1. Tactical Asset Allocation 2 session 6
Andrei Simonov
Tactical Asset Allocation
11/17/2018

2. Agenda Statistical properties of volatility.
Persistence
Clustering
Fat tails
Is covariance matrix constant?
Predictive methodologies
Macroecon variables
Modelling volatility process: GARCH process and related methodologies
Volume
Chaos
Skewness
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3. Volatility is persistent
Returns2 are MORE autocorrelated than returns themselves. Volatility is indeed persistent.
Akgiray, JB89
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4. It is persistent for different holding periods and asset classes
Sources: Hsien JBES(1989), Taylor&Poon, JFB92
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5. Volatility Clustering, rt=ln(St/St-1).
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6. Volatility clustering
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7. Kurtosis & Normal distribution
Kurtosis=0 for normal dist. If it is positive, there are so-called FAT TAILS
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8. Higher Moments & Expected Returns
Data through June 2002
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9. Higher Moments & Expected Returns
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Data through June 2002
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10. Extreme events
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11. Normal distribution:
Only 1 observation in should be outside of 4 standard deviations band from the mean.
Historicaly observed:
1 in 293 for stock returns (S&P)
1 in 138 for metals
1 in 156 for agricultural futures
Tactical Asset Allocation
11/17/2018

12. What do we know about returns?
Returns are NOT predictable (martingale property)
Absolute value of returns and squared returns are strongly serially correlated and not iid.
Kurtosis>0, thus,returns are not normally distributed and have fat tails
-’ve skewness is observed for asset returns
Tactical Asset Allocation
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13. ARCH(1)
volatility at time t is a function of volatility at time t-1 and the square of of the unexpected change of security price at t-1.
Ret(t)=f Ret(t-1)+et
e(t)= s(t) z(t)
s2(t)=a0+a1e2(t-1), z~N(0, 1)
If volatility at t is high(low), volatility at t+1 will be high(low) as well
Greater a1 corresponds to more persistency
Tactical Asset Allocation
11/17/2018

14. Simulating ARCH vs Normal
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15. GARCH=Generalized Autoregressive Heteroskedasticity
volatility at time t is a function of volatility at time t-1 and the square of of the unexpected change of security price at t-1.
s2(t)=a0+b1 s2(t-1)+ a1e2(t-1), e~N(0, s2t)
If volatility at t is high(low), volatility at t+1 will be high(low) as well
The greater b, the more gradual the fluctuations of volatility are over time
Greater a1 corresponds to more rapid changes in volatility
Tactical Asset Allocation
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16. Tactical Asset Allocation
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17. Tactical Asset Allocation
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18. Persistence
If (a1+b)>1, then the shock is persistent (i.e., they accumulate).
If (a1+b)<1, then the shock is transitory and will decay over time
For S&P500 (a1+b)=0.841, then in 1 month only =0.5 of volatility shock will remain, in 6 month only 0.01 will remain
Those estimates went down from 1980-es (in 1988 Chow estimated (a1+b)=0.986
Tactical Asset Allocation
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19. Forecasting power GARCH forecast is far better then other forecasts
Difference is larger over high volatility periods
Still, all forecasts are not very precise (MAPE>30%)
xGARCH industry
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20. Options’ implied volatilities
Are option implicit volatilities informative on future realized volatilities? YES
If so, are they an unbiased estimate of future volatilities? NO
Can they be beaten by statistical models of volatility behavior (such as GARCH)? I.e. does one provide information on top of the information provided by the other?
Lamoureux and Lastrapes:
ht = w + ae2t-1 + bh t-1 + gsimplied
They find g significant.
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21. Which method is better? (credit due: Poon & Granger, JEL 2003)
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22. Straddles: a way to trade on volatility forecast
Profit
Straddles delivers profit if stock price is moving outside the normal range
If model predicts higher volatility, buy straddle.
If model predicts lower volatility, sell straddle X ST
Tactical Asset Allocation
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23. ht = w + ae2t-1 + bh t-1 + gVolume
Volatility and Trade
Lamoureux and Lastrapes: Putting volume in the GARCH equiation, makes ARCH effects disappear.
ht = w + ae2t-1 + bh t-1 + gVolume
Heteroscedastisity is (at least, partially) due to the information arrival and incorporation of this information into prices.
Processing of information matters!
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24. What else matters? Macroeconomy
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25. Macroeconomic variables (2)
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26. Stock returns and the business cycle: Volatility NBER Expansions and Contractions January 1970-March 1997
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27. Predicting Correlations (1)
Crucial for VaR
Crucial for Portfolio Management
Stock markets crash together in 87 (Roll) and again in 98...
Correlations varies widely with time, thus, opportunities for diversification (Harvey et al., FAJ 94)
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28. Predicting Correlations (2)
Use “usual suspects” to predict correlations
Simple approach “up-up” vs. “down-down”
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29. Predicting Correlations (3)
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30. Chaos as alternative to stochastic modeling
Chaos in deterministic non-linear dynamic system that can produce random-looking results
Feedback systems, x(t)=f(x(t-1), x(t-2)...)
Critical levels: if x(t) exceeds x0, the system can start behaving differently (line 1929, 1987, 1989, etc.)
The attractiveness of chaotic dynamics is in its ability to generate large movements which appear to be random with greater frequency than linear models (Noah effect)
Long memory of the process (Joseph effect)
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31. Example: logistic eq. X(t+1)=4ax(t)(1-x(t)) Tactical Asset Allocation
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32. A=0.9
A=0.95
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33. Hurst Exponent Var(X(t)-X(0)) t2H
H=1/2 corresponds to “normal” Brownian motion
H<(>)1/2 – indicates negative (positive) correlations of increments
For financial markets (Jan 63-Dec89, monthly returns):
IBM
Coca-Cola 0.70
Texas State Utility 0.54
S&P
MSCI UK 0.68
Japanese Yen 0.64
UK £
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34. Long Memory Memory cannot last forever. Length of memory is finite.
For financial markets (Jan 63-Dec89, monthly returns):
IBM 18 month
Coca-Cola 42
Texas State Utility 90
S&P
MSCI UK 30
Industries with high level of innovation have short cycle (but high H)
“Boring” industries have long cycle (but H close to 0.5)
Cycle length matches the one for US industrial production
Most of predictions of chaos models can be generated by stochastic models. It is econometrically impossible to distinguish between the two.
Tactical Asset Allocation
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35. Correlations and Volatility:
Predictable.
Important in asset management
Can be used in building dynamic trading strategy (“vol trading”)
Correlation forecasting is of somewhat limited importance in “classical TAA”, difference with static returns is rather small.
Pecking order: expected returns, volatility, everything else…
Good model: EGARCH with a lot of dummies
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36. Smile please! Black- Scholes implied volatilities (01.04.92)
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37. Skewness & Expected Returns
Data through June 2002
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38. Skewness & Expected Returns
Data through June 2002
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39. Skewness or ”crash” premia (1)
Skewness premium =Price of calls at strike 4% above forward price/ price of puts at strike 4% below forward price- 1
The two diagrams following show:
That fears of crash exist mostly since the 1987 crash
This shows also in the volume of transactions on puts compared to calls
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40. Skewness or ”crash” premia (2)
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41. Tactical Asset Allocation
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42. Skewness See also movie from Cam Harvey web site.
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43. Where skewness is coming from?
Log-normal distribution
Behavioral preferences (non-equivalence between gains and losses)
Experiments: People like +’ve skewness and hate negative skewness.
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44. Conditional Skewness, Bakshi, Harvey and Siddique (2002)
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45. What can explain skewness?
Stein-Hong-Chen: imperfections of the market cause delays in incorporation of the information into prices.
Measure of info flows – turnover or volume.
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46. Co-skewness
Describe the probability of the assets to run-up or crash together.
Examples: ”Asian flu” of 98,” crashes in Eastern Europe after Russian Default.
Can be partially explained by the flows.
Important: Try to avoid assets with +’ve co-skewness. Especially important for hedge funds
Difficult to measure.
Tactical Asset Allocation
11/17/2018

47. Three-Dimensional Analysis
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48. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options
Source: Naik (2002)
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49. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options
Source: Naik (2002)
Tactical Asset Allocation
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50. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options
Source: Naik (2002)
Tactical Asset Allocation
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51. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options
Source: Naik (2002)
Tactical Asset Allocation
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52. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options
Source: Figure 5 from Mitchell & Pulvino (2000)
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53. Alternative Vehicles
Alternate Asset Classes Often Involve Implicit or Explicit Options 6 4 2
Event Driven Index Returns
-15
-10 -5 5 10 -2 -4
LOWESS fit -6
Source: Naik (2002) -8
Tactical Asset Allocation
Russell 3000 Index Returns
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54. Co-skewness for hedge funds
Source: Lu and Mulvey (2001)
Tactical Asset Allocation
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