
  • Risk premium on any asset = $r - r_f$
  • Expected return = $r<em>f + \beta(r</em>m - r_f)$
• Example: Stock market return of 10%, risk-free rate of return of 3%. What is the risk premium for a stock with a beta of 0.5? What is the expected return of the stock?
  • Market risk premium = $0.10 - 0.03 = 0.07$
  • Risk premium on any asset = $0.5 \times 0.07 = 0.035$
  • Expected return = $0.03 + 0.035 = 0.065$

Expected Returns

• Based on probabilities of possible outcomes.
• "Expected" means average if the process is repeated many times.
• The "expected" return does not have to be a possible return.
• Formula: $E(R) = \sum<em>{i=1}^{n} p</em>i R_i$

Expected Return (Continued)

• Consider two stocks, L and U:
  • Stock L: expected return of 25%.
  • Stock U: expected return of 20%.
• Two equally likely states of the economy:
  • Boom: Stock L (70%), Stock U (10%).
  • Recession: Stock L (-20%), Stock U (30%).
• Expected return is the return on a risky asset expected in the future.

Expected Return (Continued) Calculations

• Expected return on Stock U, $E(R_U)$: $0.50 \times 30\% + 0.50 \times 10\% = 20\%$.
• Expected return on Stock L, $E(R_L)$: $0.50 \times -20\% + 0.50 \times 70\% = 25\%$.

Expected Return (Concluded)

• Projected risk premium: difference between the expected return on a risky investment and the risk-free rate.
• Risk-free investments offering 8% (R_f = 8\%$).
• Risk premium on Stock U: 20\% - 8\% = 12\%.
• Risk premium on Stock L: 25\% - 8\% = 17\%.

Calculating the Variance

• Stock U has an expected return of E(R_U) = 20\%$. Returns either 30$30\% - 20\% = 10\%$,$10\% - 20\% = -10\%.
• Variance: \sigma^2 = 0.50 \times 0.10^2 + 0.50 \times (-0.10)^2 = 0.01
• Standard deviation: \sigma = \sqrt{0.01} = 0.10$, or 10$50 / $200 = 0.25
• Percentage of the portfolio in the second asset is 150 / $200 = 0.75
• Portfolio weights are 0.25 and 0.75.

Portfolio Expected Returns

• Stocks L and U, with half the money in each. What is the pattern of returns on this portfolio? Expected return?
• Recession: R_P = 0.50 \times -20\% + 0.50 \times 30\% = 5\%.
• Boom: R_P = 0.50 \times 70\% + 0.50 \times 10\% = 40\%.
• Expected return on the portfolio, E(RP)$:$0.50 \times E(RL) + 0.50 \times E(R_U) = 0.50 \times 25\% + 0.50 \times 20\% = 22.5\%.
• With n assets in our portfolio, and xi stands for the percentage of money in Asset i, expected return is: E(RP) = \sum{i=1}^{n} xi E(R_i).

Portfolio Variance

• Variance on a portfolio is not generally a simple combination of the variances of the assets in the portfolio.
• Putting 2/11 (about 18%) in L and the other 9/11 (about 82%) in U. If a recession occurs, this portfolio will have a return of:
  R_P = (2/11) \times -20\% + (9/11) \times 30\% = 20.91\%.
• If a boom occurs, this portfolio will have a return of:
  R_P = (2/11) \times 70\% + (9/11) \times 10\% = 20.91\%.
• This portfolio would have a zero variance.

Expected and Unexpected Returns

• Return on stock is made up of two parts:
  1. Normal, or expected, return.
  2. Uncertain, or risky, part (unexpected information).
• Return on Flyers stock in the coming year: R = E(R) + U
  • R = actual total return.
  • E(R) = expected part of the return.
  • U = unexpected part of the return.

Announcements and News

• Flyers prospers when GDP grows at a relatively high rate and suffers when GDP is relatively stagnant.
• The government announces GDP figures for the year.
• The difference between actual result and forecast is called the innovation or the surprise.
• An announcement can be broken into two parts: the anticipated, or expected, part and the surprise, or innovation.

Systematic and Unsystematic Risk

• Systematic risk (market risk) influences many assets (general economic conditions, GDP, interest rates, or inflation).
• Unsystematic risk (unique or asset-specific risk) affects at most a small number of assets (oil strike announcement).
• The actual return broken down into its expected and surprise components:
  R = E(R) + U
• Since Total surprise component has systematic (m) and unsystematic ((epsilon)) components:
  R = E(R) + U = E(R) + m + \epsilon

The Principle of Diversification

• The principle of diversification implies some of the riskiness with individual assets can be eliminated by forming portfolios
• There is a minimum level of risk that cannot be eliminated by diversifying (i.e., non-diversifiable risk)

Diversification and Unsystematic Risk

• Some of the risk associated with individual assets can be diversified away and some cannot. Why is this so?
• When you combine assets into portfolios, the unique, or unsystematic, events—both positive and negative—tend to “wash out” once you have more than just a few assets.

Diversification and Systematic Risk

• Diversification cannot eliminate systematic risk
• Systematic risk affects almost all assets to some degree, so no matter how many assets we put into a portfolio, the systematic risk doesn’t go away
• The total risk of an investment, as measured by the standard deviation of its return, can be written as:
• Systematic risk is also called non-diversifiable risk or market risk
• Unsystematic risk is also called diversifiable risk, unique risk, or asset-specific risk

The Systematic Risk Principle

• States that the expected return on a risky asset depends only on that asset’s systematic risk
• Only the systematic portion of total risk is relevant in determining the expected return (and the risk premium) on that asset
• Level of systematic risk is measured using the beta coefficient, \beta
• An average asset has a beta of 1.0

Measuring Systematic Risk

• We use the beta coefficient

What does beta tell us?

• A beta of 1 implies the asset has the same systematic risk as the overall market
• A beta < 1 implies the asset has less systematic risk than the overall market
• A beta > 1 implies the asset has more systematic risk than the overall market

Portfolio Betas

• Portfolio beta calculated like a portfolio expected return
• If we had many assets in a portfolio, we would multiply each asset’s beta by its portfolio weight and then add the results to get the portfolio’s beta
• Example
• You put half of your money in Shopify and half in Coca-Cola. What would the beta of this combination be?

Beta and the Risk Premium

• Asset A has an expected return of E(RA) = 20\%$and a beta of$\betaA = 1.6$. The risk-free rate is$R_f = 8\%.
• If 25% of the portfolio is invested in Asset A, then the expected return is:
  *E(RP) = 0.25 \times E(RA) + (1 - 0.25) \times R_f = 0.25 \times 20\% + 0.75 \times 8\% = 11\%.
• The beta on the portfolio, \betaP, would be: *\betaP = 0.25 \times \beta_A + (1 - 0.25) \times 0 = 0.25 \times 1.6 = 0.40.

Beta and the Risk Premium (Continued)

• Percentage invested in Asset A exceed 100% if borrowed at risk-free rate
• Suppose an investor has $100 and borrows an additional $50 at 8 percent, the risk-free rate. The total investment in Asset A would be $150.
• The expected return in this case would be:
  E(RP) = 1.50 \times E(RA) + (1 - 1.50) \times R_f = 1.50 \times 20\% - 0.50 \times 8\% = 26\%.
• The beta on the portfolio would be:
  \betaP = 1.50 \times \betaA + (1 - 1.50) \times 0 = 1.50 \times 1.6 = 2.4

The Reward-to-Risk Ratio

[E(RA) - Rf] / \beta_A

The Basic Argument

• Asset B has a beta of 1.2 and an expected return of 16%. Which investment is better, Asset A or Asset B?
• Just as we did for Asset A, calculate different combinations of expected returns and betas for portfolios of Asset B and a risk-free asset
• If we put 25% in Asset B and the remaining 75% in the risk-free asset, the portfolio’s expected return will be:
  E(RP) = 0.25 \times E(RB) + (1 - 0.25) \times R_f = 0.25 \times 16\% + 0.75 \times 8\% = 10\%.
• Similarly, the beta on the portfolio, \betaP, will be: \betaP = 0.25 \times \beta_B + (1 - 0.25) \times 0 = 0.25 \times 1.2 = 0.30

The Fundamental Result

• No matter how many assets we have, the reward-to-risk ratio must be the same for all assets in the market.

Portfolio Risk

• Expected portfolio return: E(Rp) = x1 r1 + x2 r_2
• Portfolio variance: \sigmap^2 = x1^2 \sigma1^2 + x2^2 \sigma2^2 + 2 x1 x2 \rho{12} \sigma1 \sigma2

Example – portfolio return

You invest 60% of your portfolio in JNJ and 40% in Ford. The expected dollar return on your JNJ is 8.0% and on Ford is 18.8%. The expected return on your portfolio is:

• Expected return = (.60 \times 8.0) + (.40 \times 18.8) = 12.3\%

Example – portfolio risk with correlation coefficient one

You invest 60% of your portfolio in JNJ and 40% in Ford. The expected dollar return on your JNJ is 8.0% and on Ford is 18.8%. The standard deviation of their annualized daily returns are 13.2% and 31.0%, respectively. Assume a correlation coefficient of +1.0 and calculate the portfolio variance.

• Portfolio variance = [(.60)^2 \times (13.2)^2 ] + [(.40)^2 \times (31.0)^2 ] + 2(.40 \times .60 \times 1 \times 13.2 \times 31.0) = 412.90

• Standard deviation = \sqrt{412.90} = 20.3 \%

Example – portfolio risk with correlation coefficient 0.19

You invest 60% of your portfolio in JNJ and 40% in Ford. The expected dollar return on your JNJ is 8.0% and on Ford is 18.8%. The standard deviation of their annualized daily returns are 13.2% and 31.0%, respectively. Assume a correlation coefficient of 0.19 and calculate the portfolio variance.

• Portfolio variance = [(.60)^2 \times (13.2)^2 ] + [(.40)^2 \times (31.0)^2 ] + 2(.40 \times .60 \times 0.19 \times 13.2 \times 31.0) = 253.80

• Standard deviation = \sqrt{253.80} = 15.90 \%

Example – portfolio risk with correlation coefficient negative one

You invest 60% of your portfolio in JNJ and 40% in Ford. The expected dollar return on your JNJ is 8.0% and on Ford is 18.8%. The standard deviation of their annualized daily returns are 13.2% and 31.0%, respectively. Assume a correlation coefficient of -1.00 and calculate the portfolio variance.

• Portfolio variance = [(.60)^2 \times (13.2)^2 ] + [(.40)^2 \times (31.0)^2 ] + 2(.40 \times .60 \times -1 \times 13.2 \times 31.0) = 20.10

• Standard deviation = \sqrt{20.10} = 4.50 \%

Capital Budgeting and Project Risk

• The project cost of capital depends on the use to which the capital is being put
• Therefore, it depends on the risk of the project and not the risk of the company
• Company cost of capital:
  • Opportunity cost of capital for investment in the firm as a whole
  • The company cost of capital is the appropriate discount rate for an average-risk investment project undertaken by the firm

Example

• Based on the CAPM, ABC Company has a cost of capital of 17% [4 + 1.3(10)]. A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used?

  • 1/3 nuclear parts mfr. \beta = 2.0
  • 1/3 computer hard drive mfr. \beta = 1.3
  • 1/3 dog food production \beta = 0.6
  • Average \beta$$ of assets = 1.3

Solution

Reflects the opportunity cost of capital on an investment given the unique risk of the project

• r = 4 + 0.6(14 - 4) = 10%

Efficient Markets Hypothesis (EMH)

• Investment theory primarily derived from concepts attributed to Eugene Fama’s research
• It is virtually impossible to consistently “beat the market” – to make investment returns that outperform the overall market average as reflected by major stock indexes such as the S&P 500 Index
• Theory that suggests financial markets are efficient and incorporate all available information into asset prices.
• Impossible to consistently outperform the market by employing strategies such as technical analysis or fundamental analysis.

Forms of Efficient Market Hypothesis

• Weak Form
• Semi-Strong Form
• Strong Form

Forms of EMH:

– Weak Form:

• This form states that the stock prices indicate the public market information, and the past performance has nothing to do with future costs.

Semi-Strong Form:

• This form states that the stock prices reflect both the market and non-market public information.

Strong Form:

• This form says that public and private information instantly characterizes stock prices.

EFFICIENT MARKETS HYPOTHESIS-WEAK FORM

The weak form of the EMH assumes that the prices of securities reflect all available public market information but may not reflect new information that is not yet publicly available. It additionally assumes that past information regarding price, volume, and returns is independent of future prices.

The weak form EMH implies that technical trading strategies cannot provide consistent excess returns because past price performance can’t predict future price action that will be based on new information.

The weak form, while it discounts technical analysis, leaves open the possibility that superior fundamental analysis may provide a means of outperforming the overall market average return on investment.

EFFICIENT MARKETS HYPOTHESIS-SEMI STRONG FORM

The semi-strong form of the theory dismisses the usefulness of both technical and fundamental analysis.

The semi-strong form of the EMH incorporates the weak form assumptions and expands on this by assuming that prices adjust quickly to any new public information that becomes available, therefore rendering fundamental analysis incapable of having any predictive power about future price movements.

EFFICIENT MARKETS HYPOTHESIS-STRONG FORM

The strong form of the EMH holds that prices always reflect the entirety of both public and private information. This includes all publicly available information, both historical and new, or current, as well as insider information.

Even information not publicly available to investors, such as private information known only to a company’s CEO, is assumed to be always already factored into the company’s current stock price.

So, according to the strong form of the EMH, not even insider knowledge can give investors a predictive edge that will enable them to consistently generate returns that outperform the overall market average.

Summary of Risk and Return