Financial Markets and Institutions (ch5) Risk and Rates of Return (ch7)

Spring 2013

Jin Q Jeon Assistant Professor of Finance

Dongguk Business School Dongguk University

Types of Financial Markets

Category 1. Category 2. New vs. Seasoned

security Primary Market Stocks/Bonds issued by company to investor Ex) IPO markets

Secondary Market Stocks/Bonds sold by investor to another investor Ex) KRX, Kosdaq..

Length of financial contract

Money market Financing repayable within one year Ex) call markets, CD (certificate deposit), CP (commercial papers)

Capital market Financing repayable in more than one year Ex) bond/stock markets

Type of repayment promise

Credit market trade credit, notes, and bonds that stipulate specific payments and/or interest Ex) banks, bond markets

Equity Market stocks that do not specify repayment but instead represent a claim on residual cash flows Ex) stock markets

What is an IPO?

Primary markets. An initial public offering (IPO) is where a company issues stoc

k in the public market for the first time. “Going public” enables a company’s owners to raise capital fro

m a wide variety of outside investors. Once issued, the stock trades in the secondary market.

Becoming public companies, they are subject to additional regulations and reporting requirements.

Interesting feature of IPOs? Usually the first day return is very high, especially when the market is ho

t. (Ex, 1999-2000, Kosdaq bubble).

Looking at our financial markets, can we obtain excess returns using any kind of information? i.e, do security prices currently reflect the following information ?

• Past prices • Publicly available information • Inside/private information

Versions of EMH

Weak-form efficient: past price/volume information is fully reflected. No excess return by using past price/volume information.

Semistrong-form efficient : public information is fully reflected. No excess return by using public information.

Strong-form efficient : private/inside information is fully reflected. No excess return by using private/inside information.

Which is true? It is generally agreed that the financial market is weak and semistrong-form (with some restrictions) efficient.

Efficient Market Hypothesis (EMH)

Cumulative Abnormal Returns (CARs) at the announcement of Takeover Attempts: Target Companies

Announcement of a takeover attempt is good news for the target firm and therefore should cause stock prices to jump.

The graph indicates a large and positive abnormal return immediately at the announcement, suggesting that public information is immediately included in the stock price. This is consistent with semi-strong efficiency

Test on Semi-strong Form

Implications of Market Efficiency

A chartist recommended you to purchase a stock by showing his analysis using the trend of its past prices. Can you expect an excess returns from this transactions?

You hear in the news that a medical research company successfully created a new medicine. Can you expect to take advantage of this information by purchasing the stock?

You have heard a company’s private information that it is going to create a electric automobile. Assume that the electric automobile market is going to be hot. Can you expect an excess return from this investment?

Behavioral Finance

Even if the market is efficient, are investors rational? Behavioral finance, a new and quickly growing theory, studies this.

Tow Possible Irrationalities Investors (both institutions and individuals) do not always process information correctly. Even if they do it correctly, they often make inconsistent or systematically suboptimal decisions.

Examples of Investors’ Irrationalities Herding

• Investors trade in the same directions as other investors without fundamental analysis.

Overconfidence / Conservatism • Investors tend to overestimate (underestimate) the precision of their beliefs

especially when the market is very good (bad). Prospect theory : loss aversion.

• Ex) Average stock return is 10% for 2 years. VS. Stock return is -10% this year but had +20% last year. Which sounds better?

Mental Accounting : use their own references • One may feel O.K with a loss of $1,000 in his/her account, but feels so bad

with a loss of $100 in the account dedicated to their child’s education.

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Return and Risk

The risk/return relationship is a fundamental concept in investment analysis. Given that future income from investments are uncertain, it is necessary that

we consider the combined influence on expected return (benefit) as well as on risk (cost).

Return-Risk Tradeoff : The principle that potential return rises with an increase in risk. Invested money can render higher profits only if it is subject to the possibility of being lost.

9

Return and Risk

Expected Return “best guess” estimate of how an investment will perform Weighted average of the probability distribution of possible returns. Using historical stock prices,

• Step 1) Historical return, rt= (Pt-Pt-1)/Pt-1 , Discrete return. Alternatively, ln (Pt/Pt-1) is used, continuously compounded return. • Step 2) Find the average of historical returns.

One can use the geometric average of returns, which is the compound return during a single period. This is usually used when we calculate the average buy-and-hold returns.

Risk :

Dispersion of returns • : Investment risk is related to the probability of earning a low or negative actual

return. The greater the chance of lower than expected or negative returns, the riskier the investment.

Measured by the standard deviation of returns (called, σ) • the normal fluctuations one can expect in that particular security above and below

the mean, or average .

E(R) and σ when the Probabilities are known

Firm A Firm B Economy Probability Rate of Return Conditions Strong 0.26 96% 23% Normal 0.51 12% 12% Weak 0.23 -83% -1% Expected Return 11.99% 11.87% Standard Deviations 62.53% 8.34%

Probability Distributions

A listing of all possible outcomes, and the probability of each occurrence. Which is the riskier stock?

Expected Rate of Return

Rate of Return (%) 100 15 0 -70

Firm X

Firm Y

Risk Aversion

Risk averse investors reject investment portfolios that produce the same expected return but higher risk.

These investors are willing to purchase risk-free assets. They will consider risky assets only when there is a risk premium.

Q1) Risk Averse investors prefer 1) or 2)? How about 3)?

Game 1) Receive $10 for certain. Game 2) Receive $ 20 with 50% and $0 with 50%

• What if an investor is risk-neutral, or is a risk-taker? Game 3) Receive $ 30 with 50% and $0 with 50%

Q2) True or False? Risk averse investors will never buy stocks (risky assets), but will invest

100% in bonds (safe assets).

Utility function for Risk Averse

What do we know from the graph?

U(100,000) > U(50,000)*50%+U(150,000)*50%=E(U(W)) , prefer no-risk.

If one has to choose B), his value of this game is not $100,000, but Wce (called, Certainty equivalent). The difference between 100,000 and Wce, which is y, represents his penalty for risky game (Risk Premium).

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Dominance Principle

1

2 3 4 Expected Return

Standard Deviation

• 2 dominates 1; has a higher return • 2 dominates 3; has a lower risk • 4 dominates 3; has a higher return How about 4 vs. 1, 4 vs. 2, or 3 vs. 1?

Portfolio Theory

Now, we combine individual assets to form portfolios.

Consider a simple portfolio consisting of two assets (A, B).

Expected returns of Portfolio (ERP )= wArA + (1 – wA) rB

W = weights (%) for each stocks, r = ER of each stocks

Standard Deviations of Portfolios ?

• Correlation coefficient Measure of co-movement of two assets Excel function : =correl (..)

Three-Security Portfolio

1 1 2 2 3 3( ) ( ) ( ) ( )pE r w E r w E r w E r= + +

Portfolio with more than 2 stocks

Portfolio with more than 3 stocks Difficult to calculate the standard variation

2

1 1( , )

n n

P i j i ji j

w w Cov r rσ= =

=∑ ∑

If we include more stocks in the portfolio,

Expected Portfolio Return

Risk, σp

Efficient Frontier

v

Efficient Frontier

Efficient frontier : the set of all efficient portfolios, which dominate all of securities or

portfolios below the line. Securities or portfolios on this line give the lowest risk while having

the same expected return (or, have the highest expected return of all portfolios in the markets having the same risk.

How can find the set of portfolios located in the EF? Not in this class.

Minimum Variance Portfolio (MVP)

Diversification Effects

We need to use the computer programming to calculate the risk of well-diversified portfolios. This is the result.

Breaking Down Sources of Risk

Total risk = Market risk + Diversifiable risk Market risk (Systematic risk, Undiversifiable risk, Beta) –

portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. Beta measures a stock’s market risk, and shows a stock’s volatility

relative to the market. • What is “the market”? Market Portfolio. We use the market index the

Kospi or Kosdaq index.

Diversifiable risk (Non-systematic risk, idiosyncratic risk, firm specific risk) – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

E(Rp)

σp

Rf

σm

E(Rm) M

N

X Q

A

Y

C

a

CML

CML : New Efficient Frontier with Risk-free assets

E(Rp)

σp

Rf

σm

E(Rm) M

N

X Q

A

Y

a

A line to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio

Efficient Frontier

B

C

What does the CML tell us? We cannot beat the market!! Riskfree asset + Market Portfolio new efficient frontier Tobin’s Separation theorem

Market portfolio (M)

-Only a theoretical concept. It includes every single possible available asset,

including stocks, bonds, real estate, and anything with any worth.

-Perfectly diversified portfolio.

- What do we use for the proxy of M ? Stock Indices.

CML :

Capital Asset Pricing Model (CAPM)

What is the relationship between return and risk for every security? Model linking market risk (beta) and returns. CAPM suggests that t

here is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification.

- (rM – rRF) : Market premium - rRF : Risk-free assets. (Treasury bills in the U.S, Call or 국공채 in

Korea)

Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.

Here, ri is called “Required Rate of Returns” representing the minimum rate of return from shareholders who consider risk.

Beta

Beta

Calculating Beta of individual stocks A typical approach to estimate beta is to run a regression of the security’s past

returns against the past returns of the market (again, indices). The slope of the regression line is defined as the beta coefficient for the

security.

Calculating Beta of portfolios The beta of a portfolio is the weighted average of each of the stock’s betas.

bP = wAbA + wBbB + ….

Comments on Beta If beta = 1.0, the security is just as risky as the market. If beta > 1.0, the security is riskier than average. If beta < 1.0, the security is less risky than average. Most stocks have betas in the range of 0.5 to 1.5.

CAPM

Securities Market Line

Market Portfolio.

CAPM

Undervalued or Overvalued?

Expected Return> Required Return, So, it is undervalued.

Expected Return< Required Return, So, it is overvalued.

Discussions

It is impossible to find the “REAL” M. So, we have questioned its validity (Roll’s Critique)

Investors seem to be concerned with both market risk and total risk. Can we perfectly eliminate the firm-specific risk? Maybe not. Therefore, the SML may not produce a correct estimate of RRR.

Betas are calculated using historical data.

A company’s historical data may not reflect investors’ expectations about future riskiness.

Other models are being developed that will one day replace the CAPM, but it still provides a good framework for thinking about risk and return.

Try these

Portfolio Today 1 year later

Market value Weight of Market Market value Weight of Market

A 20000 1% 25300 1.1%

B 80000 4% 96600 4.2%

Portfolio ER Stdev Rho(i, market)

C 12% 25% 0.4

D 16% 40% 0.75

1] Under the CAPM holds, consider two well-diversified portfolios, A, B as follow. Find the betas of A and B Consider portfolio C of which beta is 0.9 and the expected return is 19%. According to the CAPM, is C’s expected return determined properly?

2] Portfolio A and B are located on the CML. The expected return and standard deviation of A are both 10%. If B’s standard deviation is 30%, what is its expected return? Assume the market expected return is 14% and risk-free rate is 6%. Plot the following two portfolios C and D on the CML and SML floor plan and find whether they are undervalued or overvalued.

Exercises

Product Demand Probability Stock #1 Stock #2 Stock #3 High 20% 30% 20% 15% Medium 60% 12% 14% 10% Low 20% -10% -5% -2%

Calculate the expected return, variance, and standard deviation for the stocks in the table below.

You analyze the prospects of several companies and come to the following conclusions about the expected return on each: Stock Expected Return Starbucks 18% Sears 8% Microsoft 16% Limited Brands 12% You decide to invest $4,000 in Starbucks, $6,000 in Sears, $12,000 in Microsoft, and $3,000 in Limited Brands. What is the expected return on your portfolio?

A particular stock sells for $30. The stock’s beta is 1.25, the risk-free rate is 4%, and the expected return on the market portfolio is 10%. If you forecast that the stock will be worth $33 next year (assume no dividends), should you buy the stock or not?

Try questions in the textbook. (pp. 147) 5-3, 5-9, 5-10, (pp. 215) 7-1, 7-2, 7-3, 7-4, 7-5, 7-7, 7-9, 7-10, 7-15, 7-23