Rebalancing February 4 2017 - Fuqua School of Businesscharvey/Teaching/... · Rebalancing Premium...

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RebalancingCampbell R. Harvey

Duke Universityand

Investment Strategy Advisor, Man Group, plc

February 12, 2017

International Finance

Campbell R Harvey 2017 2

Conventional Wisdom

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• 60/40 (Equity‐Bonds) is the best known standard for a balanced portfolio

• Note that this is 60/40 based on market cap – in terms of risk allocation, it is a more like 88/12!

Campbell R Harvey 2017

Fixed Weight Rebalancing

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• Fixed weight rebalancing (active strategy) can enhance returns– Fernholz (Journal of Finance, May 1982)– Booth and Fama (Financial Analysts Journal, May/June 1992)


Erb and Harvey (2006)

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Heating Oil S&P 500 Equal Weighted Let-It-RunExcess Return Excess Return Excess Return Excess Return

1994 19.96% -2.92% 8.52% 8.52%1995 7.73% 31.82% 19.78% 18.51%1996 67.37% 17.71% 42.54% 42.66%1997 -35.06% 28.11% -3.48% -9.13%1998 -50.51% 23.51% -13.50% -7.67%1999 73.92% 16.30% 45.11% 29.31%2000 66.71% -15.06% 25.82% 9.77%2001 -36.62% -15.97% -26.30% -25.49%2002 41.40% -23.80% 8.80% 1.78%2003 21.90% 27.62% 24.76% 24.50%

Geometric Return 8.21% 6.76% 10.95% 7.51%Standard Deviation 46.07% 21.06% 23.11% 20.34%

Average WeightsEqual Weight 50.00% 50.00%Let-It-Run 44.94% 55.06%

Weighted AverageGeometric Mean 7.49% 7.41%

Diversification Return 3.46% 0.10%

Not just variancereduction



In equally weighted strategy, the diversification return can be approximated as:(Average Variance – Average Covariance)/2= (12.83 – 5.34)/2 = 3.74%

More generally,=(Weighted Average Asset Variance – Weighted Average Asset Covariance)/2=(Weighted Average Asset Variance – Portfolio Variance)/2

6Campbell R Harvey 2017


Key Insight 1• Rebalancing is an active strategy

– While it is mechanical and no special information is needed to implement the strategy, it is an active decision.


GPFG vs. CalPERS

GPFGThe long‐term investment strategy of the GPFG stipulates a fixed equity portion of 60 percent. The fixed income portion was 40 percent until 2010. The mandate was changed in 2010. Over time, Norges Bank will invest up to 5 percent of the fund capital in a separate real estate portfolio [currently 0.9%].


GPFG vs. CalPERS

GPFGRebalanced in 2009.

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Year Fund Return

1998 8.9%

1999 11.7%

2000 2.5%

2001 ‐2.5%

2002 ‐4.9%

2003 11.9%

2004 8.6%

2005 10.5%

2006 7.6%

2007 4.2%

2008 ‐26.5%

2009 22.8%

2010 ‐9.2%

2011 ‐2.6%

2012 12.6%

Rebalance


GPFG vs. CalPERS

CalPERSThey did not rebalance in 2009.

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30.0%

35.0%

40.0%

45.0%

50.0%

55.0%

60.0%

65.0%

20112010200920082007200620052004200320022001

CalPERS Total Equity Allocation

Total Equity Actual

Total Equity Target

Source: Ang (2013) Campbell R Harvey 2017

GPFG vs. CalPERS

CalPERS“Underfunded”

11Source: Ang (2013)

0%

20%

40%

60%

80%

100%

120%

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Funding Ratios


GPFG vs. CalPERS

CalPERSWhy the quotations? Published underfunding assumes a discount rate of 7.5% for liabilities.• Novy‐Marx and Rauh (2009) report that when Treasury rates are used the liabilities

change from $484.2 billion (stated) to $805.7 billion, with the true funding status representing 415% of tax revenue and 26% of gross state product

12Source: Ang (2013) Campbell R Harvey 2017

GPFG vs. CalPERS

Two views• Norway smart and CalPERS stupid• Norway lucky and CalPERS unlucky

To answer this question, we need to understand what is going on behind rebalancing.


Rebalancing Premium

There is a premium to rebalancing• A premium does not mean that you outperform in every episode• Where does the premium come from?


Rebalancing Premium

Fixed weights vs. drift weights• Drift‐weights (buy and hold) could substantially diverge with the most volatile asset gaining a large weight– In 2013, the S&P500 delivered a total return of 31.9%, while the S&P 7‐10 Year U.S. Treasury bond index declined by 6.1%. A 60/40 portfolio would have drifted over 2013 to a 68/32 portfolio, and, with a repetition of these returns in 2014, a 74/26 portfolio.


Rebalancing Premium

Relative returns• After divergence, sell winners and buy losers• This strategy is attractive if there is mean reversion in relative asset performance.

• But if there is extended divergence, rebalancing continues to allocate to underperforming asset

• Research by, “Rebalancing Risk” by Granger, Greenig, Harvey, Rattray and Zou. http://ssrn.com/abstract=2488552


Rebalancing Premium

Rebalancing and drawdowns• During the financial crisis, rebalancing exacerbated losses, increasing the drawdowns by

about 600 bps.


Rebalancing Premium

Rebalancing and drawdowns• Similar story in 2001‐2004.


Rebalancing Premium

Rebalancing premium• Consider the following intuition.

– As an asset increases in value, you sell. This is the same as what you would do to dynamically replicate a short call option

– As an asset decreases in value, you buy. This is the same as what you would do to dynamically replicate a short put option


Short straddle (negative convexity)

Lose money if high volatility

Rebalancing Premium

Rebalancing premium• Essentially, the rebalancing strategy is a short straddle strategy*• This is sometimes referred to as a strategy that has:

– Negative convexity– Negative gamma– Short vol– Negative skew

*Note that the straddle is on the relative prices of the stocks and the bonds


Rebalancing Premium

For small divergences, rebalanced portfolio outperforms fixed weights. For large divergences, rebalanced underperforms.

21Source: Reuters, Man calculations. Date range: January 1990 to February 2014. Monthly rebalancing.


Momentum and Rebalancing

Time‐series momentum is the opposite of rebalancing. As the price increases, you buy more (long call). As the price decreases you sell more (long put).• Momentum has positive convexity, positive gamma and positive skew


Long straddle (positive convexity)

Lose money if low volatility


• What happens if you add a higher frequency momentum overlay?– Idea is that fast momentum detects trends and gets you out of trouble if there is persistence divergence



• What happens if you add a higher frequency momentum overlay?

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Fixed weights + momentum overlay minus drift weights

MomentumFixed-weight rebalancing minus drift weights

Source: Man calculationsCampbell R Harvey 2017


• What happens if you add a higher frequency momentum overlay?

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Fixed weights + 20% momentum overlay Fixed-weight rebalancing

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

Cum

ulat

ive

retu

rns

Financial crisis 2001‐2004

Source: Man calculationsCampbell R Harvey 2017

Conclusions

• Rebalancing is an active strategy• Rebalancing mechanically induces negative convexity• Leads to large draw down in periods of asset divergence• Higher frequency momentum can be used to offset the negative convexity


References

• Erb, C. B. and C. R. Harvey, “The strategic and tactical value of commodity futures,” 2006, Financial Analysts Journal, 69‐97.

• Granger, N. M., D. Greenig, C. R. Harvey, S. Rattray, D. Zou, 2015, “Rebalancing risk”, http://ssrn.com/abstract=2488552

• Martin, R. J. and D. Zou, 2012. “Momentum trading: ‘skews me” Risk Magazine.


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