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Building Convex Stock Portfolios

October 2014

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• Volatility Deciles of the SPX and Their Convexity Effects• Similarities• Mimicking Portfolios• Summary• References

Outline

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• Rationale: can we empirically confirm the “Betting Against Beta”-effect?• Literature: “Betting Against Beta” pays off like a carry strategy in the long run [e.g.,

Frazzini / Pedersen (2014), Berrada et al. (2012)]• Typically, high volatility stocks underperform low volatility stocks [cf. Ang et al.

(2009)]

• Our test implementation:• SPX members only• Sort by realised 60D volatility• Build vol deciles:

• decile #1 comprises the 50 most volatile SPX members• decile #10 comprises the 50 least volatile SPX members

• Stocks are equal weighted in each decile portfolio• Rebalancing on the last business day of the month• Transaction costs and dividends ignored

Vol Deciles

Vol Deciles

C:\Users\TradeCap\Documents\Claus Huber\Quant Models\The Screener\R output vol(60D) quantiles.xlsx4

Annual Returns (Vol Deciles)

Max

Min

Low volHigh vol

C:\Users\TradeCap\Documents\Claus Huber\Quant Models\The Screener\R output vol(60D) quantiles.xlsx

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Convexity: Vol Deciles

• Are there any convexity effects in the deciles?• , =∝ + ∙ , + ∙ → we test for• High vol stocks in decile X1 exhibit positive convexity [ >0]• Low beta stocks in decile X10 exhibit negative convexity [ <0]

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• Most volatile stocks exhibit positive convexity

Convexity: Vol Decile 1

C:\Users\TradeCap\Documents\Claus Huber\Quant Models\The Screener\R output vol(60D) quantiles.xlsx7

Convexity: Vol Decile 10

• Least volatile stocks exhibit negative convexity

C:\Users\TradeCap\Documents\Claus Huber\Quant Models\The Screener\R output vol(60D) quantiles.xlsx8

• We can empirically confirm the “Betting Against Beta” effect• How can we utilise the “Betting Against Beta” or convexity effects for robust

portfolio construction?

• Is there sufficient return variation in the SPX universe to build convex portfolios?• 52 weekly returns from 6/2013 to 5/2014• Amongst the SPX members, find the 10 stocks with the highest correlations to the

SPX• Compare their price developments: are the high correlations visible [next slide]?• Even for stocks with high correlations, there can be significant performance

differences

Similarities: Correlation

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• Highest correl = 0.85 [TROW], lowest = -0.06 [NEM]

Similarities: Correlation

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• Low correlations often come from steep drops

Similarities: Correlation

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• Can we build convex portfolios from stocks that are similar to SPX?

Similarities: Correlation

Name Correl Perf. 52W vol Name Correl Perf. 52W volSPX 1.00 18.0% 9.7% SPX 1.00 18.0% 9.7%

1 TROW 0.85 7.5% 17.1% NEM -0.06 -33.2% 37.2%2 AMP 0.83 38.1% 21.2% EXC 0.02 17.5% 20.4%3 BLK 0.82 9.2% 20.9% VFC 0.03 -65.7% 77.4%4 MMC 0.82 25.6% 13.9% COG 0.03 -48.5% 53.9%5 PPG 0.80 31.2% 17.9% NWSA 0.09 -46.9% 53.5%6 ECL 0.78 29.3% 14.6% SLM 0.10 -63.7% 68.1%7 GS 0.78 -1.4% 19.4% RRC 0.11 23.6% 18.7%8 WYN 0.77 27.2% 18.3% EXPE 0.12 27.6% 87.0%9 PAYX 0.77 10.4% 15.7% MU 0.12 144.8% 39.5%

10 PLL 0.77 24.3% 15.0% FISV 0.12 -31.0% 43.4%11 MMM 0.77 29.3% 15.1% SWY 0.13 49.2% 30.7%12 TMK 0.76 25.5% 12.5% ISRG 0.15 -25.7% 37.6%13 ABT 0.76 9.1% 20.6% DVA 0.16 -43.1% 130.2%14 JNJ 0.76 20.5% 13.3% CERN 0.16 -45.0% 54.4%15 C 0.76 -8.5% 21.9% AAPL 0.17 40.8% 25.1%16 PFG 0.76 23.6% 20.7% EOG 0.17 -18.0% 54.1%17 TRV 0.75 11.6% 13.3% SWN 0.18 20.6% 19.8%18 OMC 0.75 14.5% 16.9% SYMC 0.18 -1.8% 27.8%19 DHR 0.75 26.9% 14.6% BEN 0.18 -64.3% 70.3%20 HST 0.75 24.1% 19.6% FRX 0.18 138.4% 70.8%

Largest Lowest• High Vol / Low Vol

portfolios dooutperform the SPX inthe longer run, butthere are periods ofsignificantunderperformance

• Identify stocks thatbehave similar to SPX

• There should be lessperformance difference

1. Find stocks similar toSPX [e.g., correlation]

2. Pick those that weexpect to outperformthe index

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Mimicking Portfolios:Rationale

• When picking stocks, their portfolio beta can be far away from the benchmark’sbeta [e.g., SPX] and there can be significant underperformance

• If we pick those stocks that are similar to the SPX, beta can be more easilycontrolled, e.g., by shorting the SPX

• Implementation:• For each stock in the SPX universe, at month end calculate the Euclidean Distance

[ED] to the SPX => we get 500 ED numbers• Rank the stocks according to their EDs: stocks with highest similarities [i.e., lowest

ED] are ranked first• Select the 5 [10, 20, …] highest ranked stocks• Result: we get a portfolio of stocks similar to the SPX that should behave similar to

the SPX• After the stocks have been identified, we vol-weight the stocks:

• Calibrate their weights to a target vol [e.g., 10%]• Calibrate portfolio vol to target vol• This ensures mostly constant vol around the target vol [Managed Volatility Approach], esp. in

downturns

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Mimicking Portfolios: Results

• Long Only mimicking portfolio [VW.30_net] with remarkable performance vs. SPX• Even in bad equity years [2002, 2008] with almost stable performance• Adding a simple short call strategy (VW.30_net+SC [incl. sim. analysis]) further

enhances returns and Sharpe Ratios

All returns arein USD aftertransaction

costs [0.4% pertrade] and 1.5%

managementfees. Dividends

ignored.C:\Claus Huber\Quant Models\The Screener\R output TC, LowRisk, tv=10%.xlsx

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idx 30[no sim. analysis]

VW.30_net[incl. sim. analysis]

VW.30_net+SC[incl. sim. analysis] SPX

2002 -27% 2% 10% -22%2003 99% 25% 20% 26%2004 8% 36% 41% 9%2005 3% 19% 19% 3%2006 -4% 13% 8% 14%2007 -36% 2% 6% 4%2008 -33% -8% 2% -38%2009 119% 22% 20% 23%2010 43% 28% 24% 13%2011 -20% 15% 19% 0%2012 41% 4% 5% 13%2013 37% 25% 24% 30%

5/2014 4% 4% 1% 4%vol 17% 10% 10% 15%

avg. return 34% 14% 15% 6%SR 0.49 1.38 1.59 0.40

Mimicking Portfolio LowRiskvs. SPX• Monthly data from 2/2002 to 5/2014• Even the largest monthly drawdowns are not < -6%

All returns are in USD after transaction costs [0.4% per trade] and 1.5% management fees. Dividends ignored.

• Empiricalconvexity issmall andpositive[t=0.99], butnot negative!

• Beta = 0.45• High Sharpe

Ratio 1.38→ Almost marketneutral

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Mimicking Portfolio LowRiskwith Short Calls vs. SPX• Monthly data from 2/2002 to 5/2014• Even the largest drawdowns are not < -6%

All returns are in USD after transaction costs [0.4% per trade] and 1.5% management fees. Dividends ignored.

• By addingshort calls:

• Empiricalconvexitybecomesslightlynegative [t-value -0.17]

• Beta reduced:0.29 [R2lower]

• Averagereturn higher

• Very highSharpe Ratio1.59

→ Even moremarket neutral

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Summary

• Strongly convex equity portfolios with our managed vol and similarities approach• Earns Equity Risk Premium, but effectively market-neutral!• High Sharpe Ratios >= 1

• Simple implementation• Trading only 1x per month: low operational and transaction costs• Only 30 stocks in the equity portfolio

• Beta very low [0.3 – 0.5]• Managed volatility approach [e.g., target vol 10%] keeps low volatility even during

times of severe market declines• Identification of similarities between stocks unique, adding significant value• Selling call options in a high volatility environment helps to reduce drawdowns and

enhances long-term Sharpe Ratios

• Our equity strategies also have performed in the years after the credit crisis 2009-2014

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• Ang, A., Hodrick, R.J., Xing, Y., Zhang, X. (2009): High idiosyncratic volatility and lowreturns: International and further U.S. evidence, Journal of Financial Economics,vol. 91, 1-23.

• Berrada, T., Messigh, R.J., Oderda, G., Pictet, O.V. (2012): Beta-Arbitrage strategies:when

• Frazzini, A., Pedersen, L.J. (2014): Betting against beta, Journal of FinancialEconomics, Vol. 111, Iss. 1, January, 1–25.

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References