BUA321 Chapter 8 Class notes

Risk and Return

• If you are thinking of investing in a stock, what things would you investigate?• What is inside trading?• What does this mean: “There is

no such thing as a free lunch”?

Stock Fraud

• Bernie Madoff http://www.youtube.com/watch?feature=player_detailpage&v=s68FR1MXT8Q

HPR

• Calculate the holding period return for TAP. Dividends totaled $3.90.

TAP closing pricesDate Close

4/1/2013 52.654/22/2010 44.36

Beginning Value $44.36Ending Value $52.65Investment Cash Flows $3.90Investment Time (Yrs) 3.000

Return 27.48%HPR (annualized return) 8.43%

Returns

• What does history tell us about stock returns?• How would you describe Risk?

Return distribution

• If you purchased a stock for $27 last year and this year it is worth $45. What was the return?

• Calculate the statistics for this asset. $45 Change % Predicted

pricePredicted Return

Probability

Next year Good economy

Average Economy

Bad Economy

Return distribution

• If you purchased a stock for $37 last year and this year it is worth $45. What was the return?

• Calculate the statistics for this asset. $45 Change % Predicted

priceProbability

Next year Good economy 15% 51.75 .30

Average Economy 7% 48.15 .60

Bad Economy -2% 44.10 .10

Economic Conditions Probability Asset AVery GoodGood 0.300 15.00%Average 0.600 7.00%Bad 0.100 -2.00%Very BadTotal Probabilities 1.000

Portfolio WeightsStatistics Asset AExpected Return 8.50%Variance 0.25%Standard Deviation 5.00%Coefficient of Var 0.59

Risk Example• Combine your prices with 2 other people.

Create 3 portfolios. Complete the following table.

Asset Expected return Standard Deviation CV

1

2

3

Port1

Port2

Port3

Portfolio Weights 0.50 0.30 0.20Statistics Asset A Asset B Asset C PortfolioExpected Return 8.50% 12.50% 4.70% 8.94%Variance 0.25% 0.26% 0.03% 0.19%Standard Deviation 5.00% 5.12% 1.62% 4.33%Coefficient of Var 0.59 0.41 0.34 0.48 Range 17.00% 15.00% 5.00%95% Confidence Interval High 18.31% 22.54% 7.87% 17.42%

Low -1.31% 2.46% 1.53% 0.46%

Efficient Frontier

• Combine 2 assets into a portfolio. Insert the picture of the efficient frontier of the portfolio.

What can you say about the information in the following table:

Terminology

• What is meant by “Do Not Put All Your Eggs in One Basket”

Calculate the return on the following portfolio:

Asset $ invested ReturnA 5,000 9%B 7,000 12%C 1,000 6%D 10,000 19%E 1,500 4%F 2,000 7%G 7,000 10%

Investment ($ or weights)Weights ReturnsA 5,000.00 0.149 9.000%B 7,000.00 0.209 12.000%C 1,000.00 0.030 6.000%D 10,000.00 0.299 19.000%E 1,500.00 0.045 4.000%F 2,000.00 0.060 7.000%G 7,000.00 0.209 10.000%H 0.000Portfolio Investment $33,500.00

Portfolio Return 12.388%

Portfolio

• What does correlation describe?• What does CAPM describe?• What things create diversifiable

risk? Non-diversifiable risk?• What is beta?

Portfolio Beta

Asset $ invested Return Beta

A 5,000 9% 1.25

B 7,000 12% 1.75

C 1,000 6% .54

D 10,000 19% 2.79

E 1,500 4% .32

F 2,000 7% .75

G 7,000 10% 1.95

Investment ($ or weights)Weights Returns BetasA 5,000.00 0.149 9.000% 1.250B 7,000.00 0.209 12.000% 1.750C 1,000.00 0.030 6.000% 0.540D 10,000.00 0.299 19.000% 2.790E 1,500.00 0.045 4.000% 0.320F 2,000.00 0.060 7.000% 0.750G 7,000.00 0.209 10.000% 1.950H 0.000Portfolio Investment $33,500.00

Portfolio Return 12.388%Portfolio Beta 1.868

CAPM and SML

• Use the beta of the above portfolio to calculate the expected return of a portfolio. Use the 30 year Treasury yield for the risk free rate and 12% for the average return of the market.

CAPM (SML)Risk Free Rate 3.490%Avg Return of Market 12.000%Portfolio Beta 1.868Ks (Expected Return) 19.387%Market Risk Premium

Group activity• Complete the following exercise– Find the expected returns for your individual asset

using this spreadsheet• Use the same market and RF returns

– You are given $100,000 to invest in your groups stocks

– Find the betas for you company and input into the portfolio beta and return worksheet

– Decide how much to invest in each asset– Calculate the expected returns for this portfolio

Numbers investors should know.

• http://youtu.be/SXLkP4_gX1Y

BUA321 Chapter 08 Web 80 points1) calculate the statistics for the following investments:

event Pr rx ry rz

very good .30 12 -8 8good .20 8 - 3 8Avg .25 2 6 8Bad.15 -5 10 8Very Bad .10 -10 19 8

Asset X Asset Y Asset ZE( R)

Variance

Standard deviation

CV

2) For the above assets, create the portfolios below

a) 40% X, 35% Y, 25% Zb) 60% X, 40% Yc) 35% Y, 65% Z

Portfolio a Portfolio b Portfolio c

E( R)

Variance

Standard deviation

CV

3) Calculate the portfolio statistics for the following assets:

weight return variance betaXYZ .35 12 7 1.23DEF.25 9 12 1.98HIJ .40 15 20 2.98

correlationXYZ DEFHIJXYZ 1.0 -.25.75DEF1.0 .45HIJ 1.0

Portfolio A (.35, .25, .40) Portfolio B (.45, .25, .30)Portfolio C (.10, .75, .15)

Portfolio A(.35, .25, .40)

Portfolio B(.45, .25, .30)

Portfolio C (.10, .75, .15)

E( R)

Variance Standard deviation

Beta CV

SML

4) If the risk free rate of return is 3.75% and the stock market averages 12%, What is the expected return on the portfolios using the SML?

A B

C

5) Go to Yahoo Finance• find your company. • Go to historical prices and download the past 5 years of

prices and dividends. (Hint select monthly prices, download, then select dividends only)

• a) delete all prices except the first month and the last month.• b) add all the dividends.• c) calculate the holding period return for your stock• d) combine this return with the returns of two other

classmates and insert in the table below.

Stock Ticker Return

e) Determine the growth and probabilities you expect in the upcoming economic conditions.

Economic condition Growth Probability

Very Good

Good

Average

Bad

Very Bad

f) Determine the expected returns one year from today using the above information

Economic condition

Stock 1 Stock 2 Stock 3

Very Good

Good

Average

Bad

Very Bad

g) create a portfolio using stocks and calculate the returns:

1) 1 & 22) 2 & 33) 1 & 3

Portfolio Returns Stand Deviation CV

1

2

3

h) copy and paste the efficient frontiers from the worksheet

SML• What are the betas of the company

stocks? • Create a portfolio using the three

stocks and calculate the portfolio beta.

Assets Betas Weights

• j) Use the beta above and the 30 year risk free rate and stock market average return of 12% the determine the expected return of the portfolio return.