Institutional investor high-volume trading

Will be further updated.

– static (deterministic and indifferent to price motion during trading) solution of market impact vs slow execution trade-off way worse than the one exploiting adaptive trading – adaptive bidding, and this boils down to “aggressive” acceleration on positive prime movement, with spending part of gains to reduce risk (to be analyzed, as does not seem optimal)

– price appreciation (trend): investor wants to trade before other participants trade the same direction

– aggressive bidder incurs high market impact cost,

– daily cycle: large decisions in the morning/night, day for bidding,

– multiperiod portfolio section, optimal execution of portfolio transactions,

– defining trading as an online search problem k-search,

– loopback options

– option allows to buy at historical min price

– Black-Scholes option pricing model as a delta hedging algorithm (creates riskless hedge of an option)

– optimal execution portfolio transactions: optimal risk-averse execution under market impact and bayesian adaptive trading with price appreciation

– costs for an institutional investor come mainly from slippage: price appreciation and market impact, not from tranaction costs (e.g. brokerage costs),

– slippage not an issue for an invidual investor (trade size << market liquidity), for institutional investors slippage playes a big role – implementation cost ca. 1% for a typical trade and 2-3% in illiquid stocks,

– “to avoid market impact would be to trade more slowly to allow market liquidity recover between trader .. slower trading increases the trader’s susceptibility to market volatility and prices may potentially move disadvantageous to the trader.”

– “Do trade and push the market. Don’t trade and the market pushes you.” – “Optimal trade schedules seek to balance the market impact cost of rapid execution against the volatility risk of slow execution.”

– arrival price algorithms in tradings due to implementation shortfall

– mean-variance framework algos minimize variance for a max level of cost expectation

– pure random walk with no serial correlation for mean-variance as risk-reward trade-off – mean-variance portfolio selection solved in multiperiod setting

– “optimal adaptive trade schedules coincide with the optimal static trade schedules of Almgren and Chriss”

– “the improvement stems from introducing a correlation between the trading gains (or losses) in earlier parts of the execution and market impact costs incurred in later parts” – “trader becomes more risk-averse after positive performance”

– urgency in aggressive bidding stems from anticipated drift (expected: market impact due to the actions of a financial buyer), not from being risk-averse

– price appreciation comes from increased trading of other financial traders

– stock price modelled with brownian motion with a drift (market impact and price appreciation)

– risk measured not only with variance but also with covariance with all other securities in portfolio

– capital asset pricing model (CAPM)

– MPT from Markowitz (Nobel Prize in 1990)

– mean-variance problem intro an auxiliary one with utility function

– k-search generic trading problem with loopback options

– implementation shortfall of a portfolio transaction

– difference between the pre-trade and the post-trade book value of the portfolio

Advertisements

About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
This entry was posted in Mathematics. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s