academy #4 risk and the
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Academy #4Risk and the
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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
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France of the 17th century: ◦ Drinking and gambling◦ Birthplace of the idea of probability
The idea of probability
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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
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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
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The word “risk” is derived from the latin word “risicare”, which means to dare
Risk is a relatively new concept:
Risk:
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How do you measure risk?
Standard deviation:◦ Most used measure of market risk
◦ Dispersion around the mean
Risk:
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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
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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
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Should you take the raw return as a measure of performance?
◦ Why?
◦ Why not?
Risk:
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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
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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:
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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
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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
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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
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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
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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%
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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
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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
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The M-2 measure:
◦ Outperformance
Measured in percent
Comparable
Adjusting returns for risk
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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
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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
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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
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More professional
More industry related
Technically feasible
Why a new performance measure?
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Questions?
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