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Project 2: Volatility as an Asset Class
—improving the mean-variance efficient frontier using volatility as an asset class...
Project 2: Volatility as an Asset Class
Introduction
Part I: Portfolio Optimization & Role of Volatility
Construct the eff...
Part I: Portfolio Optimization
& Role of Volatility
Part I: Portfolio Optimization & Role of Volatility
Efficient Frontier with Market Indices
S&P 500
NASDAQ
S&P 100
DJIA
Eff...
Part I: Portfolio Optimization & Role of Volatility
Volatility: Negative Correlation
S&P
500
Volatility S&P 500 (VIX)
Part I: Portfolio Optimization & Role of Volatility
Price
Today Maturity
Expected Future
Spot Price
Forward Price in Norma...
Part I: Portfolio Optimization & Role of Volatility
Choice of Volatility Vehicles
iPath S&P 500 VIX Short Term Futures TM ...
Part I: Portfolio Optimization & Role of Volatility
Comparing the Effects
Part I: Portfolio Optimization & Role of Volatility
Strategy: Short VXX to Speculate, Long VXZ to Hedge
Part II: Volatility Forecasting
& Estimation
Part II: Volatility Forecasting & Estimation
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.00 0.10 0.20 0.30 0.40 0.50 ...
Part II: Volatility Forecasting & Estimation
AR(1): Auto-regressive model of order 1
Key assumptions:
1) Only t-1 informat...
Part II: Volatility Forecasting & Estimation
For the whole data set of size n, half of the data points are used as trainin...
Part II: Volatility Forecasting & Estimation
We use the model to simulate the response from the 1st data point and
compare...
Part II: Volatility Forecasting & Estimation
C = 3.3802 ϕ = 0.8424
Residue Histogram
Mean RMS: 10.5836
AR(1) Model Verific...
Part II: Volatility Forecasting & Estimation
AR(1) Model Verification – Prediction
Part III: Trading and Implementation
Part III: Trading and Implementation
Active Volatility Trading
It is clear positions on volatility products can enhance ov...
Part III: Trading and Implementation
2010
15
20
25
30
35
40
45
50
55
Year
Price,$ VIX Future Closing Price
10-Period MA
+/...
Part III: Trading and Implementation
Sharpe Ratios to Compare Strategies
Trading Strategy Sharpe Ratio
Static short VXX 0....
Part III: Trading and Implementation
Exploration of Strategy Variations
2004 2006 2008 2010 2012 2014
0
10
20
30
40
50
60
...
Part III: Trading and Implementation
Trading on the AR(1) Model
• Recall AR(1) Model of the form:
• Fit the AR(1) over the...
Part III: Trading and Implementation
Tomorrows Volatility Today
• At each time step we use the today’s VIX in the AR(1) Mo...
Part III: Trading and Implementation
10 20 30 40 50 60 70 80 90
-40
-20
0
20
40
60
80
100
120
140
160
Annualized Standard ...
Part III: Trading and Implementation
Using The VIX for VXX Timing
Three criteria using the VIX to generate a short signal ...
Part III: Trading and Implementation
Part III: Trading and Implementation
Returns Using the PPO Indicator
ν = 18.6%
σ = 51.3%
SR = -0.1418
Part III: Trading and Implementation
Another Method Using RSI Indicator
• When RSI is above 70, VIX is overbought
 Cover ...
Part III: Trading and Implementation
Results Using the RSI indicator
ν = 15.8%
σ = 35.6%
SR = -0.1406
Part III: Trading and Implementation
Conclusions
 Use of volatility ETFs significantly expands efficient frontier
• Short...
Project 2: Volatility as an Asset Class
—improving the mean-variance efficient frontier using volatility as an asset class...
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Volatility as an Asset Class

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Improving the mean-variance efficient frontier using volatility as an asset class

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Volatility as an Asset Class

  1. 1. Project 2: Volatility as an Asset Class —improving the mean-variance efficient frontier using volatility as an asset class MS&E 445 Projects in Wealth Management Professor Peter Woehrmann Ian Schultz, Linda He Yi, Hai Wei, J.R. Riggs, Andrew Tsai, Vicky Wang, Henry Chen, Erica Jiang
  2. 2. Project 2: Volatility as an Asset Class Introduction Part I: Portfolio Optimization & Role of Volatility Construct the efficient frontier for universe of 30 (DJIA), 100 stocks (S&P100), 500 stocks (S&P500) & 2600+ stocks (NASDAQ) Include volatility using ETFs tracking the VIX (VXX, VXZ) Part II: Volatility Forecasting & Estimation Volatility forecasting using AR(1) Model Minimize estimation errors by using the Shrinkage Approach to estimate the covariance matrix Part III: Trading & Implementation Comparing selective long/short volatility trading strategies
  3. 3. Part I: Portfolio Optimization & Role of Volatility
  4. 4. Part I: Portfolio Optimization & Role of Volatility Efficient Frontier with Market Indices S&P 500 NASDAQ S&P 100 DJIA Efficient Frontier - Markowitz Formula to find two efficient portfolio; i.e. minimum variance for a given return - Two-Fund Theorem to construct the efficient frontier
  5. 5. Part I: Portfolio Optimization & Role of Volatility Volatility: Negative Correlation S&P 500 Volatility S&P 500 (VIX)
  6. 6. Part I: Portfolio Optimization & Role of Volatility Price Today Maturity Expected Future Spot Price Forward Price in Normal Backwardation Forward Price in Contango Volatility: Contango Effect of VIX Futures - Each subsequent expiration month of VIX futures prices are traded higher than the closer month's VIX futures prices and the spot VIX overall How to take advantage of the decay effect that is very consistent and significant over time?
  7. 7. Part I: Portfolio Optimization & Role of Volatility Choice of Volatility Vehicles iPath S&P 500 VIX Short Term Futures TM ETN (VXX) iPath S&P 500 VIX Mid-Term Futures ETN (VXZ)
  8. 8. Part I: Portfolio Optimization & Role of Volatility Comparing the Effects
  9. 9. Part I: Portfolio Optimization & Role of Volatility Strategy: Short VXX to Speculate, Long VXZ to Hedge
  10. 10. Part II: Volatility Forecasting & Estimation
  11. 11. Part II: Volatility Forecasting & Estimation -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Annualized Return Annualized Standard Deviation Using Calculated Cov S&P500 S&P100 DJIA NASDAQ VXX VXZ After Cov Shrinkage -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.00 0.10 0.20 0.30 0.40 0.50 0.60 Annualized Return Annualized Standard Deviation With Calculated Cov S&P500 S&P100 DJIA NASDAQ After Cov Shrinkage Traditional covariance estimation methods based on historical data incur lots of error and therefore degrade the results through mean-variance optimization Covariance Matrix Shrinkage gives better estimation of covariance coefficients [Ledoit & Wolf 2003] Covariance Matrix Shrinkage
  12. 12. Part II: Volatility Forecasting & Estimation AR(1): Auto-regressive model of order 1 Key assumptions: 1) Only t-1 information is used to predict the result at t 2) Error term ɛt is independent of time and X AR(1) Model
  13. 13. Part II: Volatility Forecasting & Estimation For the whole data set of size n, half of the data points are used as training data. Parameters c, ɛt, ϕ are estimated from data points 1, 2, … n/2 AR(1) Model Training
  14. 14. Part II: Volatility Forecasting & Estimation We use the model to simulate the response from the 1st data point and compare the simulated value with the original data For each method we run the simulation 100 times and calculate the RMS value from the simulated data for each run X  difference between real and simulated data AR(1) Model Testing
  15. 15. Part II: Volatility Forecasting & Estimation C = 3.3802 ϕ = 0.8424 Residue Histogram Mean RMS: 10.5836 AR(1) Model Verification Accurate in the short term
  16. 16. Part II: Volatility Forecasting & Estimation AR(1) Model Verification – Prediction
  17. 17. Part III: Trading and Implementation
  18. 18. Part III: Trading and Implementation Active Volatility Trading It is clear positions on volatility products can enhance overall portfolio performance But… • Does active volatility trading outperform static volatility positions? • How can we actually compare performance of different trading strategies? • What is the best way for a long/short volatility hedge fund to operate? Here we will try to address these issues: 1. Examine simple momentum strategies 2. Incorporate AR(1) volatility predictions to increase returns 3. See how the best returns in active volatility trading can increase efficient portfolios
  19. 19. Part III: Trading and Implementation 2010 15 20 25 30 35 40 45 50 55 Year Price,$ VIX Future Closing Price 10-Period MA +/- 5% of MA Moving Average Momentum Trading Rules: 1. Enter long VXX position when VIX futures cross n% above N-day moving average 2. Close long VXX position when VIX futures cross N-day moving average 3. Enter short VXX position when VIX futures cross n% below N-day moving average 4. Close short VXX position when VIX futures cross N-day moving average First attempt of a simple momentum strategy Short entry Short close Long entry Long close
  20. 20. Part III: Trading and Implementation Sharpe Ratios to Compare Strategies Trading Strategy Sharpe Ratio Static short VXX 0.181 Static VXX+VXZ 0.012 PPO & RSI -0.14 Momentum trading 0.524 ARCH Model 0.403 Sharpe Ratio is used to compare excess return and variance against a benchmark SR = E[Ra - Rb ] cov Ra - Rb( ) Ra = Asset return vector Rb = Benchmark return vector Expected Excess Return Variance of Excess Return Here we use the static short VXX as our benchmark portfolio, except for VXX itself
  21. 21. Part III: Trading and Implementation Exploration of Strategy Variations 2004 2006 2008 2010 2012 2014 0 10 20 30 40 50 60 Year Price,$ VIX Future Closing Price 10-Period MA +/- 5% of MA 2004 2006 2008 2010 2012 2014 0 10 20 30 40 50 60 Year Price,$ VIX Future Closing Price 5-Period MA +/- 10% of MA ν = 73.8% σ = 44.5% SR = 0.501 2004 2006 2008 2010 2012 2014 0 10 20 30 40 50 60 Year Price,$ VIX Future Closing Price 10-Period MA +/- 10% of MA ν = 78.1% σ = 45.5% SR = 0.516 2004 2006 2008 2010 2012 2014 0 10 20 30 40 50 60 Year Price,$ VIX Future Closing Price 10-Period MA +/- 15% of MA ν = 79.8% σ = 45.4% SR = 0.524 ν = 63.3% σ = 44.4% SR = 0.453
  22. 22. Part III: Trading and Implementation Trading on the AR(1) Model • Recall AR(1) Model of the form: • Fit the AR(1) over the first half of historical VIX (1993-2003) • Test the returns of this strategy on the second half of data (2003-2013) • These results look promising, but perhaps we can simulate many times to eliminate εt noise 1995 2000 2005 2010 0 10 20 30 40 50 60 Year VIXLevel Actual VIX Price Movement ARCH Prediction
  23. 23. Part III: Trading and Implementation Tomorrows Volatility Today • At each time step we use the today’s VIX in the AR(1) Model to predict tomorrow’s VIX level • Repeat this at each step 30 times and take the average to get tomorrows volatility prediction • When tomorrow’s volatility is higher than today’s, buy the VIX • Tomorrow lower, vice versa Annualized Return = 167% Standard Deviation = 59.9% Sharpe Ratio = 0.403 Qualitative performance of this method looks exceptional. 1995 2000 2005 2010 10 15 20 25 30 35 40 45 50 55 60 Year VIXLevel Actual VIX Price Movement ARCH Prediction Model Fitting Backtesting
  24. 24. Part III: Trading and Implementation 10 20 30 40 50 60 70 80 90 -40 -20 0 20 40 60 80 100 120 140 160 Annualized Standard Deviation, % AnnualizedReturn,% no vol w/ VXX w/ ARCH-based active trading Excess Returns Expand Efficiency Massive expansion in efficiency frontier due to excess returns from trading on AR(1) predictions of VIX What’s the catch? • The VIX itself is not a tradable product • Can generate VIX sensitivity, however through: - Volatility Swaps - Options Positions - Volatility Futures
  25. 25. Part III: Trading and Implementation Using The VIX for VXX Timing Three criteria using the VIX to generate a short signal in VXX (and sell long position in VXX): 1.The monthly low is above its 10-month moving average 2.The monthly close is at least 10% above its 10-month moving average (PPO more than 10) - Use the PPO (Percent Price Oscillator) - PPO = (1-day EMA – 10-day EMA)/10-day EMA 3.The monthly close is above the monthly open (Filled Candle Stick) Three criteria using the VIX to generate a cover signal in VXX (and enter long position in VXX): 1. The high of the VIX is below the 10-day moving average (candlestick must be below the 10- day moving average) 2. The monthly close is at least 10% below the 10-month moving average 3. The close is below the open (Hollow Candlestick)
  26. 26. Part III: Trading and Implementation
  27. 27. Part III: Trading and Implementation Returns Using the PPO Indicator ν = 18.6% σ = 51.3% SR = -0.1418
  28. 28. Part III: Trading and Implementation Another Method Using RSI Indicator • When RSI is above 70, VIX is overbought  Cover VXX position • When RSI is below 30, VIX is oversold  Initiate short VXX position • RSI = 100 – 100/(1+RS) RS = (Average Gain / Average Loss ) in a 5 period (5 month) setting
  29. 29. Part III: Trading and Implementation Results Using the RSI indicator ν = 15.8% σ = 35.6% SR = -0.1406
  30. 30. Part III: Trading and Implementation Conclusions  Use of volatility ETFs significantly expands efficient frontier • Short position on VXX to speculate • Long position on VXZ to hedge  Covariance Matrix Shrinkage technique gives us more reliable covariance estimations and a more accurate efficient frontier  AR(1) model helps us predict future movement in VIX  Simple momentum trading strategies and trading using AR(1) predictions exhibit promising excess returns above benchmark returns  RSI and PPO trading strategies are less viable, returning negative Sharpe ratios
  31. 31. Project 2: Volatility as an Asset Class —improving the mean-variance efficient frontier using volatility as an asset class Q & A

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