Investment Analysis Bus350 Return and Risk Calculation
description
Transcript of Investment Analysis Bus350 Return and Risk Calculation
![Page 1: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/1.jpg)
Investment Analysis Investment Analysis Bus350Bus350
Return and Risk Return and Risk CalculationCalculation
![Page 2: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/2.jpg)
• Professor Tao WangProfessor Tao Wang
• Tel: x5445Tel: x5445
• E-mail: [email protected]: [email protected]
• 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.
![Page 3: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/3.jpg)
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%.
![Page 4: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/4.jpg)
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
![Page 5: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/5.jpg)
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
![Page 6: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/6.jpg)
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
![Page 7: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/7.jpg)
•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
![Page 8: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/8.jpg)
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
![Page 9: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/9.jpg)
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
![Page 10: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/10.jpg)
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
![Page 11: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/11.jpg)
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
![Page 12: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/12.jpg)
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%
![Page 13: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/13.jpg)
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%
![Page 14: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/14.jpg)
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?
![Page 15: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/15.jpg)
Holding Period ReturnHolding Period Return
15.0 $200
10200$220
Price Beginning
Dividend Price Beginning-Price EndingHPR
![Page 16: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/16.jpg)
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
![Page 17: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/17.jpg)
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
![Page 18: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/18.jpg)
• 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
![Page 19: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/19.jpg)
Measure volatilityMeasure volatility
• Historical volatilityHistorical volatility– Standard deviationStandard deviation
– Realized volatilityRealized volatility
• Future volatilityFuture volatility
![Page 20: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/20.jpg)
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
![Page 21: Investment Analysis Bus350 Return and Risk Calculation](https://reader035.fdocuments.us/reader035/viewer/2022062722/56813b22550346895da3ddbb/html5/thumbnails/21.jpg)
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