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JP Omega Ltd.
Discussion Document
Munich,
April 22, 2015
JP Omega Ltd.
Performance Evaluation
STOXX 600 Europe Sector - Johnson Omega optimized
JP Omega Ltd.
Optimized w.r.t. Johnson OmegaPortfolio Type LongOnlyLeverage 813Risfree Rate EUR Libor 1MBenchmark STOXX 600 Europe TR €
Rebalancing Exposure Long (rhs)Frequency MonthlyDay LastBusinessDayOffset DaysLag Days
Transaction CostLong bpsShort bps 206
Exposure Turnover (p.a.) 952%
Min Exposure Short (rhs)Max
Constraints
AssetClassRiskfree
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YTD BenchConstituent (Assets): 2015 10,6% 7,8% 3,4% 23,4% 16,8%
2014 -2,1% 7,1% 0,0% 1,1% 3,3% 0,9% -4,2% 2,7% 2,1% -1,3% 3,4% -1,2% 12,2% 7,8%STOXX 600 Europe Total Return €: 2013 6,4% 1,8% -1,0% 0,7% 1,6% -6,3% 4,5% -2,2% 8,9% 6,8% 1,7% 2,3% 27,0% 21,5%
2012 0,0% 6,0% -0,5% 0,7% -4,9% 4,7% 6,8% -0,3% 0,6% -0,8% 3,9% 3,1% 20,2% 19,0%1. AUTO & PARTS 10. INSURANCE 2011 -1,2% 2,0% -2,9% 5,6% -2,8% -3,7% -0,3% -0,3% 0,1% 0,2% 0,2% 0,3% -3,2% -8,1%2. BANKS 11. MEDIA 2010 -5,0% 1,1% 9,5% -0,6% -4,6% 1,3% -0,3% -1,8% 5,1% 2,6% 2,4% 6,3% 16,2% 12,2%3. BASIC RESOURCE 12. OIL & GAS 2009 -2,9% 0,1% 0,1% 9,0% 0,1% -3,7% 17,2% 1,9% 4,8% -6,2% 0,5% 9,1% 31,6% 33,3%4. CHEMICALS 13. PERS & H/H GDS 2008 -0,2% 0,1% -2,0% 0,4% 0,6% 0,0% -3,4% 0,3% 0,2% 1,1% 0,1% 0,3% -2,6% -43,4%5. CON & MAT 14. RETAIL 2007 3,4% -1,8% 5,6% 3,8% 6,6% -0,4% -3,5% -2,1% 4,5% 3,9% -4,5% 0,4% 16,3% 2,8%6. FINANCIAL SVS 15. TECHNOLOGY 2006 7,6% 4,6% 5,0% 2,7% -7,1% 2,1% 4,1% 3,4% 3,0% 3,0% 1,8% 7,2% 43,3% 21,3%7. FOOD & BEV 16. TELECOM 2005 4,5% 1,3% -2,3% -3,1% 7,5% 3,5% 3,6% 0,6% 5,8% -6,3% 5,1% 7,4% 30,1% 27,2%8. HEALTH CARE 17. TRAVEL & LEIS 2004 4,7% 6,0% -2,1% -5,8% 1,1% 2,2% -1,8% -0,3% 0,3% 0,5% 0,7% 3,1% 8,5% 12,7%9. INDS GDS & SVS 18. UTILITIES 2003 0,1% -0,9% -0,5% 12,8% 1,2% 0,2% 0,8% 2,6% -8,8% 10,5% -1,1% 2,2% 18,9% 17,2%
2002 0,3% 0,3% 2,6% -3,7% 0,2% 0,0% -2,4% 0,3% 0,3% 0,3% 0,3% -2,9% -4,7% -30,8%
1994 JP Omega Ltd.
Monthly Returns
00
min max
-30% 100%
0% 30%0% 130%
0% 0%
0
130% 130%
0
Basic Information, Performance Chart & Table HFRI Strategies - JP Omega optimizedDescription
30%
Gross Net
Performance & Exposure Chart Start: End:31-Dec-01 31-Mar-15
-30%
-10%
10%
30%
50%
70%
90%
110%
130%
0
100
200
300
400
500
600
700
800
900
Dec-01 Dec-03 Dec-05 Dec-07 Dec-09 Dec-11 Dec-13
Optimized Benchmark Magnitude t-stat Optimized Benchmark
Return comp. ann. 17,1% 5,6% Mean Exc. Return ann. 10,2% 2,94 worst 0,28% -14,06%
Volatility ann. 13,7% 15,6% Tracking Error ann. 12,6% na 2nd worst 1,09% -13,18%
Skewness 0,53 -0,64 Jensen Alpha ann. 12,3% 4,20 3rd worst -0,20% -11,57%
p-value 11% 5% Market Beta 0,56 10,52 4th worst 0,19% -11,03%
Kurtosis 3,16 2,79 5th worst -2,43% -10,29%
p-value 0,8% 0,6% 5th best 0,17% 7,72%
Downside Deviation ann. 8,7% 17,4% 4th best 17,25% 9,41%
Magnitude 9,3% 54,0% 1. Clearly higher annualized compounded return 3rd best 0,28% 9,46%
Peak 31-Oct-07 31-May-07 2. Lower Volatility 2nd best 12,81% 11,16%
Trough 30-Jan-09 27-Feb-09 3. Outperformance at 99,8363% Confidence Level best 9,00% 14,52%
Recovery 6 56 4. Positive Skewness of Strategy
5. Lower downside deviation
6. Substantially lower Maximum Drawdown
Optimized Benchmark 7. Much faster recovery from Max Drawdown Optimized Benchmark
Sharpe 1,09 0,31 8. Higher Sharpe, Sortino , Calmar Ratio 0,1% -7,74% -10,83%
Sortino 1,72 0,28 9. Positive Treynor Ratio 1,0% -4,53% -5,92%
Calmar 1,83 0,10 10. Excellent Information Ratio 2,5% -3,18% -4,02%
Treynor 18,0% 11. Substantial Skill: Jensen Alpha, significant at 99,9986851% CL 5,0% -2,07% -2,59%
Information 0,81 12. No Luck: Returns not generated through excessive exposure. 10,0% -0,85% -1,12%
Maximum Exp. Gain 19,7% 9,8% 13. Better outliers to the upside versus downside ratio 50,0% 3,50% 2,98%
Maximum Exp. Loss -6,0% -9,1% 14. Better overall upside potential versus downside risk 90,0% 1,22% 1,34%
Gain vs. Loss Ratio 3,30 1,08 15. Performed 5 times better within 5 CL brackets on downside 95,0% 8,84% 6,25%
Call (Upside) 3,6% 2,6% 16. Performed 4 times better within 5 CL brackets on upside 97,5% 10,74% 7,17%
Put (Downside) 0,4% 0,5% 17. Performed 5 times better in 5 worst months 99,0% 12,59% 7,99%
Omega 9,85 5,71 18. Performed 2 times better in 5 best months 99,9% 15,01% 9,01%
JP Omega Ltd.
Excess Returns
Market Model
Absolute Performance Measures Relative Performance Measures
Detailed Performance Measurement - Entire Period
Confidence Level
Advanced
Traditional
Performance Ratios
HFRI Strategies - JP Omega optimized
Best/Worst Benchmark vs Strategy
Probabilities for Minimum Realized Returns
Best Months
Maximum Drawdown
Worst MonthsReturn and
Moments
Comments & Portfolio Highlights
10 Y since 31-Mar-05 5 Y since 31-Mar-10 3 Y since 30-Mar-12 1 Y since 31-Mar-14
Portfolio Optimized Benchmark Optimized Benchmark Optimized Benchmark Optimized Benchmark
Return comp. ann. 20,4% 7,9% 17,7% 12,5% 26,1% 18,8% 31,9% 22,8%
Volatility ann. 13,9% 14,9% 12,3% 11,8% 13,3% 10,0% 13,8% 10,5%
Skewness 0,50 -0,63 0,33 -0,61 0,10 -0,32 0,56 0,75
p-value 7% 4% 8% 5% 36% 16% 7% 2%
Kurtosis 1,07 1,78 -0,07 1,08 -0,05 0,57 0,81 -0,15
p-value 14,9% 0,2% 43,6% 11,3% 45,1% 14,8% 23,8% 43,7%
Downside Deviation ann. 8,9% 16,0% 7,5% 11,1% 7,8% 7,4% 6,5% 3,9%
Magnitude 9,3% 54,0% 7,0% 18,9% 6,3% 7,2% 4,2% 2,1%
Peak 31-Oct-07 31-May-07 29-Apr-11 31-May-11 31-May-13 30-Mar-12 30-Jun-14 30-May-14
Trough 30-Jan-09 27-Feb-09 31-Aug-11 30-Sep-11 28-Jun-13 31-May-12 31-Jul-14 31-Jul-14
Recovery (Months) 6 56 11 12 3 2 2 2
Mean Exc. Return ann. 10,9% 4,7% 6,4% 7,7%
t-stat 2,92 1,18 1,85 1,55
Tracking Error ann. 11,8% 8,9% 6,0% 4,9%
Jensen Alpha ann. 13,6% 7,5% 2,8% 2,4%
t-stat 4,09 1,88 0,75 0,47
Market Beta 0,62 0,77 1,20 1,25
t-stat 9,84 8,19 12,45 9,87
Sharpe 1,29 0,48 1,35 1,02 1,81 1,77 2,09 2,01
Sortino 2,04 0,45 2,23 1,08 3,09 2,40 4,46 5,44
Calmar 2,18 0,15 2,54 0,66 4,14 2,61 7,58 10,85
Treynor 17,4% 6,1% 5,3% 6,2%
Information 0,92 0,53 1,07 1,55
Max Gain vs. Loss 3,14 1,08 3,37 1,10 2,43 1,43 3,77 8,41
Omega 8,41 5,06 6,32 3,90 4,44 2,78 3,99 2,28
JP Omega Ltd.
Relative Performance
Measures
Advanced
Excess Returns
Market Model
Performance Ratios
Traditional
Maximum Drawdown
Return and Moments
Absolute Performance
Measures
HFRI Strategies - JP Omega optimizedPerformance Measurement - Subperiods
1. Return (ann., comp.): Return per anno including compounding (profits reinvested)
2. Volatility (ann.):
3. Skewness (p-value): Asymmetry of distribution: Negative/positive indicates a tendency for extreme returns to downside/upside. P-value indicates the significance.
4. Kurtosis (p-value):
5. Downside Deviation:
6. Maximum Drawdown:
7. Excess Returns:
8. Market Model:
JP Omega Ltd.
Relative Performance Measures
A) Jensen Alpha (SKILL) is the intercept from a regression line for strategy excess returns w.r.t. riskfree on benchmark excess returns w.r.t. riskfree. It is a measure for the skill inherent in a strategy. Significance indicates whether Jensen Alpha was not generated by chance.
Excess returns from strategy versus benchmark. It is required that those are significant. Necessary, but not sufficient to evaluate a strategy as significant excess returns generated in a bull market might be simply generated by plain leverage. Here Jensen Alpha required for complete picture.
B) Beta (LUCK) is the slope of the regression line and the explanatory variable for returns in this simple factor model. Returns explained by beta are considered to be generated by luck, supposed market timing is impossible.
Tail fatness of distribution: Large indicates fat tails (whether to upside/downside or neutral depends on skew). P-value indicates the significance of excess kurtosis with respect to kurtosis equals 3 of Normal distribution.
Standard Deviation of returns below mean of excess returns with respect to risk-free rate. To be compared with plain volatility can shown asymmetry in returns and is supplementary to skewness. Remark: Whereas volatility may also discriminate upside risk, downside volatility exclusively measures downside risk.
Worst possible loss from investing at highest level and selling at subsequent lowest level. Peak is start date for decline. Trough is date of highest loss. Recovery is the time until prior peak was reached again.
Monthly volatility (stdev) of absolute returns multiplied by sqrt(12). Basic risk measure for fluctuation of returns. Does not distinguish between upside and downside risk.
Glossary I
Absolute Performance Measures
Jensen Alpha(mthly, i.e. intercept)
=0.7%
Market Beta(i.e. Slope)=0.75
-10%
-5%
0%
5%
10%
15%
-10% -8% -6% -4% -2% 0% 2% 4% 6% 8%
JP O
meg
a St
rate
gy E
xces
s Ret
urn
vers
us
Risk
free
Rat
e
Equally Weighted HFRI Indices Excess versus Riskfree Rate
Market Model
7. Sharpe:
8. Sortino:
9. Calmar:
10. Treynor:
11. Information:
12. JP Gain vs Loss:
13. JP Omega:
Portfolio Moments:Strategy Benchmark
Mean 0,26% -0,79%
Volatility 1,19% 1,97%
Skew 0,33 -0,65
Kurtosis (Excess) 0,22 3,06
-> Both better upside potential and risk protection.
-> Preferred by any rational investor, irrespective utility.
JP Omega Ltd.
Definition of "First Order Stochastic Dominance": Strategy CDF stricly below benchmark CDF.
Please note: Minimum Expected Returns at any confidence level (CL) can be drawn from the CDF.
Glossary II
Minimum Expected Returns of Strategy and Benchmark subject to given Confidence Levels
Performance Ratios (upside per risk)
Excess returns mean over excess returns volatility (excess returns w.r.t. Risk free rate). Does not distinguish between up-/downside risk. Ignores asymmetry and fat tails. Annualized by multiplying monthly Sharpe by sqrt(12)
Excess returns mean over excess returns downside volatility (excess returns w.r.t. Risk free rate). Distinguishes between up-/downside risk. Ignores asymmetry and fat tails. Annualized by multiplying monthly Sortino by sqrt(12)
The portfolio moments (mean, variance, skewness and kurtosis) uniquely determine the Johnson distribution. The minimum expected returns at given confidence levels can then be drawn directly from the Johnson distribution. The JP Omega optimized portfolio of a hedge fund strategy is compared to the equally weighted benchmark portfolio.
Returns p.a. compounded over maximum drawdown. This can be interpretet as recovery speed, e.g. Calmar ratio of 1 indicates that the maximum drawdown took in average 1 year to be recovered).
Excess returns mean over market beta. Market beta only covers market risk. In contrast volatility in addition covers specific risk. Does not distinguish between up-/downside risk. Ignores specific risk, asymmetry and fat tails. Annualized by multiplying monthly Treynor by 12.
Excess returns mean over excess returns volatility (i.e. tracking error; excess returns w.r.t. benchmark). Does not distinguish between up-/downside risk. Ignores asymmetry and fat tails. Annualized by multiplying monthly Information Ratio by sqrt(12)
Ratio of max. exp. gain over max. exp. loss, i.e. the implied strike of call (upside) over the implied strike of a put (downside) ratio, where the strike is implied by imposing JP call and JP put, accounting for tail fatness, are "costfree", in the sense that the price of an option is 0.5 basispoints.
Ratio of entire upside potential (JP Call) over entire downside risk (JP Put). In contrast to the JP Gain vs Loss ratio the strike equals the equally weighted portfolio mean, and is therefore not in the tails. The pricing reflects the overall ratio and not only the asymmetry of (un-)likely extrem events.
CDF indicates a 5% likelihood that Strategy and Benchmark will undershoot -4,1% and -1,6%; respectively.
5% CL
95% CL
0%
25%
50%
75%
100%
-6% -3% 0% 3% 6%
Johnson Cumulative Densities
Strategy
Benchmark
0
10
20
30
40
-6% -3% 0% 3% 6%
Johnson Densities
Strategy
Benchmark