A Second Look at the Role of Hedge Funds In a Balanced Portfolio

1. A Second Look at the Role of Hedge Funds In a Balanced Portfolio The CFA Society of Victoria Victoria, BC September 21st, 2010 Jean L.P. Brunel, C.F.A

2. Three main points … • A highly heterogeneous universe • Different optimization needs • What about leverage

3. A highly heterogeneous universe The term hedge fund is misleading as it does not cover a well-defined universe. Rather, it describes many differing strategies … • A very wide risk spectrum • Justified by a wide variety of strategies • Looking for a better classification • Recognizing differing return distributions

4. Last 5 Year Data - Risk/Return Scatter 20.00% 15.00% 10.00% Average Returns 5.00% 0.00% -5.00% -10.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% Volatility of Returns A wide risk spectrum … Does this look as one set of strategies or quite a number of different ones?

5. Last 15 Year Data - Risk/Return Scatter 20.00% 18.00% 16.00% 14.00% 12.00% Average Returns 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% Volatility of Returns A wide risk spectrum … Moving from a 5-year to a 15-year analysis does not really change the picture that much …

6. What do these managers do? Convertible Merger/Risk Statistical Fixed Income Pair Trades Market Neutral Equity Long/Short Sector Concentrated Portfolios Global Macro Managed Futures Implied Leverage Implied Leverage Leverage Leverage Concentration Market Market Market Valuation Valuation Valuation Valuation Model Model Model Model Model Return volatility < 6% Return volatility > 6%

7. Last 5 Year Data - Risk/Return Scatter Absolute Return Strategies in Orange 20.00% 15.00% 10.00% Average Returns 5.00% 0.00% -5.00% -10.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% Volatility of Returns There seems to be two clusters … It looks as if one can classify the various strategies according to whether they take fixed income- or equity-type risks …

8. Last 15 Year Data - Risk/Return Scatter Absolute Return Strategies in Orange 20.00% 18.00% 16.00% 14.00% 12.00% Average Returns 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% Volatility of Returns There seems to be two clusters … The 15-year picture confirms the insights gained from the shorter term time horizon …

9. These clusters make sense … An analysis of risk and return history within traditional and non-traditional clusters shows the grouping makes sense … • The fixed income cluster makes sense: • absolute return and bonds: similar volatility • despite at times differing returns • The equity cluster similarly makes sense:

10. In short … The term hedge fund is misleading as it does not cover a well-defined universe. Rather, it describes many differing strategies … • The universe is indeed highly heterogeneous • The strategy risk spectrum is very wide … • … because managers do very different things • It makes sense to classify hedge funds as: • those that look like fixed income • those that look like equities • … and use that to build balanced portfolios

11. Three main points … • A highly heterogeneous universe • Different optimization needs • What about leverage

12. Important differences … The returns on non-traditional strategies are often not normally distributed… • Traditional returns are normally distributed • That is not true for non-traditional returns: • often showing a negative skew • often substantial excess kurtosis

13. Same return and volatility, and yet … The high “manager” risk incurred in non-traditional strategies disturbs the normal distributions we would typically expect …

14. First, consider negative skew … Negative skew means more points right of the mean, but also a wider range on the left (i.e. down) side of it as well

15. Then, how about excess kurtosis? Excess kurtosis mean that the return distribution is “peaky” and that it has “fat tails” …

16. In plain English … A look at third and fourth statistical moments helps make sense of the high Sharpe ratio of non-traditional strategies … • Strategies combining: • negative skew and • more highly positive kurtosis • Have a higher risk of bad surprises: • Which must be “compensated” by either: • higher expected returns, or • lower expected return volatility • Which mean-variance optimization misses …

17. Traditional optimization results … The traditional mean-variance model over-allocates to absolute return strategies and ignores bonds … • Note the very low allocations to bonds:

18. Traditional optimization results … Similarly, it totally ignores traditional equities to “pile” into equity hedge strategies, despite the tail risk … • Note the lack of allocation to traditional equities

19. Let us try and experiment … A simple experiment will helps us set early ground rules • Let’s divide fixed income market history: • periods when bond returns were positive • periods when bond returns were negative • Let’s divide equity market history: • periods when returns were high • periods when returns were “normal” • periods when returns were low • Let’s re-run the traditional optimization:

20. Traditional optimization results … In periods when bond returns are positive, a mean-variance optimization model will not shun bonds … • Note that the model CAN allocate to bonds:

21. Traditional optimization results … In periods when bond returns are negative, a mean-variance optimization model will seemingly shun bonds • Note also that the model can ignore bonds:

22. Traditional optimization results … In periods when equity returns are high, a mean-variance optimization model will not shun traditional equities … • Note that the model CAN allocate to equities:

23. Traditional optimization results … In periods when bond returns are normal, the mean-variance optimization model seems to ignore traditional equities … • The model mostly ignores equities:

24. Traditional optimization results … In periods when equity returns are negative, the model does not want to hear about them … • The model still ignores equities:

25. What have we learned? • The optimizer does not like losses!!! • It can allocate to bonds: • When they offer competitive returns • But not when they are “normal” • It can allocate to equities: • When they offer competitive returns • Or when they are the lowest risk choice • These strategies do not always make sense

26. Let us try a final experiment … Though this experiment is not a “solver,” but a calculator, it can help demonstrate the power of a more detailed model … • Mean-variance optimization only uses: • return and risk expectations, and … • … covariance among each pair of assets • Let’s design a different model: • return and risk observations • skew and kurtosis observations” • implicit preferences for skew and kurtosis • the same covariance matrix • Let’s re-run the optimization:

27. The goals for that model would be ... Rather than focusing on mean-variance, we calculate a “Z-Score” which incorporates all four moments … • On the one hand: • to capture as much return as possible • while avoiding as much risk as possible • At the same time, we would like: • to minimize the risk of negative surprises • minimizing negative skew” • minimizing excess kurtosis • In “Greek” our “Z-Score” will be: • Max (E[r] - s + l*skew - g*Kurtosis)

28. Z-Score fixed income optimization: This model produces results that ignore absolute return strategies if the aversion to manager risk is set at a high level • The model ignores absolute return strategies:

29. Z-Score fixed income optimization: These results are much more intuitively satisfying, with a better balance between traditional and non-traditional strategies .. • With a lesser manager risk aversion, the model allocates to absolute return strategies:

30. a b g = + + + + + Minimize Z ( 1 d ) ( 1 d ) ( 1 d ) , 1 3 4 ~ T + t + = * Subject to E [ X R ] x d Z , + n 1 1 1 ~ ~ T - + = 3 * E { X ( R E [ R ] )} d Z , 3 3 ~ ~ T - - + = - 4 * E { X ( R E [ R ])} d Z , 4 4 ³ d , d , d 0 , 1 3 4 T = X VX 1 ; ³ X 0 ; T = - x 1 I X + n 1 A much better potential formulation This model has the potential to address our problem, but it still needs to be tested on balanced portfolios ... • Neil Davies, Harry Kat and Sa Lu have proposed an interesting “solver” formulation:

31. Three main points … • A highly heterogeneous universe • Different optimization needs • What about leverage

32. Naïve expectations for L/S … We can dispense with the detailed analysis of statistical results and rather look at how similar or not these are to naïve expectations • If systematic leverage is the key, on should • Find a relatively high R Square • A Beta coefficient greater than 1 • A negative Alpha coefficient

33. Equity L/S vs. equity indexes … In fact, the R Squares are relatively low, the betas are very low and significant and the alphas are all positive and significant …

34. Equity L/S vs. equity indexes … Again, the R Squares are relatively low, the betas are very low and significant and the alphas are all positive and significant …

35. Leverage and manager alpha … Now the idea is to test the alpha of managers in rising and falling markets against the benchmark • Managers can add value in two ways: • Market timing: varying market exposure • Bottom up security selection • If managers are great market timers: • positive and strong correlation in up markets • negative and equally strong in down markets • Caveat: multiple sources of alpha …

36. In rising markets… Whatever relationship there is does appear quite weak and in the wrong direction: managers find it harder to add value in up markets…

37. In rising markets… Whatever relationship there is now appear a bit stronger, but still weak and in the wrong direction …

38. How about falling markets? There appears to be virtually no relationship in view of the very low R Squares, and the direction is mostly wrong…

39. How about falling markets? There appears to be a bit more of a relationship (still weak though) and the sign is in the right direction at least…

40. Naïve expectations for A/R … Though the test variables will be different, the naïve expectations we form are the same as in the case of long/short managers … • If systematic leverage is the key, one should • Find a relatively high R Square • A Beta coefficient greater than 1 • A negative Alpha coefficient

41. Absolute return vs. benchmarks … In fact, the R Squares are quite low, the betas are very low and mostly significant and the alphas are all positive and significant …

42. Is there a static mix? We can test this by looking at whether absolute return strategy returns can be regressed against the same variables…

43. Leverage and manager alpha … Again, the idea is to test the alpha of managers in rising and falling markets against the benchmark • Managers can add value in two ways: • Market timing: varying market exposure • Bottom up security selection • If managers are great market timers: • positive and strong correlation in up markets • negative and equally strong in down markets • Caveat: multiple sources of alpha …

44. Alphas in rising markets … There is virtually no evident relationship and it is in the wrong direction for half of the variables and often not significant …

45. Alphas in falling markets … There is virtually no evident relationship and it is in the wrong direction more often than not. No statistical significance save HY bds

46. In short … It is hard to substantiate the notion that one can replace non-traditional managers with leveraged long only strategies … • In most instances, the observed alpha is: • not really related to market beta • not readily replicable with a static mix • More often than not, alpha is: • Statistically unrelated to market timing • The more recent past can be less clear-cut

47. Three main points … • A highly heterogeneous universe • Different optimization needs • What about leverage Questions?

48. A Second Look at the Role of Hedge Funds In a Balanced Portfolio The CFA Society of Victoria Victoria, BC September 21st, 2010 Jean L.P. Brunel, C.F.A