Whenever I see a fit personality, I conclude that person should be exercising well. In the same manner if I see a person doing exercise and his schedule then I should be able to tell how fit and unfit his body turns out to be. This needs keen observation and sense of understanding of exercise and human body. Also how these relations existed historically.
How this relates to economy and trading. To undertake trading as a serious business it needs understanding of how various movements can happen. What scenarios can prevail? Strong economies are symbols for stronger factors leading to growth. So what factors contribute towards growth can be inferred by looking at economic indicators. If that is the case then why we make so many poor judgments with regards to understanding economy. Markets (people) are collectively blind and individually wise. They swing from one side to other when cool breeze pass by them. In other words as Benjamin Graham said in the short term markets are like voting machine, but over the long term they are weighing machine.
When looking at individual economic indicators we can tell what is happening in that sector. But we fail to predict what will happen to economy as a whole. Economic indicators are a snapshot of the economy at a particular point of time. Extrapolating the economic potential from scattered economic indicators with some empirical reasoning might be akin to predicting stock markets with number of sun spots. No doubt, economic indicators play a role in measuring the economy. There is one aspect which we might be missing. People adjust their activities according to market environment. A classic example is cut back (adjusting) in personal consumption with a gloomy outlook of economy. Sophisticated predicting models may be adaptive and also they can factor most of the changes and kinks in economic growth but they cannot assimilate the human nature. Human nature can be detected by human alone. There are plenty of human actions that can be automated but to predict a human you need a human. Similarly to predict markets you need humans. Therefore trading remained as a human activity since the dawn of civilization. To predict the markets we need, flair to understand and relate the past. A good understanding of economic indicators and their functional relations to traded instruments. On top of this it requires a human touch of understanding human behavior. By blending all these insights properly we can come up with a good forecast. So for instance to predict gold prices, we need to understand the nature of this commodity, its historical performance under various environments (inflation-deflation). From here we need to understand forces that will drive the price of gold. Towards the end market madness need to be included to come up with a genuine forecast.
This tells me clearly to trade an instrument, I need to know its past, present and market madness.
Thursday, March 12, 2009
Wednesday, March 11, 2009
Generic Execution Algo-definitions
Generic algorithms: Systematic execution of securities in the market can be performed in various ways. Each of these ways will serve one particular purpose. These Algorithms can belong to categories of Iceberg, TWAP, VWAP, Participation and Seek and Destroy.
Each algorithm has certain basic features that it shares commonly with all other algorithms. Limit price, Maximum or minimum price at which the algorithm will send orders to the market. Order quantity, the amount of quantity to trade.
ICE Berg: This algorithm sends out limited quantities of order at certain fixed price and continues to do so till the order is completed. Good thing about this algorithm is it will execute trades at desired price but on negative side some times order gets unfilled.
TWAP: Time weighted average Price algorithm is used to trade a fixed quantity in set time period. Order is broken down into discrete time intervals (waves) with an equal quantity to be traded in each wave.
VWAP: Volume weighted average price algorithm executes orders proportional to average historical market volume over the same period.
Participation (% Volume): This algorithm is used to trade up to the order quantity using a rate of execution that is proportional to the actual volume trading in the market.
Seek and destroy: This algorithm is designed to hide on the passive side of the order book until there is sufficient liquidity available on the aggressive side.
Limit on Close: The limit on close algorithm aims to trade the target quantity during the closing auction of the exchange. If no limit price is set it will trade at a limit of 2.5% of the last traded price before the auction.
Each algorithm has certain basic features that it shares commonly with all other algorithms. Limit price, Maximum or minimum price at which the algorithm will send orders to the market. Order quantity, the amount of quantity to trade.
ICE Berg: This algorithm sends out limited quantities of order at certain fixed price and continues to do so till the order is completed. Good thing about this algorithm is it will execute trades at desired price but on negative side some times order gets unfilled.
TWAP: Time weighted average Price algorithm is used to trade a fixed quantity in set time period. Order is broken down into discrete time intervals (waves) with an equal quantity to be traded in each wave.
VWAP: Volume weighted average price algorithm executes orders proportional to average historical market volume over the same period.
Participation (% Volume): This algorithm is used to trade up to the order quantity using a rate of execution that is proportional to the actual volume trading in the market.
Seek and destroy: This algorithm is designed to hide on the passive side of the order book until there is sufficient liquidity available on the aggressive side.
Limit on Close: The limit on close algorithm aims to trade the target quantity during the closing auction of the exchange. If no limit price is set it will trade at a limit of 2.5% of the last traded price before the auction.
Tuesday, March 10, 2009
option trading -Basics
In this article, short summary of Black, Scholes and Merton model, ways to measure and forecast volatility and dynamics of implied volatility surface are discussed.
BSM Model: Delta hedged portfolio consists of a call option and ∆ units of underlying short stock or future. With passage of time this portfolio will be rebalanced to make it delta neutral.
Option prices change due to passage of time, change in underlying and change in volatility. Of three components, change in underlying impacts the option price most.
From Taylor’s rule, we get a relation between volatility, theta and gamma.
Option trading using quoted prices and estimate of option volatility can have P/L effects in the following fashion.
GAMMA profits:
(½)*S2*Γ*(σ2- σ2implied)
Vega Profits:
Vega*(σ- σimplied)
Assumptions:
1) Underlying is a trade able asset
2) Underlying pays no dividends
3) Can short the underlying in any size
4) Interest rates are constant
5) Volatility is constant
6) Underlying changes continuously
Defining and measuring volatility
Volatility is defined as square root of variance. Variance is measured as
Unbiased estimate
To get unbiased estimate of volatility needs correction factor. This correction factor depends on the assumption of the underlying process follows particular distribution (Normal distribution).
There are other estimators that can be used to measure volatility. But due to simplicity and well understood sampling properties make this estimator most desirable.
Forecasting volatility:
Volatility is a mean reverting process
Volatility of volatility is positively related to level.
In making an estimate of volatility, we need to understand primarily what events are being included and what are getting excluded. Exponentially weighted moving average model does a good job in giving higher weights to recent events and lower weighting to past events.
In the above equation most recent return values are given weightings. Λ values used generally range between 0.9 and 0.99. One draw back of exponential moving averages is that they do not address the mean reversion nature of volatility. High volatility regimes follow calm and low volatility ranges.
GARCH (generalized auto-regressive conditional heteroskedasticity) models address the above issue of mean reversion. These models are developed by Engle-Bollerslev. But this model is not Holy Grail for forecasting volatility.
This equation is specification for GARCH (1,1) Model.
This model does good job in some situations. One undesirable feature for this model is that it needs estimation of calibration parameters. These estimates are not persistent and some times they tend to be highly unstable.
Volatility cones: Forecasting volatility involves in coming up with point estimates for the volatility. When we need a range of volatilities then volatility cones will come in aid for such analysis. This analysis was initially developed by Bughardt. In this analysis, what we try to find is chart a series of 10, 20, 40, 100, 300 days volatility for securities for non-overlapping periods. This will give a context to today’s volatility.
Implied volatility dynamics: Implied volatilities for a particular stock at different strikes and maturities form a 3D surface. This volatility surface will have different shapes and contours. From time to time market changes cause the shape to undergo changes. PCA (principal component analysis) when applied to yield curve data it provides insights to level, slope and curvature changes in the yield curve. Similarly when applied to implied volatilities as a deviation from ATM (at the money volatilities) we get similar factors that explain variation.
Level Dynamics: VIX Index published by CBOE.
Level of VIX has 3 regimes, less than 20, above 20 and below 40 and above 40.
Volatility of the index is positively related to the level.
There are more large ups compared to downs.
It is mean reverting and settles with new level at each regime.
ATM volatility level for contracts maturing from front month to last month will have embedded event volatility. In other words contract maturing after event will see a sharp drop in volatility.
Smile dynamics: Good understanding of volatility smile will give us a handle to spot best strike to trade. Volatility smile is a phenomena where OTM/ITM strikes trade at different volatilities compared to ATM. These volatilities can be higher or lower compared to ATM vol subjected to market conditions.
1) retail investors buy OTM strike options (akin to lottery ticket)
2) Large funds who buy downside protection and writing covered calls
Skewness and kurtosis are 3rd and 4th moments for a distribution. These two elements additionally required to specify a particular distribution. Jarrow and Rudd (1982) have made first attempt to include these two elements into option pricing. Corrado and Su (1996) have provided a better solution to estimate these parameters.
The European call price is given by
This equation will be solved for ATMVOL, SKEW and Kurtosis.
BSM Model: Delta hedged portfolio consists of a call option and ∆ units of underlying short stock or future. With passage of time this portfolio will be rebalanced to make it delta neutral.
Option prices change due to passage of time, change in underlying and change in volatility. Of three components, change in underlying impacts the option price most.
From Taylor’s rule, we get a relation between volatility, theta and gamma.
Option trading using quoted prices and estimate of option volatility can have P/L effects in the following fashion.
GAMMA profits:
(½)*S2*Γ*(σ2- σ2implied)
Vega Profits:
Vega*(σ- σimplied)
Assumptions:
1) Underlying is a trade able asset
2) Underlying pays no dividends
3) Can short the underlying in any size
4) Interest rates are constant
5) Volatility is constant
6) Underlying changes continuously
Defining and measuring volatility
Volatility is defined as square root of variance. Variance is measured as
Unbiased estimate
To get unbiased estimate of volatility needs correction factor. This correction factor depends on the assumption of the underlying process follows particular distribution (Normal distribution).
There are other estimators that can be used to measure volatility. But due to simplicity and well understood sampling properties make this estimator most desirable.
Forecasting volatility:
Volatility is a mean reverting process
Volatility of volatility is positively related to level.
In making an estimate of volatility, we need to understand primarily what events are being included and what are getting excluded. Exponentially weighted moving average model does a good job in giving higher weights to recent events and lower weighting to past events.
In the above equation most recent return values are given weightings. Λ values used generally range between 0.9 and 0.99. One draw back of exponential moving averages is that they do not address the mean reversion nature of volatility. High volatility regimes follow calm and low volatility ranges.
GARCH (generalized auto-regressive conditional heteroskedasticity) models address the above issue of mean reversion. These models are developed by Engle-Bollerslev. But this model is not Holy Grail for forecasting volatility.
This equation is specification for GARCH (1,1) Model.
This model does good job in some situations. One undesirable feature for this model is that it needs estimation of calibration parameters. These estimates are not persistent and some times they tend to be highly unstable.
Volatility cones: Forecasting volatility involves in coming up with point estimates for the volatility. When we need a range of volatilities then volatility cones will come in aid for such analysis. This analysis was initially developed by Bughardt. In this analysis, what we try to find is chart a series of 10, 20, 40, 100, 300 days volatility for securities for non-overlapping periods. This will give a context to today’s volatility.
Implied volatility dynamics: Implied volatilities for a particular stock at different strikes and maturities form a 3D surface. This volatility surface will have different shapes and contours. From time to time market changes cause the shape to undergo changes. PCA (principal component analysis) when applied to yield curve data it provides insights to level, slope and curvature changes in the yield curve. Similarly when applied to implied volatilities as a deviation from ATM (at the money volatilities) we get similar factors that explain variation.
Level Dynamics: VIX Index published by CBOE.
Level of VIX has 3 regimes, less than 20, above 20 and below 40 and above 40.
Volatility of the index is positively related to the level.
There are more large ups compared to downs.
It is mean reverting and settles with new level at each regime.
ATM volatility level for contracts maturing from front month to last month will have embedded event volatility. In other words contract maturing after event will see a sharp drop in volatility.
Smile dynamics: Good understanding of volatility smile will give us a handle to spot best strike to trade. Volatility smile is a phenomena where OTM/ITM strikes trade at different volatilities compared to ATM. These volatilities can be higher or lower compared to ATM vol subjected to market conditions.
1) retail investors buy OTM strike options (akin to lottery ticket)
2) Large funds who buy downside protection and writing covered calls
Skewness and kurtosis are 3rd and 4th moments for a distribution. These two elements additionally required to specify a particular distribution. Jarrow and Rudd (1982) have made first attempt to include these two elements into option pricing. Corrado and Su (1996) have provided a better solution to estimate these parameters.
The European call price is given by
This equation will be solved for ATMVOL, SKEW and Kurtosis.
Wednesday, March 4, 2009
Market perspectives- March - 09
A friend of mine asked me how low markets will go from here. If I knew that I would be playing GOD. But I can provide a rational basis for predictably irrational markets. To able to see end of tunnel we need some lights to at least start glowing in terms of stabilizing housing prices, resumption in credit markets functioning, improvements in consumer and business confidence and most importantly the new stimulus package should put some sort of damper around growing unemployment rate. If these events happen then we can say signs of life coming to economy.
Treasury is working jointly with Federal Reserve and created various plans under the umbrella of financial stabilization plan to bring life into economy. It is tackling various problems in the economy through its bailout programs. Housing sector is being supported by treasury’s purchase of agency debt and mortgage backed securities. These two activities were part of Fannie and Freddie’s activities. Treasury is ensuring that mortgage rates remain lower and bring more buyers into the market. Also it is plugging the pressure on housing markets coming from foreclosures. Will these actions bear some fruits? Only time will decide but at least we can say it will not deteriorate drastically. Treasury is doing everything possible to bailout financial sectors. Treasury is pumping money into the recapitalization programs, working plans for removal of toxic securities on banks balance sheets. These actions will start showing slow improvements in the economy. Treasury’s new TALF program will start aiding credit starved nation and jump start securitization industry. Recent stimulus package is aimed at providing state and local governments to start new projects and reduce the rise of unemployment. These factors jointly shall improve consumer and business confidence and leads to increased consumption expenditure and industrial activity.
Risks to above scenario is coming from further weakness in banking sector, ineffective stimulus and further deterioration in real estate sector coming in the form of commercial real estate sector. Also some macro themes that can work against broad based recovery are rise of global protectionism measures.
From here what can be said about individual financial markets
FX markets
USD has become safe haven currency. It will strengthen during this despite domestic weakness
Interest rates markets
Short term libor rates are totally anchored to lower levels.
Long term treasury rates will be rising due to supply of treasury. But international investors purchases will keep a cap on this from going too high.
Equity markets:
Stock markets will weaken further but rally on small good news events.
Commodity sector:
Oil will live for rest of the year under 50. Reason being global unwinding and lack of industrial activity. Even If dollar weakens, gold will benefit but not oil.
Treasury is working jointly with Federal Reserve and created various plans under the umbrella of financial stabilization plan to bring life into economy. It is tackling various problems in the economy through its bailout programs. Housing sector is being supported by treasury’s purchase of agency debt and mortgage backed securities. These two activities were part of Fannie and Freddie’s activities. Treasury is ensuring that mortgage rates remain lower and bring more buyers into the market. Also it is plugging the pressure on housing markets coming from foreclosures. Will these actions bear some fruits? Only time will decide but at least we can say it will not deteriorate drastically. Treasury is doing everything possible to bailout financial sectors. Treasury is pumping money into the recapitalization programs, working plans for removal of toxic securities on banks balance sheets. These actions will start showing slow improvements in the economy. Treasury’s new TALF program will start aiding credit starved nation and jump start securitization industry. Recent stimulus package is aimed at providing state and local governments to start new projects and reduce the rise of unemployment. These factors jointly shall improve consumer and business confidence and leads to increased consumption expenditure and industrial activity.
Risks to above scenario is coming from further weakness in banking sector, ineffective stimulus and further deterioration in real estate sector coming in the form of commercial real estate sector. Also some macro themes that can work against broad based recovery are rise of global protectionism measures.
From here what can be said about individual financial markets
FX markets
USD has become safe haven currency. It will strengthen during this despite domestic weakness
Interest rates markets
Short term libor rates are totally anchored to lower levels.
Long term treasury rates will be rising due to supply of treasury. But international investors purchases will keep a cap on this from going too high.
Equity markets:
Stock markets will weaken further but rally on small good news events.
Commodity sector:
Oil will live for rest of the year under 50. Reason being global unwinding and lack of industrial activity. Even If dollar weakens, gold will benefit but not oil.
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