Investment Analysis Investment Analysis Bus350Bus350

Return and Risk Return and Risk CalculationCalculation

• Professor Tao WangProfessor Tao Wang

• Tel: x5445Tel: x5445

• E-mail: tao_wang@qc.eduE-mail: tao_wang@qc.edu

• Room: PH154Room: PH154

• Office Hour: W, F 12:15pm – 1:15pmOffice Hour: W, F 12:15pm – 1:15pm

• Coursepage: Coursepage: http://www.qc.edu/~twang/course/3http://www.qc.edu/~twang/course/350/investments.html50/investments.html. Announcements, homework, cases, . Announcements, homework, cases, exam dates are all on the webpage.exam dates are all on the webpage.

Course OverviewCourse Overview

• Book: Book: Investment Analysis and Investment Analysis and Portfolio ManagementPortfolio Management by Reilly and by Reilly and BrownBrown

• CFA-designated TextbookCFA-designated Textbook

• Group case (10%), three homework Group case (10%), three homework (5%), two midterms (50%) and one (5%), two midterms (50%) and one final (30%). Class participation is final (30%). Class participation is 5%.5%.

ContentsContents

• Calculate return and risk based on Calculate return and risk based on distribution for a single assetdistribution for a single asset

• Calculate return and risk for a portfolio of Calculate return and risk for a portfolio of assetsassets

• Holding Period ReturnHolding Period Return

• Real life indicesReal life indices

• Calculate return and risk from index Calculate return and risk from index example, geometric mean and arithmetic example, geometric mean and arithmetic mean comparisonmean comparison

Probability Distributions of Probability Distributions of ReturnsReturns

• Assume that there are two stock Assume that there are two stock available, GENCO and RISCO, and available, GENCO and RISCO, and each responds to the state of the each responds to the state of the economy according to the following economy according to the following tabletable

Returns on GENCO & Returns on GENCO & RISCORISCO

State ofEconomy

Return onRISCO

Return onGENCO

Prob-ability

Strong 50% 30% 0.20

Normal 10% 10% 0.60

Weak -30% -10% 0.20

•50%•30%

•10%•-10%

•-30%

•RISCO

•GENCO•0

•0.1

•0.2

•0.3

•0.4

•0.5

•0.6

•Probability

•Return

•Probability Distributions of Returns of GENCO and RISCO

ObservationObservation

• Both companies have the same Both companies have the same expected return, but there is expected return, but there is considerably more risk associated considerably more risk associated with RISCOwith RISCO

Equations: MeanEquations: Mean

%10

: Also

%1010.0

)10.0(2.010.06.03.02.0

...

1

332211

RISCO

GENCO

GENCO

r

r

r

n

iii

nnr

rP

rPrPrPrPrE

rP

Equations: Standard Equations: Standard DeviationDeviation

2530.0

: Also

1265.0016.0

)10.010.0(2.010.010.06.010.030.02.0

...

222

1

2

2222

211

2

RISCO

GENCO

GENCO

r

r

r

n

irii

rnnrr

r

rP

rPrPrP

rErE

ObservationObservation

• The expected returns of GENCO and The expected returns of GENCO and RISCO happen to be equal, but the RISCO happen to be equal, but the volatility, or standard deviation, of volatility, or standard deviation, of RISCO is twice that of GENCO’sRISCO is twice that of GENCO’s

• Which stock would a typical investor Which stock would a typical investor preferprefer

ExampleExample1.1. Calculate the expected return and standard Calculate the expected return and standard

deviation of the following stock A:deviation of the following stock A:

StateState ProbabilityProbability ReturnReturn

11 20%20% 15%15%

22 60%60% 10%10%

33 20%20% -8%-8%

The mean is 0.2*0.15+0.6*0.1+0.2*(-0.08) = 7.4%The mean is 0.2*0.15+0.6*0.1+0.2*(-0.08) = 7.4%

The standard deviation is:The standard deviation is:

S.D. = Sqrt[0.2*(0.15-0.074)^2+0.6*(0.1-S.D. = Sqrt[0.2*(0.15-0.074)^2+0.6*(0.1-0.074)^2+0.2*(-0.08-0.074)^2] = 7.9%0.074)^2+0.2*(-0.08-0.074)^2] = 7.9%

Portfolio Return and RiskPortfolio Return and Risk

• Suppose you invest in two assets: Suppose you invest in two assets: stocks and bonds.stocks and bonds.

• Stocks offer a return of 10% with Stocks offer a return of 10% with standard deviation of 15%standard deviation of 15%

• Bonds offer a return of 6% with Bonds offer a return of 6% with standard deviation of 8%standard deviation of 8%

Portfolio weightPortfolio weight

• If the investment weight on stocks is If the investment weight on stocks is 50%, on bonds is 50%, what’s the 50%, on bonds is 50%, what’s the return on the portfolio?return on the portfolio?

• What about the risk of the portfolio?What about the risk of the portfolio?

Holding Period ReturnHolding Period Return

15.0 $200

10200$220

Price Beginning

Dividend Price Beginning-Price EndingHPR

Measures of Measures of Historical Rates of Historical Rates of ReturnReturn

yields period holding

annual of sum the HPR

:where

HPR/AM

:Mean Arithmetic

n

Measures of Measures of Historical Rates of Historical Rates of ReturnReturn• Geometric MeanGeometric Mean

n

n

HPR1HPR1HPR1

:follows as returns period holding

annual theofproduct the

:where

1HPR)(1GM

21

1

• Arithmetic mean is used for Arithmetic mean is used for forecasting future returnsforecasting future returns

• Geometric mean is used to calculate Geometric mean is used to calculate real past returnsreal past returns

• Geometric mean has upward biasGeometric mean has upward bias

Measure volatilityMeasure volatility

• Historical volatilityHistorical volatility– Standard deviationStandard deviation

– Realized volatilityRealized volatility

• Future volatilityFuture volatility

Stylized factsStylized facts

• Stock/Bond returns are fairly Stock/Bond returns are fairly difficult to predictdifficult to predict

• But return volatilities are But return volatilities are predictable to a degreepredictable to a degree

Yahoo financeYahoo finance

• Most indices historical data can be Most indices historical data can be downloaded from downloaded from http://finance.yahoo.comhttp://finance.yahoo.com