FINC-220 Lecture Notes - Lecture 10: Economic Equilibrium, Expected Return, Capital Asset Pricing Model

44 views10 pages

blackcrocodile4

8 May 2018

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Chapter 13

Return, risk and the security market line

Chapter outline

• Expected Returns and Variances

• Portfolios

• Announcements, Surprises, and Expected Returns

• Risk: Systematic and Unsystematic

• Diversification and Portfolio Risk

• Systematic Risk and Beta

• The Security Market Line

• The SML and the Cost of Capital: A Preview

Expected returns

• Expected returns are based on the probabilities of possible outcomes



ii RpRE

)(

find more resources at oneclass.com

Unlock document

This preview shows pages 1-3 of the document.
Unlock all 10 pages and 3 million more documents.

Already have an account? Log in

Example: expected returns

• Suppose you have predicted the following returns for stocks C and T in three possible

states of the economy.

What are the expected returns?

State Probability C T

Boom 0.3 15 25

Normal 0.5 10 20

Recession 0.2 2 1

RC = (15*0.3) + (10*0.5) + (2*0.2) = 9.9%

RT = (25*0.3) + (20*0.5) + (1*0.2) = 17.7%

• The three states of the economy still apply to stocks C and T.

• If the risk-free rate (from chapter 12) is 4.15%, what is the risk premium for C & T?

o RC = 9.9%

o RT =17.7%

o Stock C’s risk premium = 5.75%

o Stock T’s risk premium = 13.55%

Variance and standard deviation

• Variance and standard deviation measure the volatility of returns

• Weighted average of squared deviations

RERp

))((σ

Example: variance and standard deviation

What is the variance and standard deviation for C? for T?

State Probability C T

Boom 0.3 15 25

Normal 0.5 10 20

Recession 0.2 2 1

Expected return 9.9% 17.7%

Stock C

2 = .3(15-9.9)2 + .5(10-9.9) 2 + .2(2-9.9) 2 = 20.29

 = 4.50%

Stock T

2 = 74.41;  = 8.63%

find more resources at oneclass.com

Unlock document

This preview shows pages 1-3 of the document.
Unlock all 10 pages and 3 million more documents.

Already have an account? Log in

Practice example

Consider the following information:

State Probability ABC, Inc. (%)

Boom .25 15

Normal .50 8

Slowdown .15 4

Recession .10 - 3

What is the expected return, variance and standard deviation?

E(R) = 8.05%

Variance = σ2= 26.7475

σ = √ 26.7475 = 5.17%

Portfolios

• A portfolio is a collection of assets

• An asset’s risk and return are important in how they affect the risk and return of the

portfolio

Example: portfolio weight

Suppose you have $15,000 to invest and you have purchased securities in the following amounts:

What are your portfolio weights in each security?

.133, .200, .267, .400

Portfolio expected return and variance

• Compute the portfolio return for each state:

RP = w1R1 + w2R2 + … + wmRm

• Compute the expected portfolio return, the variance, and the standard deviation using the

same formula as for an individual asset

Example: portfolio variance

Consider the following information:

State Probability A B

Boom .4 30% -5%

Bust .6 -10% 25%

• What is the expected return for asset A?

o Asset A: E(RA) = .4(30) + .6(-10) = 6%

• What is the variance for asset A?

o Variance(A) = .4(30-6)2 + .6(-10-6)2 = 384

• What is the standard deviation for asset A?

o Std. Dev.(A) = 19.6%

Consider the following information:

State Probability A B

Boom .4 30% -5%

Bust .6 -10% 25%

• What is the expected return for asset B?

o Asset B: E(RB) = 13%

find more resources at oneclass.com

Unlock document

This preview shows pages 1-3 of the document.
Unlock all 10 pages and 3 million more documents.

Already have an account? Log in

Document Summary

Chapter outline: expected returns and variances, portfolios, announcements, surprises, and expected returns, risk: systematic and unsystematic, diversification and portfolio risk, systematic risk and beta, the security market line, the sml and the cost of capital: a preview. Expected returns: expected returns are based on the probabilities of possible outcomes n. Example: expected returns: suppose you have predicted the following returns for stocks c and t in three possible. Rc = (15*0. 3) + (10*0. 5) + (2*0. 2) = 9. 9% Rt = (25*0. 3) + (20*0. 5) + (1*0. 2) = 17. 7% 1: the three states of the economy still apply to stocks c and t. If the risk-free rate (from chapter 12) is 4. 15%, what is the risk premium for c & t: rc = 9. 9, rt =17. 7, stock c"s risk premium = 5. 75, stock t"s risk premium = 13. 55% Variance and standard deviation: variance and standard deviation measure the volatility of returns, weighted average of squared deviations.

Related Questions

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. Whatâs the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%

3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?

a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?

a.

1.0
b.

-1.0
c.

0.0
d.

0.5

5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate

7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, whatâs the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27

8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%

9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.

a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

What is the taxable equivalent yield on a municipal bond with a yield to maturity of 4.5 percent for an investor in the 39 percent marginal tax bracket?

1.76 percent

4.50 percent

7.38 percent

11.54 percent

Rank the following bonds in order from lowest credit risk to highest risk all with the same time to maturity, by their yield to maturity: JM Corporate bond with yield of 12.25 percent, IB Corporate bond with yield of 4.49 percent, TC Corporate bond with yield of 8.76 percent, and B&O Corporate bond with a yield of 5.99 percent.

JM bond, TC bond, B&O bond, IB bond

IB bond, B&O bond, TC bond, JM bond

TC bond, B&O bond, IB bond, JM bond

JM bond, IB bond, B&O bond, TC bond

A 5.75 percent coupon bond with 12 years left to maturity is offered for sale at $978.83. What yield to maturity is the bond offering? (Assume interest payments are paid semi-annually and par value is $1,000.)

3.00 percent

3.09 percent

5.75 percent

6.00 percent

A client in the 28 percent marginal tax bracket is comparing a municipal bond that offers a 3.25 percent yield to maturity and a similar-risk corporate bond that offers a 4.10 percent yield. Which bond will give the client more profit after taxes?

The municipal bond.

The corporate bond.

Both give the client equal profits after taxes.

There is not enough information given to determine answer.

Portfolio Weights An investor owns $15,000 of Adobe Systems stock, $15,500 of Dow Chemical, and $17,000 of Office Depot. What are the portfolio weights of each stock?

Adobe System = 0.3333, Dow Chemical = 0.3333, Office Depot = 0.3333

Adobe System = 0.3158, Dow Chemical = 0.3263, Office Depot = 0.3579

Adobe System = 0.3263, Dow Chemical = 0.3158, Office Depot = 0.3579

Adobe System = 0.2667, Dow Chemical = 0.3333, Office Depot = 0.4000

Portfolio Return Year-to-date, Company O had earned a -7.4 percent return. During the same time period, Company V earned 9.65 percent and Company M earned 2.68 percent. If you have a portfolio made up of 20 percent Company O, 40 percent Company V, and 40 percent Company M, what is your portfolio return?

4.93%

6.41%

3.45%

19.73%

Average Return The past five monthly returns for K and Company are 4.55 percent, 4.72 percent, -.65 percent, -.15 percent, and 9.30 percent. What is the average monthly return?

3.874%

1.614%

1.481%

3.554%

Portfolio Weights If you own 270 shares of Air Line Inc at $18.95, 170 shares of BuyRite at $9.9, and 370 shares of Motor City at $45.95, what are the portfolio weights of each stock?

Air Line = .2700, BuyRite = .1700, MotorCity = .3700

Air Line = .3333, BuyRite = .3333, MotorCity = .3333

Air Line = .3333, BuyRite = .2099, MotorCity = .4568

Air Line = .2150, BuyRite = .0707, MotorCity = .7143

Portfolio Return At the beginning of the month, you owned $6,500 of Company G, $8,900 of Company S, and $2,800 of Company N. The monthly returns for Company G, Company S, and Company N were 8.15 percent, -1.59 percent, and -.14 percent. What is your portfolio return?

2.14%

6.42%

3.29%

2.13%

The standard deviation of the past five monthly returns for PG Company are 2.75 percent, -0.75 percent, 4.15 percent, 6.29 percent, and 3.84 percent. What is the standard deviation?

2.309 percent

2.581 percent

3.256 percent

3.406 percent

Rank the following three stocks by their risk-return relationship, best to worst. Rail Haul has an average return of 10 percent and standard deviation of 19 percent. The average return and standard deviation of Idol Staff are 12 percent and 22 percent; and of Poker-R-Us are 11 percent and 25 percent.

Idol Staff, Rail Haul, Poker-R-Us

Rail Haul, Idol Staff, Poker-R-Us

Idol Staff, Poker-R-Us, Rail Haul

Poker-R-Us, Rail Haul, Idol Staff

Which of the following statements is correct?

A single stock has a lot of diversifiable risk.

A single stock has more market risk than a diversified portfolio of stocks.

Bonds and stocks have a high correlation because they are both financial assets.

None of these statements is correct.

Which of the following statements is correct with regards to diversification?

Diversifying reduces the return of the portfolio.

Diversifying reduces the market risk of the portfolio.

Diversifying reduces the dollar return of the portfolio.

None of these statements is correct.

Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns:

Economic State	Probability	Return
Fast Growth	.1	29%
Slow Growth	.8	14%
Recession	.1	-29%

14.0%

14.3%

11.2%

17.0%

Risk Premium If the annual return on the S&P 500 Index was 14.00 percent. The annual T-bill yield during the same period was 6.50 percent. What was the market risk premium during that year?

20.50%

14.00%

7.50%

6.50%

CAPM Required Return A company has a beta of .69. If the market return is expected to be 13.9 percent and the risk-free rate is 5.95 percent, what is the company's required return?

11.44%

15.54%

17.39%

9.59%

Portfolio Beta You have a portfolio with a beta of .94. What will be the new portfolio beta if you keep 40 percent of your money in the old portfolio and 60 percent in a stock with a beta of 1.54?

1.24

1.00

1.30

2.48

Under/Over Valued Stock A manager believes his firm will earn a 17.8 percent return next year. His firm has a beta of 1.68, the expected return on the market is 15.8 percent, and the risk-free rate is 5.8 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is under-valued or over-valued.

22.6%, under-valued

27.544%, under-valued

27.544%, over-valued

22.6%, over-valued

What is the taxable equivalent yield on a municipal bond with a yield to maturity of 4.5 percent for an investor in the 39 percent marginal tax bracket?

1.76 percent

4.50 percent

7.38 percent

11.54 percent

JM bond, TC bond, B&O bond, IB bond

IB bond, B&O bond, TC bond, JM bond

TC bond, B&O bond, IB bond, JM bond

JM bond, IB bond, B&O bond, TC bond

3.00 percent

3.09 percent

5.75 percent

6.00 percent

The municipal bond.

The corporate bond.

Both give the client equal profits after taxes.

There is not enough information given to determine answer.

Portfolio Weights An investor owns $15,000 of Adobe Systems stock, $15,500 of Dow Chemical, and $17,000 of Office Depot. What are the portfolio weights of each stock?

Adobe System = 0.3333, Dow Chemical = 0.3333, Office Depot = 0.3333

Adobe System = 0.3158, Dow Chemical = 0.3263, Office Depot = 0.3579

Adobe System = 0.3263, Dow Chemical = 0.3158, Office Depot = 0.3579

Adobe System = 0.2667, Dow Chemical = 0.3333, Office Depot = 0.4000

4.93%

6.41%

3.45%

19.73%

Average Return The past five monthly returns for K and Company are 4.55 percent, 4.72 percent, -.65 percent, -.15 percent, and 9.30 percent. What is the average monthly return?

3.874%

1.614%

1.481%

3.554%

Portfolio Weights If you own 270 shares of Air Line Inc at $18.95, 170 shares of BuyRite at $9.9, and 370 shares of Motor City at $45.95, what are the portfolio weights of each stock?

Air Line = .2700, BuyRite = .1700, MotorCity = .3700

Air Line = .3333, BuyRite = .3333, MotorCity = .3333

Air Line = .3333, BuyRite = .2099, MotorCity = .4568

Air Line = .2150, BuyRite = .0707, MotorCity = .7143

2.14%

6.42%

3.29%

2.13%

The standard deviation of the past five monthly returns for PG Company are 2.75 percent, -0.75 percent, 4.15 percent, 6.29 percent, and 3.84 percent. What is the standard deviation?

2.309 percent

2.581 percent

3.256 percent

3.406 percent

Idol Staff, Rail Haul, Poker-R-Us

Rail Haul, Idol Staff, Poker-R-Us

Idol Staff, Poker-R-Us, Rail Haul

Poker-R-Us, Rail Haul, Idol Staff

Which of the following statements is correct?

A single stock has a lot of diversifiable risk.

A single stock has more market risk than a diversified portfolio of stocks.

Bonds and stocks have a high correlation because they are both financial assets.

None of these statements is correct.

Which of the following statements is correct with regards to diversification?

Diversifying reduces the return of the portfolio.

Diversifying reduces the market risk of the portfolio.

Diversifying reduces the dollar return of the portfolio.

None of these statements is correct.

Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns:

Economic State	Probability	Return
Fast Growth	.1	29%
Slow Growth	.8	14%
Recession	.1	-29%

14.0%

14.3%

11.2%

17.0%

Risk Premium If the annual return on the S&P 500 Index was 14.00 percent. The annual T-bill yield during the same period was 6.50 percent. What was the market risk premium during that year?

20.50%

14.00%

7.50%

6.50%

CAPM Required Return A company has a beta of .69. If the market return is expected to be 13.9 percent and the risk-free rate is 5.95 percent, what is the company's required return?

11.44%

15.54%

17.39%

9.59%

1.24

1.00

1.30

2.48

22.6%, under-valued

27.544%, under-valued

27.544%, over-valued

22.6%, over-valued

lemoncrab271

What is the taxable equivalent yield on a municipal bond with a yield to maturity of 4.5 percent for an investor in the 39 percent marginal tax bracket?

1.76 percent

4.50 percent

7.38 percent

11.54 percent

JM bond, TC bond, B&O bond, IB bond

IB bond, B&O bond, TC bond, JM bond

TC bond, B&O bond, IB bond, JM bond

JM bond, IB bond, B&O bond, TC bond

3.00 percent

3.09 percent

5.75 percent

6.00 percent

The municipal bond.

The corporate bond.

Both give the client equal profits after taxes.

There is not enough information given to determine answer.

Portfolio Weights An investor owns $15,000 of Adobe Systems stock, $15,500 of Dow Chemical, and $17,000 of Office Depot. What are the portfolio weights of each stock?

Adobe System = 0.3333, Dow Chemical = 0.3333, Office Depot = 0.3333

Adobe System = 0.3158, Dow Chemical = 0.3263, Office Depot = 0.3579

Adobe System = 0.3263, Dow Chemical = 0.3158, Office Depot = 0.3579

Adobe System = 0.2667, Dow Chemical = 0.3333, Office Depot = 0.4000

4.93%

6.41%

3.45%

19.73%

Average Return The past five monthly returns for K and Company are 4.55 percent, 4.72 percent, -.65 percent, -.15 percent, and 9.30 percent. What is the average monthly return?

3.874%

1.614%

1.481%

3.554%

Portfolio Weights If you own 270 shares of Air Line Inc at $18.95, 170 shares of BuyRite at $9.9, and 370 shares of Motor City at $45.95, what are the portfolio weights of each stock?

Air Line = .2700, BuyRite = .1700, MotorCity = .3700

Air Line = .3333, BuyRite = .3333, MotorCity = .3333

Air Line = .3333, BuyRite = .2099, MotorCity = .4568

Air Line = .2150, BuyRite = .0707, MotorCity = .7143

2.14%

6.42%

3.29%

2.13%

The standard deviation of the past five monthly returns for PG Company are 2.75 percent, -0.75 percent, 4.15 percent, 6.29 percent, and 3.84 percent. What is the standard deviation?

2.309 percent

2.581 percent

3.256 percent

3.406 percent

Idol Staff, Rail Haul, Poker-R-Us

Rail Haul, Idol Staff, Poker-R-Us

Idol Staff, Poker-R-Us, Rail Haul

Poker-R-Us, Rail Haul, Idol Staff

Which of the following statements is correct?

A single stock has a lot of diversifiable risk.

A single stock has more market risk than a diversified portfolio of stocks.

Bonds and stocks have a high correlation because they are both financial assets.

None of these statements is correct.

Which of the following statements is correct with regards to diversification?

Diversifying reduces the return of the portfolio.

Diversifying reduces the market risk of the portfolio.

Diversifying reduces the dollar return of the portfolio.

None of these statements is correct.

Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns:

Economic State	Probability	Return
Fast Growth	.1	29%
Slow Growth	.8	14%
Recession	.1	-29%

14.0%

14.3%

11.2%

17.0%

Risk Premium If the annual return on the S&P 500 Index was 14.00 percent. The annual T-bill yield during the same period was 6.50 percent. What was the market risk premium during that year?

20.50%

14.00%

7.50%

6.50%

CAPM Required Return A company has a beta of .69. If the market return is expected to be 13.9 percent and the risk-free rate is 5.95 percent, what is the company's required return?

11.44%

15.54%

17.39%

9.59%

1.24

1.00

1.30

2.48

22.6%, under-valued

27.544%, under-valued

27.544%, over-valued

22.6%, over-valued

ultramarinelion8

FINC-220 Lecture Notes - Lecture 10: Economic Equilibrium, Expected Return, Capital Asset Pricing Model

Document Summary

Get access

Related Documents

FINA 2710 Chapter Notes - Chapter 12: Capital Asset Pricing Model, Economic Equilibrium, Risk Premium

COMM 2202 Lecture Notes - Lecture 13: Squared Deviations From The Mean, Expected Return, Standard Deviation

BSNS108 Lecture Notes - Capital Asset Pricing Model, Standard Deviation

Related Questions