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Introduction to EconomicsIntroduction to Economics

Linking Personal Investment with the Linking Personal Investment with the US EconomyUS Economy

MacroeconomicsMacroeconomics

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Part TwoMacroeconomics and the US Economy

5. Tuesday, Oct. 13, Lecture Five: "Capital Asset Pricing Model"Tracking asset markets and the US economy

capital asset pricing modelGrowth rate of your personal wealthValue of a share of stockThe impact of business cycles on corporate profits

Reading Assignment:O’Sullivan and Sheffrin, Ch. 20, “The Big Ideas in Macroeconomics”emphasis: measuring the ouput of the economy, unemployment, inflation O’Sullivan and Sheffrin, Ch. 21, “Behind the Economic Statistics”Problems O & S Text

p. 420: 1, 2, 3, 4, 5, 6, 7, 8p. 441: 1, 2, 3, 4, 5, 6, 7, 8

Thursday, Oct. 15 , 25 minute QUIZ, You will need scantron sheet and #2 pencil.

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Outline: Lecture FiveOutline: Lecture Five Tracking Asset Markets and the US EconomyTracking Asset Markets and the US Economy Growth Rate of Personal WealthGrowth Rate of Personal Wealth

the importance of savings relative to rate of return on wealththe importance of savings relative to rate of return on wealth Value of a share of stockValue of a share of stock

depends on the stream of expected future net earnings per depends on the stream of expected future net earnings per shareshare

The Impact of the Business Cycle on Corporate Profits The Impact of the Business Cycle on Corporate Profits

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Your Stocks

Market Indices

The Economy

corporate earnings(profits)

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UC Funds: Monthly Rate of Return

-6

-4

-2

0

2

4

6

8

95.0995.11 96.0196.03 96.0596.07 96.0996.11 97.0197.03 97.05

Year:Month

Rate

Equity

Insurance

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UC Funds Monthly Rate of Return

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

95.0995.1196.0196.0396.0596.0796.0996.1197.0197.0397.05Year:Month

Rate

InsuranceMoney MarketSavings

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UC Funds: Monthly Rates of Return

-6

-4

-2

0

2

4

6

8

95.09 95.11 96.01 96.03 96.05 96.07 96.09 96.11 97.01 97.03 97.05

Year:Month

Rate

BondEquityMulti-Asset

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Two Kinds of AssetsTwo Kinds of Assets low rate of return-low low rate of return-low

variabilityvariability want high rate of want high rate of

return return on return return on averageaverage

want low variabilitywant low variability predictable average predictable average

returnreturn

high return-high high return-high variabilityvariability

want high rate of want high rate of return on averagereturn on average

want low variabilitywant low variability

Dilemma: which kind of asset to hold?

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Investment Principles or MaximsInvestment Principles or Maxims Don’t put all of your eggs in one basketDon’t put all of your eggs in one basket

hold a diversified portfoliohold a diversified portfolio cashcash bondsbonds stocksstocks real estatereal estate

advantage of a mutual fundadvantage of a mutual fund instead of holding one stock, e.g. Coca-Cola, you instead of holding one stock, e.g. Coca-Cola, you

hold a bundle of stockshold a bundle of stocks

Choose the asset with the highest reward Choose the asset with the highest reward for a given level of riskfor a given level of risk

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Measures of Average Rate of Return and Variability: Mean & Std. Dev.Date Bond Equity Insurance

95.09 2.66 4 0.6495.1 2.4 -0.26 0.66

95.11 3.9 4.07 0.6495.12 2.83 -0.13 0.6696.01 -0.51 3.32 0.6496.02 -5.42 2.35 0.696.03 -0.63 -0.24 0.6496.04 -0.75 1.6 0.6196.05 0.78 2.56 0.6396.06 1.68 -0.12 0.6196.07 0.34 -5.01 0.6396.08 0.35 2.33 0.6396.09 4.21 4.59 0.61

96.1 7 0.39 0.6396.11 5.56 7.69 0.6196.12 -4.16 -1.25 0.6297.01 0.04 4.59 0.6297.02 1.35 0.42 0.5697.03 -3.59 -2.33 0.6497.04 2.23 4.09 0.697.05 2.59 6.16 0.6297.06 2.75 3.5 0.6

standard deviation 3.00 2.95 0.02mean 1.16 1.92 0.62

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Distribution of Monthly Rates of Return, UC Equity Fund, Sept. '95- Aug. '98

0

1

2

3

4

5

6

-13 -11-9 -7 -5 -3 -1 1 3 5 7

Monthly Rate

Number

Aug. ‘98

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Mean Returns & Standard DeviationsMean Returns & Standard DeviationsUC Funds: Mean Return Vs. Risk (Standard Deviation)

Equity

BondMulti-Asset

Money Market

Savings

Insurance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Standard Deviation

Mean Return

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Efficient Investment PortfolioEfficient Investment PortfolioUC Funds: Mean Return Vs. Risk (Standard Deviation)

Equity

BondMulti-Asset

Money Market

Savings

Insurance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Standard Deviation

Mean Return

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Your portfolio should be on the efficient frontier

Your portfolio should be on the efficient frontier

But where on the frontier?But where on the frontier? depends on your taste for reward and riskdepends on your taste for reward and risk

reward, i.e. the mean rate of return is a reward, i.e. the mean rate of return is a goodgood risk is a risk is a badbad

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Economic Paradigm: Valuation of Mean Return and Risk

Assumption: Mean Return is Good, Risk is Bad: U =U(M,R)

MeanReturn,M

Risk, R

better

worse

Iso - Preference CurvesA

B

C

Prefer B to A; Prefer B to C

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Efficient Investment PortfolioEfficient Investment PortfolioUC Funds: Mean Return Vs. Risk (Standard Deviation)

Equity

BondMulti-Asset

Money Market

Savings

Insurance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Standard Deviation

Mean Return

Investor A: very risk averse

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Efficient Investment PortfolioEfficient Investment PortfolioUC Funds: Mean Return Vs. Risk (Standard Deviation)

Equity

BondMulti-Asset

Money Market

Savings

Insurance

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Standard Deviation

Mean Return

Investor B: not very risk averse

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Efficient UC Investment PortfolioEfficient UC Investment Portfolio f*insurance contract + (1-f)*equity fundf*insurance contract + (1-f)*equity fund

where f can range from zero to onewhere f can range from zero to oneexample: 50:50, i.e one half of your nest egg example: 50:50, i.e one half of your nest egg

is invested in the Insurance Contract and the is invested in the Insurance Contract and the other half is invested in the Equity Fund.other half is invested in the Equity Fund.

• mean return: 1/2 *0.62 + 1/2*1.92 = 1.27 % per mean return: 1/2 *0.62 + 1/2*1.92 = 1.27 % per monthmonth

• expected risk(standard deviation: 1/2*0.02 + expected risk(standard deviation: 1/2*0.02 + 1/2*3.02 =1.521/2*3.02 =1.52

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Tracking Assets and MarketsTracking Assets and Markets

What is the relationship between the What is the relationship between the monthly rate of return on the UC Index monthly rate of return on the UC Index Fund and an index of the stock market, such Fund and an index of the stock market, such as the Standard and Poor’s Index of 500 as the Standard and Poor’s Index of 500 Stocks (S&P 500) ?Stocks (S&P 500) ?

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Example: The UC Index Fund and the Standard & Poor’s 500Example: The UC Index Fund and the Standard & Poor’s 500 mean rate of return on the UC Index Fund mean rate of return on the UC Index Fund

varies with the mean rate of return on varies with the mean rate of return on Standard & Poor’s Index of 500 StocksStandard & Poor’s Index of 500 Stocks capital asset pricing modelcapital asset pricing model

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Monthly Rates of Return: UC Index Fund, S&P500

-6

-4

-2

0

2

4

6

8

95.09 95.11 96.01 96.0396.05 96.07 96.09 96.11 97.01 97.03 97.05

Date

Percent

UC EquityS&P 500

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Variation of Rewards: UC Index Fund Vs. S&P 500

96.11

96.07

y = 0.8127x + 0.0474

R2 = 0.8727

-6

-4

-2

0

2

4

6

8

-6 -4 -2 0 2 4 6 8

S&P 500

UC Index

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Capital Asset Pricing ModelCapital Asset Pricing Model return to an asset varies with the return to return to an asset varies with the return to

the marketthe market if the relationship is perfect, Rif the relationship is perfect, R2 2 =1, and all the =1, and all the

risk in the asset is market riskrisk in the asset is market risk if the relationship is nonexistent, Rif the relationship is nonexistent, R2 2 =0, and all =0, and all

of the risk is asset specificof the risk is asset specific In symbolsIn symbols

rrUC UC = = + + rrS&P S&P + e + e r is the return r is the return if if is greater than 1, the asset is riskier than is greater than 1, the asset is riskier than

the marketthe market e is the residual or errore is the residual or error

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Sources of Information: stock prices Sources of Information: stock prices Daily QuotesDaily Quotes

Business Section of Business Section of Los Angeles TimesLos Angeles Times Wall Street JournalWall Street Journal

Internet graphicsInternet graphics http://www.stockmaster.comhttp://www.stockmaster.com http://www.networth.galt.comhttp://www.networth.galt.com

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http://www.stockmaster.com

beta for Apple = 0.67

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http://www.networth.galt.com

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Apple Computer

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How do you make your nest egg grow?How do you make your nest egg grow?

Do you need to take risks and get a high Do you need to take risks and get a high rate of return?rate of return? not if your ratio of savings to wealth is highnot if your ratio of savings to wealth is high

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Relative Importance of SavingsRelative Importance of Savings Younger YearsYounger Years income & savings are lowerincome & savings are lower wealth is smallerwealth is smaller ratio of savings to wealth ratio of savings to wealth

may be highmay be high savings is most important, savings is most important,

rate of return less sorate of return less so exampleexample

income of $60,000income of $60,000 savings of $6,000savings of $6,000 wealth of $50,000wealth of $50,000 ratio of savings to wealth of 0.12ratio of savings to wealth of 0.12

Older YearsOlder Years wealth accumulateswealth accumulates ratio of savings to ratio of savings to

wealth fallswealth falls rate of return on rate of return on

wealth becomes wealth becomes more importantmore important

exampleexample income of $100,000income of $100,000 savings of $20,000savings of $20,000 wealth of $500,000wealth of $500,000 ratio of savings to ratio of savings to

wealth of 0.04wealth of 0.04

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Rate of Growth of Personal Wealth

savings, s

+

increasein wealth, ∆w Stock of

wealth, w

rate ofreturn, r

+

yield, r*w

rate of growth of wealth, ∆w/w rate of return, r + savings/wealth

∆w/w r + s/w

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Rate of Growth of Personal WealthRate of Growth of Personal Wealth If the rate of return, r, on wealth is zeroIf the rate of return, r, on wealth is zero

then the only source of growth in wealth is savings: then the only source of growth in wealth is savings: ∆w/w = s/w∆w/w = s/w

i.e. the only change in wealth, ∆w, is savings: ∆w = si.e. the only change in wealth, ∆w, is savings: ∆w = s If savings is zeroIf savings is zero

then the only source of growth in wealth is rate of then the only source of growth in wealth is rate of return, r, and wealth will grow exponentially at the return, r, and wealth will grow exponentially at the rate r: ∆w/w = rrate r: ∆w/w = r

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Years to Double WealthYears to Double Wealth

Rate of Growth ofWealth, 100*∆w/w

Years to Double

4% 17.3

8% 8.7

10% 6.9

16% 4.3

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rate of returnon wealth, r

4%

8%

12%

4% 8% 12% ratio of savings to wealth, s/w

rate of growth of wealth, ∆w/w∆w/w r + s/w

0

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Where does the growth in financial wealth come from?Where does the growth in financial wealth come from? What is the relationship between financial What is the relationship between financial

markets and the economy?markets and the economy?

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Index of Dow Jones Industrials, Weekly Closing .

10/9/98

1/3/86

y = 1601.9e0.0023x

R2 = 0.933

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

9000.00

10000.00

0 100 200 300 400 500 600 700Week

DJI

DJIWKLYexponential trend

weekly rate of growth = .0023

annual rate of growth = 52*.0023 =.12

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Economic ConceptEconomic Concept present value of a stream of expected future present value of a stream of expected future

net earnings, or profits, per sharenet earnings, or profits, per share PV(t) = ENE(t) + ENE(t+1)/(1+i)PV(t) = ENE(t) + ENE(t+1)/(1+i)

may know this year’s net earnings, NE(t)may know this year’s net earnings, NE(t) your expectations of the future affect your best your expectations of the future affect your best

guess for next year, ENE(t+1)guess for next year, ENE(t+1) at an interest rate of 7%, $1.07 next year is at an interest rate of 7%, $1.07 next year is

equivalent to a $1 this yearequivalent to a $1 this year• to compare dollar values for different years, they have to to compare dollar values for different years, they have to

be discounted to a common year be discounted to a common year

PV(t) = ENE(t) + ENE(t+1)/(1+i) + PV(t) = ENE(t) + ENE(t+1)/(1+i) + ENE(t+2)/(1+i)ENE(t+2)/(1+i)22 + ... + ...

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Income-Expense Statement for an Individual

Income Expenditure

Savings

Income-Expense Statement for a Business Firm

Gross Revenue Cost

Profit (net revenue, net earnings)

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http://www.globalexposure.com/

Last Ten YearsLast Ten Years

1948-

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Corporate profits after taxesCorporate profits after taxes

doubled from $160 billion in early 1987 to doubled from $160 billion in early 1987 to $320 billion in early 1994$320 billion in early 1994

doubling in about seven years implies an doubling in about seven years implies an average rate of growth of about 10% per average rate of growth of about 10% per yearyear

this rate of growth is comparable to the 11% this rate of growth is comparable to the 11% rate of growth in the Dow since 1986rate of growth in the Dow since 1986

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Your Stocks

Market Indices

The Economy

corporate earnings(profits)

Index of Leading Economic IndicatorsGross Domestic ProductUnemployment Rate

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1948-

Index of Leading Indicators

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Recall Lab One: Resources for Economists on the Internethttp://rfe.wustl.edu/

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The US Business CycleThe US Business Cycle

expansions, or recoveries, the period from expansions, or recoveries, the period from trough to peak, tend to last a lot longer than trough to peak, tend to last a lot longer than recessions, the period from peak to trough recessions, the period from peak to trough

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US Postwar ExpansionsUS Postwar ExpansionsTrough - Peak Duration, MonthsOct. ‘45 - Nov. ‘48 37Oct. ‘49 - July ‘53 45May ‘54 - Aug. ‘57 39April ‘58 - April ‘60 24Feb. ‘61 - Dec. ‘69 106Nov. 70 - Nov. ‘73 36March ‘75 - Jan. ‘80 58July’80 - July ‘81 12Nov. ‘82 - July ‘90 92March ‘91 - ? ?, 77+ 90

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US Business CycleUS Business Cycle Note the long expansions in the eighties and Note the long expansions in the eighties and

the ninetiesthe nineties is there a new economic regime or order?is there a new economic regime or order? are business cycles a relic of the past?are business cycles a relic of the past?

Note the long expansion in the sixtiesNote the long expansion in the sixties economists then talked about “fine tuning” the economists then talked about “fine tuning” the

economyeconomy then came along the problems of the seventiesthen came along the problems of the seventies

a couple of recessionsa couple of recessions inflationinflation

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Summary-Vocabulary-ConceptsSummary-Vocabulary-Concepts capital asset pricing modelcapital asset pricing model market riskmarket risk asset specific riskasset specific risk stock’s beta, stock’s beta, moving averagemoving average exponential growthexponential growth Dow Jones IndustrialsDow Jones Industrials present valuepresent value

net earnings per sharenet earnings per share expectationsexpectations discount factordiscount factor corporate profits after taxescorporate profits after taxes business cyclebusiness cycle peakpeak troughtrough index of leading indicatorsindex of leading indicators