Principles of Finance with Excel, 2nd edition

Instructor materials

Chapter 9Portfolio statistics

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Don’t be afraid!You need only minimal statistics for

Chapters 9 - 13.You can do it all in Excel!

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Finance conceptsHow to calculate stock returns and

adjust them for dividends and stock splits

Return mean, variance, and standard deviation for an asset

Return mean and variance for a portfolio of two assets

Regressions

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Excel functions and techniques

AverageVar and VarpStdev and StdevpCovar and CorrelTrendlines (Excel’s term for

regressions)Slope, Intercept, Rsq

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Main statistical conceptsMean, average, expected return: The

return you expect; here based on past returns. Denoted E(r) .

Variance of returns: A measure of the variability of returns. Denoted Var(r) or

2 .Standard deviation of returns:

Another measure of variability. Denoted .

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Main statistical concepts (2)Covariance: Do the returns on two stocks

“move” together? Meaning: When one stock goes up, does the other tend to go up also?◦ If “on average, yes,” then Covariance > 0◦ If “on average, no, they move in opposite

directions,” then Covariance < 0.Correlation: Another measure of how much

two stocks “move” together.

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The average annual return of Kellogg in 1998-2008 was 6.00%. The standard deviation of the return was 13.06%.

Technical notes:

1. The returns have been adjusted for dividends.

2. Note the use of the Excel functions Average, VarP, StDevP to compute the expected return, the variance of the returns, and the standard deviation.

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A B C D E

Date Price DividendAnnualreturn

31-Dec-98 34.13 0.9231-Dec-99 30.81 0.96 -6.89% <-- =(B4+C4)/B3-129-Dec-00 26.25 0.99 -11.59%31-Dec-01 30.10 1.01 18.51%31-Dec-02 34.27 1.01 17.21%31-Dec-03 38.08 1.01 14.06%31-Dec-04 44.66 1.01 19.93%30-Dec-05 43.22 1.06 -0.85%29-Dec-06 50.06 1.14 18.46%31-Dec-07 52.43 1.20 7.14%31-Dec-08 42.73 1.30 -16.02%

Average return, E(rK) 6.00% <-- =AVERAGE(D4:D13)

Variance of return, s2K 0.0171 <-- =VARP(D4:D13)

Standard deviation of return, sK 13.06% <-- =STDEVP(D4:D13)

PRICE AND DIVIDEND DATA FOR KELLOGG (K)1998 - 2008

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Dividend adjustmentShareholders get two kinds of returns:

◦Capital gains/losses: Increase/decrease in stock price

◦DividendsExample: Buy stock for $20, sell it

one year later for $25. If stock paid dividend of $2, then your return was

$25 $235%

$20

Kellogg over longer period

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A B C D E

Date Price DividendAnnualreturn

31-Dec-90 18.9931-Dec-91 32.69 1.08 77.82% <-- =(B4+C4)/B3-131-Dec-92 33.50 0.60 4.32%31-Dec-93 28.38 0.66 -13.33%30-Dec-94 29.06 0.70 4.89%29-Dec-95 38.63 0.75 35.48%31-Dec-96 32.81 0.81 -12.95%31-Dec-97 49.63 1.29 55.17%31-Dec-98 34.13 0.92 -29.38%31-Dec-99 30.81 0.96 -6.89%29-Dec-00 26.25 0.99 -11.59%31-Dec-01 30.10 1.01 18.51%31-Dec-02 34.27 1.01 17.21%31-Dec-03 38.08 1.01 14.06%31-Dec-04 44.66 1.01 19.93%30-Dec-05 43.22 1.06 -0.85%29-Dec-06 50.06 1.14 18.46%31-Dec-07 52.43 1.20 7.14%31-Dec-08 42.73 1.30 -16.02%

Average return, E(rK) 6.32% <-- =AVERAGE(D9:D18)

Variance of return, s2K 0.0509 <-- =VARP(D9:D18)

Standard deviation of return, sK 22.56% <-- =STDEVP(D9:D18)

PRICE AND DIVIDEND DATA FOR KELLOGG (K)1990 - 2008

Download data from YahooYahoo data includes dividends and

stock splits into the priceYou can thus compute the returns

directly from the Yahoo adjusted price data

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A typical Yahoo screen for historical prices

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For more details on downloading data from Yahoo, see Appendix 9.1

Return data for Exxon (XOM)

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Date Price Return31-Dec-98 29.1231-Dec-99 32.79 12.60% <-- =B4/B3-129-Dec-00 36.15 10.25%31-Dec-01 33.40 -7.61%31-Dec-02 30.44 -8.86%31-Dec-03 36.72 20.63%31-Dec-04 47.03 28.08%30-Dec-05 52.57 11.78%29-Dec-06 73.11 39.07%31-Dec-07 90.87 24.29%31-Dec-08 78.96 -13.11%

Average return, E(rXOM) 11.71% <-- =AVERAGE(C4:C13)

Variance of return, s2XOM 0.0267 <-- =VARP(C4:C13)

Standard deviation of return, sXOM 16.34% <-- =STDEVP(C4:C13)

EXXON (XOM) STOCK PRICESAdjusted for dividends and splits

XOM and K together

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Date Kellogg Exxon

31-Dec-99 -6.89% 12.60%29-Dec-00 -11.59% 10.25%31-Dec-01 18.51% -7.61%31-Dec-02 17.21% -8.86%31-Dec-03 14.06% 20.63%31-Dec-04 19.93% 28.08%30-Dec-05 -0.85% 11.78%29-Dec-06 18.46% 39.07%31-Dec-07 7.14% 24.29%31-Dec-08 -16.02% -13.11%

Average return E(rK) and E(rXOM) 6.00% 11.71% <-- =AVERAGE(C3:C12)

Variance of returns, s2K and s2

XOM 0.0171 0.0267 <-- =VARP(C3:C12)

Standard deviation of returns, sK and sXOM 13.06% 16.34% <-- =STDEVP(C3:C12)

Covariance of returns Cov(rK,rXOM) 0.0074 <-- =COVAR(B3:B12,C3:C12)

Correlation of returns rK,XOM 0.3482 <-- =CORREL(B3:B12,C3:C12)

0.3482 <-- =B17/(B16*C16)

KELLOGG (K) AND EXXON (XOM) ANNUAL RETURN DATA

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Covariance and correlation

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DateGM

returnMSFT return

31-Dec-90 -11.54% 72.99%31-Dec-91 -11.35% 121.76%31-Dec-92 16.54% 15.11%31-Dec-93 72.64% -5.56%30-Dec-94 -21.78% 51.63%29-Dec-95 28.13% 43.56%31-Dec-96 8.46% 88.32%31-Dec-97 19.00% 56.43%31-Dec-98 21.09% 114.60%31-Dec-99 21.34% 68.36%

Average return, E(rGM) and E(rMSFT) 14.25% 62.72%

Variance of return, s2GM and s2

MSFT 6.38% 14.43%

Standard deviation of return, GM and MSFT 25.25% 37.99%

Covariance of returns, Cov(rGM,rMSFT) -0.0552 <-- =COVAR(B3:B12,C3:C12)

Correlation of returns, GM,MSFT -0.5755 <-- =CORREL(B3:B12,C3:C12)-0.5755 <-- =B17/(B16*C16)

GM AND MSFT, ANNUAL RETURN DATA

Excel functions: Covar and Correl.

Note that correlation = Covar(GM,MSFT)/(GM* MSFT) (cell B19) .

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Facts about covariance and correlation (1)Covariance affected by units,

correlation is not. If you measure returns in decimals (15% = 0.15), covariance different than if you measure returns in whole numbers (15% = 15).

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Facts about covariance and correlation (2)Covariance between GM and MSFT

same as Covariance between MSFT and GM

Ditto for correlation

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Correlation facts (1)Correlation always > -1 and < +1Correlation +1 or -1 means perfect

linear relation between two assets (examples to come)

Correlation usually between -1 and +1

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Correlation facts (2)If correlation = 1, then returns on

one asset can be predicted by returns on second asset.

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Year

AdamsFarm stock

return

MorganSausage

stockreturn

1990 30.73% 21.44% <-- =3%+0.6*B31991 55.21% 36.13%1992 15.82% 12.49%1993 33.54% 23.12%1994 14.93% 11.96%1995 35.84% 24.50%1996 48.39% 32.03%1997 37.71% 25.63%1998 67.85% 43.71%1999 44.85% 29.91%

Correlation 1.00 <-- =CORREL(B3:B12,C3:C12)

CORRELATION +1Adams Farm and Morgan Sausage Stocks

rMorgan Sausage,t = 3% + 0.6*rAdams Farm,tMorgan Sausage’s return is perfectly predictable from Adams Farm return.

Moreover, When Adams Farm , so does Morgan Sausage.

Correlation = +1.

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Annual Stock Returns, Adams Farm and Morgan Sausage

0%

5%

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35%

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45%

50%

10% 20% 30% 40% 50% 60% 70%Adams Farm

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rgan

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Perfect negative correlation

Whenever Francisca does well, Jeremy does poorly, and vice versa. Jeremy’s performance is perfectly predictable from Francisca’s.

The correlation is -1.

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Year

Francescaportfolio

return

Jeremy portfolio

return1990 30.73% 26.12% <-- =63%-1.2*B31991 55.21% -3.25%1992 15.82% 44.02%1993 33.54% 22.75%1994 14.93% 45.08%1995 35.84% 19.99%1996 48.39% 4.93%1997 37.71% 17.75%1998 67.85% -18.42%1999 44.85% 9.18%

Correlation -1.00 <-- =CORREL(B3:B12,C3:C12)

CORRELATION -1Francesca and Jeremy, portfolio managers

rJeremy,t = 63% - 1.2*rFrancesca,t

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Annual Returns--Francesca & Jeremy

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Francesca

Jere

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Portfolio mean and standard deviation

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A B C D E F G H I J K

KelloggK

ExxonXOM

Mean 6.00% 11.71%Variance 1.71% 2.67%Standard deviation 13.06% 16.34%Covariance 0.0074

Proportion of Kin portfolio

PortfolioVarianceVar(rp)

Portfoliostandarddeviation

sp

PortfoliomeanE(rp)

0% 2.67% 16.34% 11.71%10% 2.31% 15.21% 11.14%20% 2.01% 14.19% 10.57%30% 1.77% 13.32% 10.00%40% 1.59% 12.61% 9.43%50% 1.47% 12.10% 8.85%60% 1.40% 11.82% 8.28%70% 1.39% 11.78% 7.71%80% 1.44% 11.98% 7.14%90% 1.54% 12.42% 6.57%

100% 1.71% 13.06% 6.00%

=SQRT(B19)

=A19*$B$3+(1-A19)*$C$3

CALCULATING PORTFOLIO RETURNS AND THEIR STATISTICS FROM THE FORMULAS

=A19^2*$B$4+(1-A19)^2*$C$4+2*A19*(1-

5%

6%

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10% 11% 12% 13% 14% 15% 16% 17%

Portf

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ecte

d re

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E(r

p)

Portfolio standard deviation sp

Portfolio Mean and Standard Deviation

Formulas

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How to do a regression in Excel

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Date S&P 500 IBM S&P 500 IBM3-Jan-07 1438.24 95.081-Feb-07 1406.82 89.39 -2.18% -5.98% <-- =C5/C4-11-Mar-07 1420.86 90.66 1.00% 1.42% <-- =C6/C5-12-Apr-07 1482.37 98.31 4.33% 8.44%1-May-07 1530.62 102.93 3.25% 4.70%1-Jun-07 1503.35 101.62 -1.78% -1.27%2-Jul-07 1455.27 106.84 -3.20% 5.14%1-Aug-07 1473.99 113.07 1.29% 5.83%4-Sep-07 1526.75 114.14 3.58% 0.95%1-Oct-07 1549.38 112.52 1.48% -1.42%1-Nov-07 1481.14 102.28 -4.40% -9.10%3-Dec-07 1468.36 105.12 -0.86% 2.78%2-Jan-08 1378.55 104.15 -6.12% -0.92%1-Feb-08 1330.63 111.14 -3.48% 6.71%3-Mar-08 1322.70 112.39 -0.60% 1.12%1-Apr-08 1385.59 117.82 4.75% 4.83%1-May-08 1400.38 126.85 1.07% 7.66%2-Jun-08 1280.00 116.17 -8.60% -8.42%1-Jul-08 1267.38 125.43 -0.99% 7.97%1-Aug-08 1282.83 119.77 1.22% -4.51%2-Sep-08 1164.74 115.08 -9.21% -3.92%1-Oct-08 968.75 91.48 -16.83% -20.51%3-Nov-08 896.24 80.74 -7.48% -11.74%1-Dec-08 903.25 83.27 0.78% 3.13%2-Jan-09 825.88 90.68 -8.57% 8.90%

Price at beginning of month

Return for the month

MONTHLY RETURNS ON S&P 500 AND IBMJanuary 2007 - December 2008

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IBM

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IBM Monthly Returns vs S&P 5002007-2008

Highlighted data is graphed in XY-Scatter chart.

Regression in ExcelMark the points on the chartRight-click on mouse

Add Trendline

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Excel’s regression screen

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Date S&P 500 IBM S&P 500 IBM3-Jan-07 1438.24 95.081-Feb-07 1406.82 89.39 -2.18% -5.98% <-- =C5/C4-11-Mar-07 1420.86 90.66 1.00% 1.42% <-- =C6/C5-12-Apr-07 1482.37 98.31 4.33% 8.44%1-May-07 1530.62 102.93 3.25% 4.70%1-Jun-07 1503.35 101.62 -1.78% -1.27%2-Jul-07 1455.27 106.84 -3.20% 5.14%1-Aug-07 1473.99 113.07 1.29% 5.83%4-Sep-07 1526.75 114.14 3.58% 0.95%1-Oct-07 1549.38 112.52 1.48% -1.42%1-Nov-07 1481.14 102.28 -4.40% -9.10%3-Dec-07 1468.36 105.12 -0.86% 2.78%2-Jan-08 1378.55 104.15 -6.12% -0.92%1-Feb-08 1330.63 111.14 -3.48% 6.71%3-Mar-08 1322.70 112.39 -0.60% 1.12%1-Apr-08 1385.59 117.82 4.75% 4.83%1-May-08 1400.38 126.85 1.07% 7.66%2-Jun-08 1280.00 116.17 -8.60% -8.42%1-Jul-08 1267.38 125.43 -0.99% 7.97%1-Aug-08 1282.83 119.77 1.22% -4.51%2-Sep-08 1164.74 115.08 -9.21% -3.92%1-Oct-08 968.75 91.48 -16.83% -20.51%3-Nov-08 896.24 80.74 -7.48% -11.74%1-Dec-08 903.25 83.27 0.78% 3.13%2-Jan-09 825.88 90.68 -8.57% 8.90%

MONTHLY RETURNS ON S&P 500 AND IBMJanuary 2007 - December 2008

Price at beginning of month

Return for the month

y = 0.9149x + 0.0204R² = 0.4225 -25%

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IBM

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IBM Monthly Returns vs S&P 5002007-2008