CF Chapter 11 Excel Master Student

7/27/2019 CF Chapter 11 Excel Master Student

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Ross, Westerfield, and Jaffe's Spreadsheet Master

Corporate Finance, 9th edition

by Brad Jordan and Joe Smolira

Version 9.0

Chapter 11In these spreadsheets, you will learn how to use the follo

The following conventions are used in these spreadsheets:

1) Given data in blue

2) Calculations in red

NOTE: Some functions used in these spreadsheets may require that

the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.

To install these, click on the Office button

then "Excel Options," "Add-Ins" and select

"Go." Check "Analysis ToolPak" and"Solver Add-In," then click "OK."

SQRT

COVAR

CORREL

Adding a trendline

Regression estimates

SLOPE

INTERCEPT


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ing Excel functions:


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Chapter 11 - Section 2

Expected Return, Variance, and Covariance

(1)

State of

Economy

(2)

Probability of

State

(3)

Return if State

Occurs

(4)

Product

(2) (3)

(5)

Deviation from

Expected Return

(3) - E(R)

Depression 0.25 -0.20 -0.05 -0.375

Recession 0.25 0.10 0.025 -0.075

Normal 0.25 0.30 0.075 0.125

Boom 0.25 0.50 0.125 0.325Expected return = 0.175

The standard deviation is the square root of the variance, so the standard deviation is:

Standard deviation: 25.86%

In Chapter 10, we used the AVERAGE, VAR, and STDEV functions to calculate the average, va

have built-in functions that handle unequal probabilities, so we need to create our own equ

RWJ Excel Tip

We should also note that the square root (or any other power) can be calculated using the c

Excel has a built-in function, SQRT, that finds the square root of a number. SQRT is found un

Supertech

And for Slowpoke:

Slowpoke


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(1)

State of

Economy

(2)

Probability of

State

(3)

Return if State

Occurs

(4)

Product

(2) (3)

(5)

Deviation from

Expected Return

(3) - E(R)

Depression 0.25 0.05 0.0125 -0.005

Recession 0.25 0.20 0.0500 0.145

Normal 0.25 -0.12 -0.0300 -0.175Boom 0.25 0.09 0.0225 0.035

Expected return = 0.055


State of

Economy

Probability of

State

Deviation of

SupertechReturn from

the

Expected

Return

Deviation of

SlowpokeReturn from

the

Expected

Return

Product of the

Deviations

Depression 0.25 -0.375 -0.005 0.001875

Recession 0.25 -0.075 0.145 -0.010875

Normal 0.25 0.125 -0.175 -0.021875

Boom 0.25 0.325 0.035 0.011375

Covariance =

Correlation: -0.1639

Suppose we have the following returns for the market and a stock:

Year Market return Stock return

1 18% 7%

2 27% 25%

3 5% 21%

4 13% 4%

5 -17% -16%

6 6% 19%

To calculate the covariance and correlation, we need to calculate the product of the return d

then sum to find the covariance. Doing so, we find:

Since the correlation is the covariance divided by the product of the standard deviations, the

Covariance and Correlation with Historic Data

While we just discussed the calculation of covariance and correlation using unequal probabil

data, Excel has built-in functions that will calculate the covariance and correlation for you.


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7 -21% -38%

8 34% 29%

9 19% 15%

10 11% 16%

What is the covariance and correlation of the returns between this stock and the market?

Covariance: 0.0281

Correlation: 0.8648

A Quick Statistics Review

The main difference between covariance and correlation is the interpretation. Covariance istwo variables is large, or because of a strong relationship between the two variables. Thus, t

or negative.

Correlation is standardized and will be between -1 and 1. The closer the correlation is to -1, t

correlation is to 1, the stronger the positive relationship between the two variables. Therefo

between two variables.

To use COVAR and CORREL, select the first data array, tab to Array2, and select the second dbetween A and B is equal to the correlation between B and A.

RWJ Excel Tip

The functions for covariance (COVAR) and correlation (CORREL) are both located under Mor

data is located.

then the other variable tends to be above its expected value too), then the covariance and c

them is above its expected value the other variable tends to be below its expected value, th


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Correlation and Diversification

So why is correlation important to diversification? Correlation (and covariance) measure ho

assets, the greater the diversification benefit. If you think of two assets with a negative corre

below its average. This will smooth out the returns of a portfolio of these two assets. Howev

the other asset will also have a return above its mean, so there is less benefit to diversificati

be expected to have a high correlation because many of the firm specific risks that would affMicrosoft, so we would expect GM and Microsoft to have a lower correlation than GM and F


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(6)

Squared Value

of Deviation

(7)

Product

(2) (5)

0.140625 0.0351563

0.005625 0.0014063

0.015625 0.0039063

0.105625 0.0264063Variance = 0.0668750

iance, and standard deviation for historical returns. Unfortunately, Excel does not

tions.

ret key (^). For example, we could have entered an equation as H13^(1/2).

er the Math & Trig tab. The function looks like this:


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(6)

Squared Value

of Deviation

(7)

Product

(2) (5)

0.000025 0.0000062

0.021025 0.0052563

0.030625 0.00765630.001225 0.0003063

Variance = 0.0132250

Probability ofState of the

Economy times

Product of the

Deviations

0.000469

-0.002719

-0.005469

0.002844

-0.004875

eviations, multiply this product by the probability of the state of the economy, and

correlation between Supertech and Slowpoke is:

ties, both calculations are often done using historic market data. When using historic


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n unstandardized number. A large covariance can arise because the variance of thee only interpretation we can take from the covariance is the direction, either positive

he stronger the negative relationship between the variables, and the closer the

e, correlation measures both the direction and magnitude of the relationship

ta array. It is irrelevant which data array you select first. That is, the correlation

Functions, Statistical. Both functions use similar inputs, namely the arrays that the

rrelation between the two variables will be positive. On the other hand, when one of

n the covariance and correlation between the two variables will be negative.


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two assets move together. All else the same, the lower the correlation between two

lation, as one asset has a return above its average, the other asset will have a return

r, if the assets have a positive correlation, as one asset has a return above its mean,

n. For an application, think of GM and Ford. Both are auto manufacturers and would

ct GM also affect Ford. However, GM is less likely to share firm specific risk withord, and therefore have a greater diversification benefit.


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The Return and Risk for Portfolios

Stock A Stock B

Expected return 9% 14%

Standard deviation 19% 55%

Weight of stock 30% 70%

Correlation 0.10

Expected return: 12.50%


Weight of Stock A

Expected

Return

Standard

Deviation

0% 14.00% 55.00%5% 13.75% 52.35%

10% 13.50% 49.73%

15% 13.25% 47.12%

20% 13.00% 44.54%

25% 12.75% 41.99%

30% 12.50% 39.48%

35% 12.25% 37.01%

40% 12.00% 34.60%

45% 11.75% 32.25%

50% 11.50% 29.98%55% 11.25% 27.81%

60% 11.00% 25.77%

65% 10.75% 23.89%

70% 10.50% 22.20%

75% 10.25% 20.77%

80% 10.00% 19.63%

85% 9.75% 18.86%

90% 9.50% 18.48%

In the textbook, the equation for the standard deviation of a portfolio is presented. Given the follo

deviation of the portfolio?

The expected return and standard deviation of the portfolio are:

Of course, we could be interested in examining the opportunity set for the two assets. To see this,

expected return and standard deviation of the two assets for various portfolio weights is:


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95% 9.25% 18.53%

100% 9.00% 19.00%

So how do we find the minimum variance portfolio? The best way is to use Solver. Try this for yours

portfolio is about 92.93%

So what does the opportunity set for these two assets look like? Below, you will see. To examine ho

correlation in the cell above.

5%

7%

9%

11%

13%

15%

10% 15% 20% 25% 30% 35% 40% 45%

TotalReturnonPortf

olio

Risk (Standard Deviation of Portfolio's Return)

Opportunity Set of Two Assets


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ing information concerning two stocks, what is the expected return and standard

e can create a table for various portfolio weights and then graph the results. The


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lf and see if you don't agree that the weight of Stock A in the minimum variance

a change in the correlation will affect the shape of the opportunity set, change the

50% 55% 60%


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Market Equilibrium

To add a trend line to a chart, do the following:

In this section, you will learn how beta is estimated. Before we begin that discussion, we wa

month end values for the S&P 500, a common proxy for the market as a whole, and the adjubeta, 60 monthly returns is a commonly used number of historical returns. Since we are goin

possible. However, the further back in time we go, the less the company is like the current c

years. But is AT&T in its current form actually comparable to AT&T in 1930? Not really. For t

estimating beta.

To begin, we would like to graph the returns of Amazon.com stock against the returns of the

Notice that we have added a trend line in this graph. This trend line is called the characterist

market returns. The slope of this line is the beta of the stock.

RWJ Excel Tip

2) On the Layout tab, in the Analysis group, click Trend line.

1) Click anywhere in the chart. This displays the Chart Tools, adding the Design, Layout,

y = 1.454x + 0.0217

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

-20% -15% -10% -5% 0%Amazon.c

om

Return

S&P 500 Retur

Performance of Amazon.com StIndex M


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The Y input range is the dependent variable, in this case the stock returns, and the X input ra

data and selected the Labels box, which will put a label on the output for the variables. Finall

interval. The output for this regression is below.

The equation in the graph above is a linear regression. We can use the trend line option on a

regression as well as give us more statistical information about the regression estimate.

RWJ Excel Tip

To estimate a linear regression, go to the Data tab, Data Analysis, and select Regression, the

The input box for our linear regression looks like this:

3) You can use any of the predefined options. Note that on the chart there is an equati

graph. We will have more to say about this equation later.


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SUMMARY OUTPUT

Regression Statistics

Multiple R 0.442264434R Square 0.19559783

Adjusted R Square 0.181728827

Standard Error 0.133348438

Observations 60

ANOVA

df SS MS F

Regression 1 0.250781015 0.250781015 14.10323659

Residual 58 1.031344739 0.017781806

Total 59 1.282125754

Coefficients Standard Error t Stat P-value

Intercept 0.021665877 0.017237604 1.256896101 0.213829509

X Variable 1 1.454009866 0.38717558 3.755427617 0.000403123

More Regression

Beta (slope): 1.45401

Intercept: 0.02167

Both the SLOPE and INTERCEPT functions are located under More Functions, Statistical. The i

inputs we used for our results.

If you are just interested in the slope and intercept for a regression, Excel has functions that

RWJ Excel Tip


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t to start with a graph of actual stock returns. On the next tab, you will find the

sted closing price for Amazon.com stock over a 60 month period. When estimatingg to be using a statistical process to estimate beta, we would like as much data as

mpany. For example, with AT&T, we could get stock prices for more than 100

is and other reasons, 60 monthly returns has become relatively standard when

S&P 500. In this case, we used a scatter plot which resulted in the graph below.

ic line. The slope of this line represents how the stock's returns respond to the

and Format tabs.

5% 10% 15% 20%

n

ck and the S&P 500: Singledel


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nge is the independent variable, or market return. We included the row above the

y, we selected the Confidence Interval box and asked for a 90 percent confidence

graph to estimate a linear regression, but Excel has a tool that will estimate a linear

OK.

n. We went to More Options and selected the box to display the equation on the


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Significance F

0.000403123

Lower 95% Upper 95% Lower 90.0% Upper 90.0%

-0.012838936 0.05617069 -0.007147687 0.050479441

0.678993744 2.229025988 0.806825456 2.101194277

nputs for each function are the Y values and the X values. Below, you will see the

will calculate these values separately, SLOPE and INTERCEPT.


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Return Data

Date S&P 500 Amazon.com

S&P 500

return

Amazon

return

5/3/2004 1120.68 48.50$6/1/2004 1140.84 54.40$ 1.80% 12.16%

7/1/2004 1101.72 38.92$ -3.43% -28.46%

8/2/2004 1104.24 38.14$ 0.23% -2.00%

9/1/2004 1114.58 40.86$ 0.94% 7.13%

10/1/2004 1130.2 34.13$ 1.40% -16.47%

11/1/2004 1173.82 39.68$ 3.86% 16.26%

12/1/2004 1211.92 44.29$ 3.25% 11.62%

1/3/2005 1181.27 43.22$ -2.53% -2.42%

2/1/2005 1203.6 35.18$ 1.89% -18.60%

3/1/2005 1180.59 34.27$ -1.91% -2.59%4/1/2005 1156.85 32.36$ -2.01% -5.57%

5/2/2005 1191.5 35.51$ 3.00% 9.73%

6/1/2005 1191.33 33.09$ -0.01% -6.81%

7/1/2005 1234.18 45.15$ 3.60% 36.45%

8/1/2005 1220.33 42.70$ -1.12% -5.43%

9/1/2005 1228.81 45.30$ 0.69% 6.09%

10/3/2005 1207.01 39.86$ -1.77% -12.01%

11/1/2005 1249.48 48.46$ 3.52% 21.58%

12/1/2005 1248.29 47.15$ -0.10% -2.70%

1/3/2006 1280.08 44.82$ 2.55% -4.94%2/1/2006 1280.66 37.44$ 0.05% -16.47%

3/1/2006 1294.87 36.53$ 1.11% -2.43%

4/3/2006 1310.61 35.21$ 1.22% -3.61%

5/1/2006 1270.09 34.61$ -3.09% -1.70%

6/1/2006 1270.2 38.68$ 0.01% 11.76%

7/3/2006 1276.66 26.89$ 0.51% -30.48%

8/1/2006 1303.82 30.83$ 2.13% 14.65%

9/1/2006 1335.85 32.12$ 2.46% 4.18%

10/2/2006 1377.94 38.09$ 3.15% 18.59%

11/1/2006 1400.63 40.34$ 1.65% 5.91%12/1/2006 1418.3 39.46$ 1.26% -2.18%

1/3/2007 1438.24 37.67$ 1.41% -4.54%

2/1/2007 1406.82 39.14$ -2.18% 3.90%

3/1/2007 1420.86 39.79$ 1.00% 1.66%

4/2/2007 1482.37 61.33$ 4.33% 54.13%

5/1/2007 1530.62 69.14$ 3.25% 12.73%

6/1/2007 1503.35 68.41$ -1.78% -1.06%

7/2/2007 1455.27 78.54$ -3.20% 14.81%


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8/1/2007 1473.99 79.91$ 1.29% 1.74%

9/4/2007 1526.75 93.15$ 3.58% 16.57%

10/1/2007 1549.38 89.15$ 1.48% -4.29%

11/1/2007 1481.14 90.56$ -4.40% 1.58%

12/3/2007 1468.36 92.64$ -0.86% 2.30%

1/2/2008 1378.55 77.70$ -6.12% -16.13%

2/1/2008 1330.63 64.47$ -3.48% -17.03%3/3/2008 1322.7 71.30$ -0.60% 10.59%

4/1/2008 1385.59 78.63$ 4.75% 10.28%

5/1/2008 1400.38 81.62$ 1.07% 3.80%

6/2/2008 1280 73.33$ -8.60% -10.16%

7/1/2008 1267.38 76.34$ -0.99% 4.10%

8/1/2008 1282.83 80.81$ 1.22% 5.86%

9/2/2008 1164.74 72.76$ -9.21% -9.96%

10/1/2008 968.75 57.24$ -16.83% -21.33%

11/3/2008 896.24 42.70$ -7.48% -25.40%

12/1/2008 903.25 51.28$ 0.78% 20.09%1/2/2009 825.88 58.82$ -8.57% 14.70%

2/2/2009 735.09 64.79$ -10.99% 10.15%

3/2/2009 797.87 73.44$ 8.54% 13.35%

4/1/2009 872.81 80.52$ 9.39% 9.64%

5/1/2009 919.14 77.99$ 5.31% -3.14%


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Chapter 11 - Master it!

E(Ri) = Rf+ b[E(RM) - Rf]

E(Ri) - Rf = b[E(RM) - Rf]

E(Ri) - Rf = b[E(RM) - Rf] + e

E(Ri) - Rf = ai+ b[E(RM) - Rf] + e

This equation, known as the market model, is generally the model used for estimating beta. The intercept term is known as Jensen's alpha and represe

return. If CAPM holds exactly, this intercept should be zero. If you think of alpha in terms of the SML, if the alpha is positive, the stock plots above the S

negative, the stock plots below the SML.

The CAPM is one of the most tested models in Finance. When beta is estimated in practice, a variation of CAPM called the maket model is often used.

market model, we start with the CAPM:

Since CAPM is an equation, we can subtract the risk-free rate from both sides, which gives us:

This equation is deterministic, that is, exact. In a regression, we realize that there is some indeterminate error. We need to formally recognize this in t

adding epsilon, which represents this error:

Finally, think of the above equation in a regression. Since there is no intercept in the equation, the intercept is zero. However, when we estimate the r

we can add an intercept term, which we will call alpha:


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a.

b.

2) Calculate the appraisal ratio for the stock and the mutual fund. Which has a better appraisal ratio?

3) Often, the appraisal ratio is used to evaluate the performance of mutual fund managers. Why do you think the appraisal ratio is used more often fo

which are portfolios, than for individual stocks?

You want to estimate the market model for an individual stock and a mutual fund. First, go to finance.yahoo.com and download the adjusted prices fo

for an individual stock and a mutual fund, and the S&P 500. Next, go to the St. Louis Federal Reserve website at www.stlouisfed.org. You should find t

on this website. Look for the 1-Month Treasury Constant Maturity Rate and download this data. This will be the proxy for the risk-free rate. When usi

should be aware that this interest rate is the annual interest rate, while we are using monthly stock returns, so you will need to adjust the 1-month T-

stock and mutual fund you select, estimate the beta and alpha of the stock using the market model. When you estimate the regression model, find the

Residuals and check this box when you do each regression. Because you are saving the residuals, you may want to save the regression output in a new

1) Are the alpha and beta for each regression statistically different from zero?

2) How do you interpret the alpha and beta for the stock and the mutual fund?

3) Which of the two regression estimates has the highest R squared? Is this what you would have expected? Why?

In part a , you asked Excel to return the residuals of the regression, which is the epsilon in the regression equation. If you remember back to statistics

linear distance from each observation to the regression line. In this context, the residuals are the part of each monthly return that is not explained by

estimate. The residuals can be used to calculate the appraisal ratio, which is the alpha divided by the standard deviation of the residuals.

1) What do you think the appraisal ratio is intended to measure?


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Master it! Solution

a. Month/Year S&P 500 Stock price

Mutual fund

price Risk-free rate

IBM FMAGX


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S&P 500 return Stock return

Mutual fund

return

Market risk

premium

Stock risk

premium

Mutual fund risk

premium


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CF Chapter 11 Excel Master Student