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CAPMMARKET RISK PREMIUM

What is a reasonableestimate of its

value ?

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What it is “Conceptually”

The annual rate of return which investors require in order to be willing to own shares of an “Average Risk” stock

The expected return on the “MARKET PORTFOLIO” minus the “RISK-FREE RATE”

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Graphic Depiction of RPm

0

2

4

6

8

10

12

14

16

18

20

0 0.5 1 1.5 2

Beta:Non-Diversifiable Risk

ExpectedReturn

RF

MarketRisk

Premium

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What is it “NUMERICALLY”

Issues in estimating RPm: Approach: Prospective or Historical Arithmetic or Geometric average past

measures Does it change (what periods should be

used) Calculation of statistical confidence

intervals Should long-term investors demand a

smaller risk premium than short-term investors

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What Approach s/b Used

ProspectiveEstimate expected return on stock market

and subtract “the” current risk-free rate

Historical Calculate the average risk premium which

investors have actually earned in the past

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Prospective Estimates of RPmExpected Future Annual Market Return 13%

minus

Current Nominal Risk-free Interest Rate 7%Prospective estimate of RPm 6%

Expected Future Market Return might consist of:

Current Dividend Yield on stock index such as S&P 500 3%

plus long-run dividend growth (must be constant growth) 10%

Expected Market Return 13%

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Prospective Estimates of RPm:Problems in Application

Requires estimates of future dividend growth-- either a constant growth assumption,-- or specified yearly dividend growth

These are difficult to estimate

Analyst forecasts of future dividend growthhave not been very accurate

Analysts often forecast futureexpected returns from past returnsSo why not simply look at past return data

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Using Historical Earned Risk Premiums as Sample Estimates of RPm

The logic is: “On average investors will receive what

they expect. So lets look at what they have received to estimate the risk

premium they have desired in the past.”

Earned Risk Premium in year t=

Actual Stock Market Return in tminus

Estimate of Risk-free Rate in year t

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How Should the Average “Earned Risk Premium” be Measured

Arithmetic Average

R = (+25% - 20%) / 2

= 2.5%

Geometric Average

G = [(1.25)(0.8)]1/2 - 1

= 0.0%

Date: 0 1 2Return between dates +25% -20%Wealth $1 $1.25 $1

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Arithmetic Average Returns1926-1996

Nominal Real

CPI 3.22% 0.00%

Treasury Bills 3.80% 0.58%

Treasury Bonds 5.47% 2.24%

Corp. Bonds 5.94% 2.72%

S&P 500 12.67% 9.45%

Smallest 20% 18.65% 15.43%

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Geometric Average Returns1926-1996

Nominal Real

CPI 3.12% 0.00%

Treasury Bills 3.75% 0.48%

Treasury Bonds 5.10% 1.70%

Corp. Bonds 5.61% 2.20%

S&P 500 10.71% 7.35%

Smallest 20% 12.46% 9.10%

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Implied Risk Premiumsusing S&P500 as Market Proxy

Proxy forRF

ArithmeticNominal

ArithmeticReal

GeometricNominal

GeometricReal

TreasuryBills

8.87% 8.87% 6.96% 6.87%

TreasuryBonds

7.20% 7.20% 5.61% 5.65%

The choice of R or G does matter

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Which is Better: R or G

G represents a compound return.

For capital budgeting purposes, we are also using compound returns.

For consistentcy, use geometric average values when estimating the Market Risk Premium RPm

This issue is much debated, no common concensus.

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Estimates of RPmUsing 30-years Geometric Returns

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1954

1957

1960

1963

1966

1969

1972

1975

1978

1981

1984

1987

1990

1993

S&P minus Tbills

S&P minus Tbonds

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Estimates of RPmUsing 20-years Geometric Returns

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1944

1947

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

S&P minus Tbills

S&P minus Tbonds

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Do Market Risk Premiums Change They probably do change

as investor perceptions of market risk change

However, any past estimates are so variable and uncertain that we simply can not identify changes.

Conclusion, use all returns available

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Statistical Confidence Limits on RPmBased on Geometric Average 1926-1996

Percentile 10th 25th 50th 75th 90th

SP500minusTbills

3.6% 5.1% 6.8% 8.5% 10.1%

SP500minusTbonds

2.0% 3.5% 5.2% 6.4% 8.4%

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Exercises

Review the worksheet “RiskPremium” on the file LectureMaterials.xls

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Review Questions1. Why are arithmetic means of security returns greater than geometric means? Develop an exampleof this using numbers other than presented in thesenotes.

2. Which type of mean return is more meaningfulto investors? (Hint: Does the investment horizonmatter.)

3. What is the logic associated with using past “earned”risk premiums” as estimates of the current market riskpremium?

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Review Questions4. Go to the “Yrly_INDXRTNS” worksheet in theFinlMgtData.xls spreadsheet. Calculate yearly earned risk premiums for all years possible as follows:

Risk Premium Earned = a. SP500 return minus Tbill returnb. SP500 return minus Tbond return

5. Find the arithmetic average and standard deviationfor both approaches.

6. Find the geometric average earned risk premium.