5- 1 © admn 3116, anton miglo admn 3116: financial management 1 lecture 6: risk anton miglo fall...

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© ADMN 3116, Anton Miglo

ADMN 3116: Financial Management 1

Lecture 6: Risk

Anton Miglo

Fall 2014

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Topics

Risk and Return Treasury bond returns Stock returns Mean-Variance Approach Excel: AVE, STDEVP, VARP Additional readings: B ch. 8

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Calculating Total Dollar and Total Percent Returns

Suppose you invested $1,400 in a stock with a share price of $35. After one year, the stock price per share is $49. Also, for each share, you received a $1.40 dividend.

What was your total dollar return? $1,400 / $35 = 40 shares Capital gain: 40 shares times $14 = $560 Dividends: 40 shares times $1.40 = $56 Total Dollar Return is $560 + $56 = $616

What was your total percent return? Dividend yield = $1.40 / $35 = 4%

Capital gain yield = ($49 – $35) / $35 = 40% Total percentage return = 4% + 40% = 44%

Note that $616 divided by $1,400 is 44%.

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A $1 Investment in Different Typesof Portfolios, 1926—2009

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Rates of Return 1926-2000

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 9520

00

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

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Average Annual Returns for Five Portfolios and Inflation

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Average Annual Risk Premiums for Five Portfolios

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What is Risk?

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-10 -5 0 5 10 15 20 25 30

Company B

return

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

return

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Frequency Distribution of Returns on Common Stocks, 1926—2009

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Benchmark risks and returns

Average Annual Variance Standard Portfolio Rate of Return Deviation

Treasury Bills 4.1 7.9 2.8

Gov’t Bonds 5.2 68 8.2

Common Stocks 11.7 402.6 20.1

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Example: Calculating Historical Variance and Standard Deviation

Let’s use data from Table 1.1 for Large-Company Stocks.

The spreadsheet below shows us how to calculate the average, the variance, and the standard deviation (the long way…).

(1) (2) (3) (4) (5)Average Difference: Squared:

Year Return Return: (2) - (3) (4) x (4)1926 11.14 11.48 -0.34 0.121927 37.13 11.48 25.65 657.921928 43.31 11.48 31.83 1013.151929 -8.91 11.48 -20.39 415.751930 -25.26 11.48 -36.74 1349.83

Sum: 57.41 Sum: 3436.77

Average: 11.48 Variance: 859.19

29.31Standard Deviation:

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Historical Risk and Return Trade-Off

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Investment returns

The rate of return on an investment can be calculated as follows:

(Amount received – Amount invested)

Return = ________________________

Amount invested

For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:

($1,100 - $1,000) / $1,000 = 10%.

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Risk and return

Average Annual Risk/Standard Investments Rate of Return (%) Deviation (%)

Treasury Bills 4.1 2.8

Gov’t Bonds 5.2 8.2

Common Stocks 11.7 20.1

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Investment Choices

A B

C

AverageRetur

n

Risk

15%

5%

20%

20%5%

AverageReturn

Risk

Risk-averse

Risk-neutral

Risk-loving

D

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Excel functions used

AVERAGE SQRT VAR STDEV

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Treasury bill example

Buy bill 1 June 2008 for $977.04 Horizon: Pays you back $1,000 in one year Safety: Payment guaranteed by U.S.

government Liquidity: Highly liquid

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One year yield on T-bill

19

1234

A B C

Purchase price 977.04Payoff on maturity 1,000.00 <-- This is the Treasury bill's face valueInterest 2.35% <-- =B3/B2-1

INTEREST ON THE TREASURY BILL

If you hold the Bill for one year, you will absolutely get the 2.35% yield. It is totally safe!

This 2.35% yield is both ex-ante and ex-post: Ex-ante: It is the predicted yield for holding the T-

bill when you buy it Ex-post: It is the yield you will get after one year if

you hold the T-bill to maturity

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Track T-bill prices throughout the year

20

123456789

1011121314151617181920

A B C D E F G H

Date Bill price1-Jun-08 977.041-Jul-08 980.25

1-Aug-08 982.751-Sep-08 986.271-Oct-08 990.901-Nov-08 993.981-Dec-08 997.661-Jan-09 998.261-Feb-09 998.011-Mar-09 998.461-Apr-09 999.14

1-May-09 999.881-Jun-09 1,000.00

THE PRICE OF THE TREASURY BILL THROUGHOUT THE YEAR

975

980

985

990

995

1,000

1-Jun-08

1-Jul-08

1-Aug-08

1-Sep-08

1-Oct-08

1-Nov-08

1-Dec-08

1-Jan-09

1-Feb-09

1-Mar-09

1-Apr-09

1-May-09

1-Jun-09

1-Year Treasury Bill Price Through the Year

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Stock price risk

McDonald’s stock (MCD) is risky Horizon risk: How long will you hold the stock? Safety: stock is inherently unsafe

• This doesn’t mean it’s not a good stock! Liquidity risk: minimal—the volume of MCD

traded daily is very large, so it should be easy to dispose of the stock.

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© ADMN 3116, Anton Miglo 22

0

10

20

30

40

50

60

70

31-Dec-98

31-Dec-99

30-Dec-00

30-Dec-01

30-Dec-02

30-Dec-03

29-Dec-04

29-Dec-05

29-Dec-06

29-Dec-07

28-Dec-08

McDonald's Stock Prices31 Dec 1998 - 31 Dec 2008

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Computing the average and standard deviation of annual returns

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1

23456789

10111213

A B C D E F G H

DateStock price

Return

4-Jan-99 31.75 Largest annual return 52.12% <-- =MAX(C3:C13)3-Jan-00 32.85 3.46% <-- =B4/B3-1 Smallest annual return -36.65% <-- =MIN(C3:C13)2-Jan-01 27.95 -14.92% <-- =B5/B4-12-Jan-02 22.29 -20.25% Average annual return 6.94% <-- =(B13/B3)^(1/10)-12-Jan-03 14.12 -36.65% Variance of annual returns 0.0723 <-- =VARP(C4:C13)2-Jan-04 21.48 52.12% Standard deviation of annual returns 26.88% <-- =STDEVP(C4:C13)3-Jan-05 28.09 30.77%3-Jan-06 30.19 7.48%3-Jan-07 40.48 34.08%2-Jan-08 55.02 35.92%2-Jan-09 62.10 12.87%

McDONALD'S--BEGINNING-YEAR STOCK PRICES, Jan 1999-Jan 2009

Statistics

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Statistics review

24

15

16171819202122232425262728293031

A B C D

MCDreturn

Return minus average, squared

3-Jan-00 3.46% 0.49% <-- =(B17-$B$28)^22-Jan-01 -14.92% 6.45% <-- =(B18-$B$28)^22-Jan-02 -20.25% 9.45%2-Jan-03 -36.65% 22.22%2-Jan-04 52.12% 17.34%3-Jan-05 30.77% 4.11%3-Jan-06 7.48% 0.09%3-Jan-07 34.08% 5.57%2-Jan-08 35.92% 6.47%2-Jan-09 12.87% 0.06%

Average 10.49% <-- =AVERAGE(B17:B26)Variance 0.0723 <-- =SUM(C17:C26)/10

0.0723 <-- =VARP(B17:B26)Standard deviation 26.88% <-- =SQRT(B29)

STATISTICAL REVIEW

Statistical note: The only consistent way of computing annual average returns is to use the continuously compounded returns, illustrated on page 273. This Excel sheet uses discrete returns, but these give contradictory results. (Compare, for example 10.49% in cell B28 with 6.94% in cell G6 .)

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For a discussion of average return versus standard deviation

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Average return

Standard deviation

Average return

Standard deviation

Abbott 4.25% 21.47% Manpower 4.29% 32.37%

Alcoa -3.43% 42.03% Marriott 2.51% 27.70%

Altria 8.65% 29.51% McGraw-Hill 0.71% 24.05%

American Airlines -8.04% 75.72% Microsoft -5.79% 35.88%

anguard High-Yield 1.79% 8.59% Nasdaq -5.11% 30.98%

Boeing 4.49% 30.95% Nicor 4.06% 27.34%

Cisco -4.89% 43.06% Nordstrom -1.56% 42.24%

Coca Cola 0.10% 24.98% Northrop 7.80% 25.31%

Dell -15.50% 41.97% Procter & Gamble 5.16% 22.31%

Exxon 10.60% 18.06% PPG 1.24% 23.08%

Ford -22.92% 48.67% S&P 500 -3.22% 15.28%

GE -4.89% 24.22% Safeway -8.13% 28.46%

Hershey 4.40% 23.17% TEVA 21.33% 29.81%

IBM 0.43% 30.36% U.S. Steel 6.11% 55.83%

Johnson & Johnson 5.30% 19.39% Value Line Equity Fund -5.14% 18.09%

Kellogg 3.79% 20.82% Vanguard Long-Term Treasury 5.44% 13.37%

Kraft 0.74% 21.01% Vanguard Windsor 1.93% 16.97%

Kroger -1.42% 25.22% Walmart 3.72% 22.89%

AVERAGE RETURN VERSUS STANDARD DEVIATION OF RETURNSA somewhat arbitrary list of assets, 1999-2008

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