In this presentation we look at Hedge Funds from a theoretical and empirical viewpoint and confirm their risk reducing characteristics in the South African context.

1. Strictly private and confidential
For discussion purposes only
Hedge Funds in South
Africa
by Peter Urbani

2. 2
•What are Hedge Funds
•Where do Hedge Funds Belong
•What Returns should I expect
Why Hedge Funds

3. 3
What is a Hedge
• A hedge is a protective barrier, designed to mitigate or reduce the adverse effects
of something.
In the case of an actual hedge, they are designed to be windbreaks that
protect fields and crops from strong winds

4. 4
What are Hedge Funds
• An extreme form of unconstrained active management that seek to generate
absolute returns by reducing downside risks
Complexity
High
Low Costs High
Equities
Index Funds
Cash
Hedge
Structured Products
Bonds
Balanced

5. 5
Bi-Lateral (both sides) Symmetry (the same shape)

6. 6
Normal Distribution Assumes Risk Symmetry
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
0.00%
500.00%
1000.00%
1500.00%
2000.00%
2500.00%
3000.00%
3500.00%
4000.00%
-6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00%
Normal
Upside ‘Risk’Downside ‘Risk’ =

7. 7
But real returns often Asymmetric –ve Skewed
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
0.00%
500.00%
1000.00%
1500.00%
2000.00%
2500.00%
3000.00%
3500.00%
4000.00%
-6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00%
Neg- Skew Normal
Upside ‘Risk’Downside ‘Risk’ ≠

8. 8
0.00%
500.00%
1000.00%
1500.00%
2000.00%
2500.00%
3000.00%
3500.00%
4000.00%
-6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00%
Normal Pos+ Skew
A hedged fund should by definition be Positively Skewed
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
Upside ‘Risk’Downside ‘Risk’ ≠

9. 9
Equities versus Equities – Beta = 1.00, Alpha = 0%
If you buy Equities you are exposed to Pure Beta
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
PureBeta
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
ALPHA = 0.00%
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

10. 10
Equities versus Equities – Beta = 1.00, Alpha = 0%
When Markets go down you go down by the same amount
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
PureBeta
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
ALPHA = 0.00%
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

11. 11
Perfectly ‘Hedged’ Fund – Downside Beta = 0, Upside Beta = 1.0, Alpha = +1.21%
A Perfectly Hedged Fund would protect your downside
ASSUMED
JOINT NORMAL
DISTRIBUTIONS
SYMMETRIC
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
PerfectlyHedged
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
ALPHA = 1.21%
THEORETICAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

12. 12
Perfectly ‘Hedged’ Fund – Downside Beta = 0, Upside Beta = 1.0, Alpha = +1.21%
Which would by definition make its returns Asymmetric
ACTUAL JOINT
DISTRIBUTIONS
BY DEFINITION
ASYMMETRIC
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
PerfectlyHedged
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
ALPHA = 1.21%
THEORETICAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

13. 13
• Joint Normal Distribution assumption can under- or over- state both positive and
negative risks and consequently tail risk and true correlation.
Normal versus Positively Skewed Distributions
-2.00%
-1.28%
-0.56%
0.16%
0.88%
1.60%
2.32%
3.04%
3.76%
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
0.1600
0.1800
-4.00%
-3.68%
-3.36%
-3.04%
-2.72%
-2.40%
-2.08%
-1.76%
-1.44%
-1.12%
-0.80%
-0.48%
-0.16%
0.16%
0.48%
0.80%
1.12%
1.44%
1.76%
2.08%
2.40%
2.72%
3.04%
3.36%
3.68%
4.00%
Test Fund
Bad
0.1600-0.1800
0.1400-0.1600
0.1200-0.1400
0.1000-0.1200
0.0800-0.1000
0.0600-0.0800
0.0400-0.0600
0.0200-0.0400
0.0000-0.0200
-3.00% -2.04% -1.08% -0.12% 0.84% 1.80% 2.76% 3.72% 4.68%
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
0.1600
-4.00%
-3.20%
-2.40%
-1.60%
-0.80%
0.00%
0.80%
1.60%
2.40%
3.20%
4.00%
Good
Bad

14. 14
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
PerfectHedge
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
Perfect Hedge Fund – Downside Beta = 0.30, Upside Beta = 0.70, Alpha = +1.50%
A Perfect Hedge Fund would give you alpha of around 1.50%
ALPHA = 1.50%
THEORETICAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

15. 15
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
MedianLSHedgeFund
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
Actual LS Hedge Fund – Downside Beta = 0.14, Upside Beta = 0.20, Alpha = +0.70%
Actual Hedge Funds have delivered about half of that
ALPHA = 0.70%
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

16. 16
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
TopQuartileLSHedgeFund
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
Top 25% LS Hedge Fund – Downside Beta = 0.12, Upside Beta = 0.32, Alpha = +1.70%
But Top Quartile Funds have delivered more
ALPHA = 1.70%
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

17. 17
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
TopDecileLSHedgeFund
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
Top 10% LS Hedge Fund – Downside Beta = 0.06, Upside Beta = 0.45, Alpha = +2.95%
And Top Decile Funds have delivered twice as much
ALPHA = 2.95%
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

18. 18
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
BottomDecileLSHedgeFund
SA Equities
Best Fit Bi-variate
Copula Lines
Piecewise
Regression
Linear Regression
Worst 10% LS Hedge Fund – Downside Beta = 0.36, Upside Beta = 0.13, Alpha = -1.36%
While Bottom Decile Funds have not done as badly
ALPHA = -1.36%
THIS IS WHAT YOU
DON’T WANT TO SEE
HIGHER 4TH QUADRANT
TAIL DEPENDENCE
ACTUAL
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

19. 19
Impact of Asymmetry on Risk Metrics - Actual
-15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%
Best Fit and Assumed Normal Distributions for Pure Beta
Best Fit Fund PDF (Normal)
Assumed Normal Fund PDF(Normal)
-2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00%
Best Fit and Assumed Normal Distributions for Median LS Hedge Fund
Best Fit Fund PDF (Johnson (Lognormal))
Assumed Normal Fund PDF(Normal)
Hedge Funds’Equities

20. 20
• Hedge Funds are complimentary assets
Where do Hedge Funds Belong
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
SA Domestic Asset Classes
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

21. 21
Efficient Frontier without Hedge Funds allowed
• Hedge Funds are complimentary assets
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Efficient Frontier Without Hedge Funds
Effic ient Frontier Without Hedge Funds ( Normal )
Optimal Without Hedge Funds ( Normal ) Vol = 9.09%
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

22. 22
Efficient Frontier with Hedge Funds allowed
• Frontier with Hedge Funds moves to the left – reducing volatility
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Efficient Frontier With Hedge Funds
Effic ient Frontier With Hedge Funds ( Normal )
Optimal With Hedge Funds ( Normal ) Vol = 2.76%
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

23. 23
Hedge Funds are Risk Diversifiers
• Adding Hedge Funds to your portfolio will reduce its volatility
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Efficient Frontier With and Without Hedge Funds
Effic ient Frontier Without Hedge Funds ( Normal )
Effic ient Frontier With Hedge Funds ( Normal )
Optimal With Hedge Funds ( Normal ) Vol = 2.76%
Optimal Without Hedge Funds ( Normal ) Vol = 9.09%
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

24. 24
Including Hedge Funds leads to better Risk Adjusted Returns
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
​​​​​​​​0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
-9.00%-8.00%-7.00%-6.00%-5.00%-4.00%-3.00%-2.00%-1.00%0.00%1.00%
Returns(Monthly)
Modified Value at Risk ( VaR )
Mean Modified Value at Risk (VaR) (Monthly) Frontier
Efficient Frontier Without Hedge Funds ( Normal )
Efficient Frontier With Hedge Funds ( Normal )
Optimal Without Hedge Funds ( Normal ) VaR @( 99.00% ) = -5.12%
Optimal With Hedge Funds ( Normal ) VaR @( 99.00% ) = -1.00%
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
• Hedge Funds are risk diversifiers

25. 25
• Hedge Funds are complimentary assets
Unconstrained Optimal Portfolio mainly in Hedge Funds

26. 26
• Hedge Funds are complimentary assets
But many SA investors subject to Reg 28 Constraints

27. 27
Reg 28 (Prudential Limit) Constrained Efficient Frontiers
• Even with Hedge Funds limited to 10% of your portfolio they still shift the frontier
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Reg 28 Constrained FrontiersWith and Without Hedge Funds
Effic ient Frontier Without Hedge Funds ( Normal )
Effic ient Frontier With Hedge Funds ( Normal )
Optimal With Hedge Funds ( Normal ) Vol = 7.84%
Optimal Without Hedge Funds ( Normal ) Vol = 8.60%
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015

28. 28
Impact of Asymmetry on Efficient Frontiers
• Even with Hedge Funds limited to 10% of your portfolio they still shift the frontier
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Mean Modified Frontiers With and Without Hedge Funds
Effic ient Frontier Without Hedge Funds ( Modified )
Effic ient Frontier With Hedge Funds ( Modified )
Optimal With Hedge Funds ( Modified ) Vol = 7.25%
Optimal Without Hedge Funds ( Modified ) Vol = 7.82%

29. 29
Impact of Asymmetry on Efficient Frontiers
• Standard Mean Variance ( Normal ) Frontier does not capture asymmetry
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Normal Frontier provides innacurate allocation advice
Effic ient Frontier With Hedge Funds ( Normal )
Effic ient Frontier With Hedge Funds ( Modified )
Optimal With Hedge Funds ( Modified ) Vol = 7.25%
Optimal With Hedge Funds ( Normal ) Vol = 7.84%

30. 30
Asymmetry causes Correlation and Vols to be Different

31. 31
Impact of Asymmetry on Efficient Frontiers
• Standard Mean Variance ( Normal ) Frontier does not capture asymmetry
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
SA Equities
SA Bonds
SA Cash
SA Property
SA Hedge
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Normal Frontier provides innacurate allocation advice
Effic ient Frontier With Hedge Funds ( Normal )
Effic ient Frontier With Hedge Funds ( Modified )
Optimal With Hedge Funds ( Modified ) Vol = 7.25%
Optimal With Hedge Funds ( Normal ) Vol = 7.84%

32. 32
Impact of Asymmetry on Hedge Fund Efficient Frontiers
• Standard Mean Variance ( Normal ) Frontier does not capture asymmetry
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
BI Fixed Income
BI LSConservative
BI LSAggressive
BI Commodities
BI Structured Finance
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00%
Returns(Annual)
Volatility (Annual)
Normal Frontier provides suboptimal allocation advice
Effic ient Frontier With Hedge Funds ( Normal )
Effic ient Frontier With Hedge Funds ( Modified )
Optimal With Hedge Funds ( Modified ) Vol = 1.44%
Optimal With Hedge Funds ( Normal ) Vol = 1.62%

33. 33
Normal ( Mean Variance ) and Modified Optimal Allocations
12.99%
30.00%
13.80%
10.97%
2.24%
30.00%
Optimal Porfolio Weights ( Normal )
BI Fixed Income BI LS Conservative BI LS Aggressive
BI Commodities BI Structured Finance BI Other
0.00%
30.00%
30.00%4.47%
5.53%
30.00%
Optimal Porfolio Weights ( Modified )
BI Fixed Income BI LS Conservative BI LS Aggressive
BI Commodities BI Structured Finance BI Other

34. 34
( Normal ) and ( Modified ) Correlation and Vols

35. 35
Giving much better Risk Adjusted Stats
• Standard Mean Variance ( Normal ) Frontier does not capture asymmetry
Source: Blue Ink Investments, Data from 1 Jan 2011 to 31 Dec 2015
BI Fixed Income
BI LSConservative
BI LSAggressive
BI Commodities
BI Structured Finance
BI Other
​​​​​​​0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
-8.00%-7.00%-6.00%-5.00%-4.00%-3.00%-2.00%-1.00%0.00%1.00%
Returns(Monthly)
Modified Value at Risk ( VaR )
Mean Modified Value at Risk (VaR) (Monthly) Frontier
Efficient Frontier With Hedge Funds ( Normal )
Efficient Frontier With Hedge Funds ( Modified )
Optimal With Hedge Funds ( Normal ) VaR @( 99.99% ) = -0.98%
Optimal With Hedge Funds ( Modified ) VaR @( 99.99% ) = -0.46%

36. 36
Looking after other people’s money requires both Defensive
(Risk Management) and Offensive ( Selection ) skills

37. 37
Hedge Funds should be a key part of your defense
• Including Hedge Funds in your portfolio can help limit downside risks