Academy #4Risk and the

2

In the old days people believed in deterministic systems:

◦ Christianity: “Fortuna’s wheel”:

◦ Buddhism: “Karma”

◦ Islam: "And in the heaven is your provision and that which ye are promised."

There was no concept of randomness

The good old days

3

France of the 17th century: ◦ Drinking and gambling◦ Birthplace of the idea of probability

The idea of probability

4

Emerged in the France of the 17th century

◦ Blaise Pascal:

“How to split a bet on a game that had been interrupted when one player was winning?”

The idea of probability

5

Gottfried von Leibnitz:

◦ ”Nature establishes standards that originate the return of events, but only in the majority of cases”

Lloyd's Coffee House

◦ Early insurance market

The idea of probability

6

The word “risk” is derived from the latin word “risicare”, which means to dare

Risk is a relatively new concept:

Risk:

7

How do you measure risk?

Standard deviation:◦ Most used measure of market risk

◦ Dispersion around the mean

Risk:

8

Example:

◦ = 2.37%

Risk:

-6.01

-4.19

-2.37

-0.56 1.2

63.0

84.9

0More

0

10

20

30

40

50

60

70

Histogram

"Deutsche Telekom""Heidelberg Cement"

Return

Freq

uenc

y

9

People, usually, do not like risk

They have to be compensated for taking risk◦ Excess return:

Risk:

0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.000.00

0.05

0.10

0.15

0.20

0.25

f(x) = 0.0668733777816456 x − 0.015596370910218R² = 0.963917638398688

Risk Return Relationship

StocksLinear (Stocks)

Standard Deviation

Aver

age

Retu

rn

10

Should you take the raw return as a measure of performance?

◦ Why?

◦ Why not?

Risk:

11

How do stocks move?

Risk:

1 12 23 34 45 56 67 78 89 1001111221331441551661771881992100

20

40

60

80

100

120

140

160

Credit AgricoleLVMH Moet HennesBMWDeutsche TelekomFresenius MediaHeidelberger Cement

12

Stocks tend to move upwards, but not always in the same direction

It is possible to decrease the risk of your investments through investing in different stocks at the same time

Diversification may reduce risk substantially

Diversification:

13

Diversification:

Correlation Credit AgricoleLVMH Moet HennesBMW Deutsche TelekomFresenius MediaHeidelberger CementCredit Agricole 1.00 0.46 0.54 0.46 0.13 0.66LVMH Moet Hennes 0.46 1.00 0.70 0.41 0.33 0.62BMW 0.54 0.70 1.00 0.43 0.31 0.65Deutsche Telekom 0.46 0.41 0.43 1.00 0.37 0.49Fresenius Media 0.13 0.33 0.31 0.37 1.00 0.28Heidelberger Cement 0.66 0.62 0.65 0.49 0.28 1.00

Correlation: Measure of linearity between -1 and 1; 0 means no relation

14

Diversification:

1 10 19 28 37 46 55 64 73 82 91 1001091181271361451541631721811901992080

20

40

60

80

100

120

140

160

Portfolio 1Portofolio 2Portfolio 3Portfolio 4

15

Diversification:

0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.000.00

0.05

0.10

0.15

0.20

0.25

f(x) = 0.0668733777816456 x − 0.015596370910218R² = 0.963917638398688

Risk Return Relationship

StocksLinear (Stocks)Portfolio

Standard Deviation

Aver

age

Retu

rn

16

Diversification:

0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.000.00

0.05

0.10

0.15

0.20

0.25

f(x) = 0.0668733777816456 x − 0.015596370910218R² = 0.963917638398688

Risk Return Relationship

StocksLinear (Stocks)Portfolio

Standard Deviation

Aver

age

Retu

rn

17

The Sharpe ratio:

◦ For =0 -> Interpretation: how much return do I receive per risk

Problem:◦ no adjustment for the amount of risk taken

Adjusting returns for risk

Credit Agricole

LVMH Moet

Hennes BMWDeutsche Telekom

Fresenius Media

Heidelberger Cement 1 2 3 4

σ 3.46 1.76 1.97 1.30 1.07 2.37 1.86 2.23 2.70 1.39Mean 0.22 0.09 0.12 0.06 0.07 0.15 0.14 0.16 0.19 0.11

Sharpe 6.31% 5.27%5.86

% 4.42% 6.91% 6.16% 7.75% 7.36% 6.88% 7.91%

18

Disadvantages:

◦ Sharpe ratio has no measurement unit How much worse is a portfolio with a shapre ratio of

-0.5 compared to a portfolio with a sharpe ratio of 0.5?

Adjusting returns for risk

19

The M-2 measure:

E[]:Average : return of the portfolio : return on the risk free asset : std. of the benchmark : std. of the portfolio : Average risk free rate

Adjusting returns for risk

20

The M-2 measure:

◦ Outperformance

Measured in percent

Comparable

Adjusting returns for risk

21

The M-2 measure:

Adjusting returns for risk

Portfolio Portofolio 2 Portfolio 3 Portfolio 4 Benchmarkσ 1.86 2.23 2.70 1.39 2.00Mean 0.14 0.16 0.19 0.11 0.10Sharpe 7.75% 7.36% 6.88% 7.91% 5.00%M^2 0.155097 0.147172 0.137694 0.158142 1

22

Different ScenariosI. Change in portfolio return by an additional 1%

II. Increase the standard deviation by 0.1

Adjusting returns for risk

Portfolio Portofolio 2 Portfolio 3 Portfolio 4 Benchmarkσ 1.87 2.24 2.71 1.40 2.00Mean 0.14 0.16 0.19 0.11 0.1M^2_old 0.155 0.147 0.138 0.158 1M^2_new 0.155 0.146 0.137 0.157 1Delta -0.001 -0.001 -0.001 -0.002 0

Portfolio Portofolio 2 Portfolio 3 Portfolio 4 Benchmarkσ 1.86 2.23 2.70 1.39 2.00Mean 0.15 0.17 0.20 0.12 0.10M^2_old 0.155 0.147 0.138 0.158 1M^2_new 0.161 0.153 0.148 0.173 1Delta 0.006 0.005 0.011 0.015 0.000

23

The M-2 measure:

Weekly observations : weekly return of the portfolio : weeks yield of a 9 month German government bond : std. of the EUROSTOXX index : std. of the portfolio : Average of the 9 month German government bond

Measurement

24

More professional

More industry related

Technically feasible

Why a new performance measure?

25

Questions?