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Optimal Volatility
Mechanics of Dynamic Risk Control
Nardin Baker
QWAFAFEW
January 16, 2018
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Achieving Good Reward for Risk
• Smart Beta strategies continue to gain favor
• Low Volatility strategies are successful and gaining AUM
• Optimization strategies provide good reward for risk
• New dynamic risk optimization strategies are emerging
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Smart Beta Classifications and Example Strategies
Fundamentals
o Book Value
o Sales
o Cash Flow
o Dividends
Risk Premia
o Value
o Size
o Momentum
o Quality
OptimizedRisk
o Minimum Volatility
o Risk Weighting
o Risk Parity (Equal Risk Weighting )
o Maximum Diversification
o Dynamic Managed Volatility
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Return vs. Risk for Smart Beta Strategies
Efficient Combinations
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Building Simple Portfolios Based on Trailing Risk
• Calculate trailing 24-month volatility for largest stocks in the USA (99.5%)
• Rank from lowest to highest volatility
• Form 10 decile and 5 quintile portfolio groups based on volatility ranks
• Create equal-weighted and capitalization-weighted portfolios for each group
• Calculate return for each portfolio over the next month
• Repeat procedure using a new 24-month window including latest month
See paper for details:
• “Low Risk Stocks Outperform within All Observable Markets of the World”, SSRN, 2012
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Risk and Return of Deciles: 1990-2017
1 2 34
5
6
7
8
9
10
-20%
-15%
-10%
-5%
0%
5%
10%
5% 10% 15% 20% 25% 30% 35%
Excess Return
Risk (std. dev.)
Excess Return vs. Risk of Decile PortfoliosUnited States
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Risk and Return of Deciles: 1990-2017
1
2
3
4
5
6
7
8
9
10
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
140%
160%
5% 10% 15% 20% 25% 30% 35%
Return /Std Dev
Risk (std. dev.)
Sharpe Ratio vs. Risk of Decile PortfoliosUnited States
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Return and Risk Results for Portfolios Grouped by Volatility
Averages Over All 12-Month Periods: 456 Observations
USA
All
Stocks
Low
Half
High
Half Q1 Q5 D1 D5
Low -
High Q1 - Q5
D1 -
D10
Return 12.2% 15.6% 9.0% 15.7% 4.4% 15.5% -0.5% 6.5% 11.3% 16.0%
Pct > 0 72.6% 84.2% 65.6% 87.7% 55.5% 88.4% 45.8% 72.6% 74.6% 78.3%
Risk (std dev) 16.1% 11.9% 21.1% 9.8% 24.7% 8.9% 26.5% -9.2% -14.9% -17.6%
Pct > 0 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 0.0% 0.0% 0.0%
Sharpe 1.03 1.68 0.65 2.06 0.33 2.22 0.09 1.04 1.73 2.12
Pct > 0 72.6% 84.2% 65.6% 87.7% 55.5% 88.4% 45.8% 88.8% 89.5% 91.7%
Annualized Results for Volatility Sorted Groups: 1980 - 2017
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-15%
-10%
-5%
0%
5%
10%
15%
1 2 3 4 5
Return and Risk of Quintiles
Excess Return (net of average) Excess Risk (net of average)
Return and Risk of USA Quintiles: 1990-2017
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Sharpe Ratio of Quintiles: 1990-2017
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1992 1995 1998 2001 2004 2007 2010 2013 2016
3-year Sharpe Ratio net of the Average Sharpe Ratio
Sharpe Q1 Sharpe Q5
United States
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Portfolio Risk Depends on Average Stock Volatilities and Correlations
Risk = Volatility Correlation
Portfolio Volatility = weighted average volatility of stocks ∙ weighted average correlation
σ2p = Σi xi ∙ σ2
i ∙ Σi xi ∙ ρi
where:
σ2p portfolio volatility
Σi xi ∙ σ2i weighted average volatility of stocks in the portfolio
Σi xi ∙ ρi weighted average correlation among stocks in the portfolio
ρi weighted average correlation of stock i with all other stocks
Price information drives Returns, Volatilities and Correlations
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Dynamic Approach - Optimal Volatility
S&P 500
Min Vol
Opt Vol
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
10.0%
0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
Ex
pe
cte
d R
ew
ard
Expected Risk
Expected Reward and Risk
Efficient Frontier
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Frontiers: Opt Vol portfolio is selected to Maximize Portfolio Reward-to-Risk
Reward
-to-Risk
Risk
Opt Vol
Portfolio at
tangent
Opt Vol
Portfolio
at tangent
S&P 500
S&P 500
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Frontiers Depend on Recent Risk and Return Market Conditions
Expected
Reward
Risk
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Sample Efficient Frontier: When Market Risk is Low and Reward is High
1
-10%
-5%
0%
5%
10%
15%
20%
25%
0% 5% 10% 15% 20% 25% 30% 35% 40%
Re
war
d-t
o-R
isk
Opt Vol Positions on Different Frontiers
Min
Vol
Max
Vol
BM
Opt Vol Risk is close to Min Vol Risk. It is only 7% of the way to the Max Vol Risk
Opt
Vol
Aggressiveness: = Opt Vol risk −Min Vol risk
(Max Vol risk −Min Vol risk )
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1
-10%
-5%
0%
5%
10%
15%
20%
25%
0% 5% 10% 15% 20% 25% 30% 35% 40%
Re
war
d-t
o-R
isk
Opt Vol Positions on Different Frontiers
Sample Efficient Frontier: When Market Risk is High and Reward is Low
Min
Vol
Max
Vol
BM
Opt Vol Risk Equals the Max Vol Risk. It is 100% of the way to through the risk range.
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1
2
3
4
5
-10%
-5%
0%
5%
10%
15%
20%
25%
0% 5% 10% 15% 20% 25% 30% 35% 40%
Re
war
d-t
o-R
isk
Opt Vol Positions on Different Frontiers
Efficient Frontiers Under Various Market Conditions
Opt Vol moves to higher risk as the frontier shifts. Efficient frontiers can both move and tilt.
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1
2
3
4
5
-10%
-5%
0%
5%
10%
15%
20%
25%
0% 5% 10% 15% 20% 25% 30% 35% 40%
Re
war
d-t
o-R
isk
Opt Vol Positions on Different Frontiers
0
1
2
3
4
5
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0% 5% 10% 15% 20% 25% 30% 35% 40%
Risk
Percent Along Frontier
Percentage Along Frontier Risk Range as Efficient Frontiers Shift
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• Volatility (60 months)
• Correlation (60 months)
• Change in Volatility (last 24 months less last 60 months)
• Change in Correlation (last 24 months less last 60 months)
Function for Determining the Optimal Volatility Index Holdings
A Reward-to-Risk
characteristic can
be calculated
using four factors
for each stock in
the Selection
Universe:
OptimizationMaximize:
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑤𝑎𝑟𝑑−𝑡𝑜− 𝑅𝑖𝑠𝑘
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑅𝑖𝑠𝑘=
E RR
E PR
𝐑𝟏𝟐 = 𝛃𝟎 + 𝛃𝟏𝐅𝟏 + 𝛃𝟐𝐅𝟐 + 𝛃𝟑𝐅𝟑 + 𝛃𝟒𝐅𝟒 + 𝛆
Where:
𝐑𝟏𝟐 = 𝐕𝐞𝐜𝐭𝐨𝐫 𝐨𝐟 𝐫eturns for stocks over the last 12 months
𝐅𝟏−𝟒 = 𝐕𝐞𝐜𝐭𝐨𝐫𝐬 𝐨𝐟 𝐯𝐨𝐥𝐚𝐭𝐢𝐥𝐢𝐭𝐲 𝐨𝐫 𝐜𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧 𝐟𝐚𝐜𝐭𝐨𝐫𝐬 𝐟𝐨𝐫 𝐬𝐭𝐨𝐜𝐤𝐬
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Optimal Volatility Increases Risk Dynamically Based on Market Conditions
• Estimated based on 4 factors
Nonlinear Volatility Relationship
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Return
Volatility
Return vs. Volatility
)'((
'
).(
.:
xCOVx
Erx
riskE
returnEMax
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• Constituents of the Standard and Poor’s 500 index.
• Market capitalization of 5 USD billion or more
• Annual dollar value traded to float adjusted cap > 1.0
• Minimum of 250,000 shares traded in prior 6 months
• Sector constraints:
+/- 10 % relative to capitalization weighted sectors
• Stock upper limits:
smaller of 3 % or 10x market weight
• Lower limit of 0% on all positions (no short selling)
• Weights in the portfolio must sum to 100%
Optimal Volatility Index Construction: GLCOV Index by S&P
Selection Universe
Constraints
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Index Construction and Performance Results
2000 - 2017 S&P 500
Minimum
Volatility
Optimal
Volatility
Return 5.4% 6.6% 10.2%
Risk (Std. Dev.) 14.5% 11.1% 13.0%
Risk / S&P 500 Risk 100% 77% 90%
Return / Risk 37% 59% 78%
Beta 100% 70% 81%
• Index is rebalanced quarterly based on Optimal Volatility solution
• Stocks must be members of updated quarterly S&P 500
• S&P 500 calculates performance of GLCOV Index
Results:
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Performance Comparison
0
1
2
3
4
5
6
2000 2002 2004 2006 2008 2010 2012 2014 2016
Optimal Volatility Performance
Minimum Volatility Optimal Volatility S&P 500
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Performance in Up vs. Down Markets is Participation Ratio Difference - PRD
2000 - 2017 S&P 500
Minimum
Volatility
Optimal
Volatility
Down Markets -3.8% -2.3% -2.5%
Up Markets 3.2% 2.4% 3.1%
Down Capture 100% 62% 66%
Up Capture 100% 76% 96%
PRD (Up – Down
Capture) 0% 14% 30%
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Up and Down Market Capture
Down Markets Up Markets
Optimal Volatility -2.5% 3.1%
Minimum Volatility -2.3% 2.4%
S&P 500 -3.8% 3.2%
UP AND DOWN MARKET PERFORMANCE
Optimal Volatility
Minimum Volatility
S&P 500
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Dynamic Volatility
• Optimal Volatility index often has lower exposure to market risk than S&P 500
• Risk is typically closer to that of the Minimum Volatility strategy
• Max Vol is constructed by maximizing portfolio beta using the same constraints
5%
10%
15%
20%
25%
30%
35%
Risk(std dev)
Opt Vol Min Vol Max Vol
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Heartbeat: Optimal Volatility Aggressiveness Ratio in High-Low Volatility Range
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%Opt Vol Ratio Min Vol Max Vol
Aggressive Portfolio
Conservative
Portfolio
Aggressiveness: = Opt Vol risk −Min Vol risk
(Max Vol risk −Min Vol risk )
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Optimal Volatility Increases Risk Tactically Based on Market Conditions
•Optimal Volatility portfolio has risk lower than the market
•Higher than market return suggest risk exposure is increase only when there is high reward
Return vs Volatility
S&P 500
Minimum Volatility
Optimal Volatility
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
10.0%
11.0%
8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0%
Retu
rn
Risk
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Optimal Volatility Summary and Investigation Directions
• Price Information: Returns, Correlations, and Volatilities
• Systematic optimization based on market reward
• Dynamically moves to higher risk when it is rewarded
• Defensive most of the time
Where does Optimal Volatility work?
• Sector Applications
• Asset Allocation
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Appendix
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Notes:
▪ The optimal volatility portfolio is created to maximize the ratio of reward-to-risk
▪ Measure the market reward to four risk factors over the last 12 months
▪ Single number expresses the expected reward-to-risk for each stock
▪ Highest reward to risk portfolio combination is selected using an optimizer
▪ Optimization is similar to finding a maximum Sharpe ratio portfolio
▪ Expected reward-to-risk is used for the numerator (return axis)
▪ Portfolio volatility over the last 60 months is used for the denominator (risk axis)
▪ Efficient Frontier changes with market conditions
▪ Cannot predict when the optimal volatility portfolio will take on high risk or low risk
▪ When market volatility is low, optimal volatility portfolio generally will be low volatility
▪ When does volatility of portfolio generally increase?
▪ Market volatility has been high recently
▪ Market is stabilizing
▪ Higher risk stocks demonstrate greater reward-to-risk
Generally, Optimal volatility portfolio will then become more aggressive
▪ There is no method to time or predict these shifts
▪ Market information related to price determines shifts: returns, correlations, and risk