Bonds = titulos
Modern Portfolio Theory: alocamento de recursos baseado em alguns pesos
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expected return for portfolio
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risk is volatility
- volatility is something to do with standard deviation and variance
- covariance measures how much two random variables vary together
- $covariance < 0 moves inversely
- $covariance > 0 moves together
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Markowitz theory
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high positive covariance does not provide very much diversification
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the aim to diversification is to eliminate the fluctuactions
- uncorrelated stocks are better
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for calculate the variance of the portfolio we need the covariance matrix containing all
the covariance of the stocks in portfolio.- covariance matrix: correlation between the stocks
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output from modern portfolio is expected variance/return matrix
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Efficient frontier are the portfolio that has high return and minor risk THE EDGE!
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Sharper ratio - risk/return measure
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it describes how much excess return you are receiving for extra volatility that
you endure holding a riskier asset. -
sharpe-ratio S(x) > 1 is considered to be good, high better
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notes on article(https://medium.com/qfx-research/im-approaching-one-year-since-diving-full-time-into-quant-trading-a1bea7bb6d05)
- Trading US stocks, forex, and bonds probably is a bad idea. It is not the wisest choice, due to too much competition with the biggest players.
- Find your liquidity sweet spot by taking a look at markets that would support your liquidity needs
- Play and win in niche markets by learning their rules
There’s so much to do in quant trading: strategy development, optimization, backtesting, execution, and risk management. Don’t focus on the wrong things in the beginning — like optimizing parameters. Rather, build very basic MVP versions of each part in the equation and optimize by iterating while in production. A perfectly optimized strategy won’t help if the execution part doesn’t work correctly. - Price stops will, as research shows, destroy a good strategy, simply due to randomness in volatility.
- By using time stops, you are setting a time constraint in terms of how long your hypothesis is valid, which almost always reduces variance (and increases Sharpe ratio).
- For each trade, know where to enter and where to exit. For me, these are set based on two rules — one being a modified formula of Average True Range. It’s almost a requirement to have pre-defined rules for entries and exits, in order to properly backtest and to know what to expect in live trading.
- For each strategy, you must know the expected value, hit rate, expected drawdown, longest drawdown, expected volatility, variance, Sharpe ratio, standard deviation of returns, skewness of returns, and value at risk. Also, proper bet sizing, risk of ruin, Kelly fraction, and optimal F should be strategically chosen based on how the strategy performs during the backtest.
- Make risk management a priority
- Use fewer parameters but know what they do
- Focus on features, not on optimization
There’s a great range of tools for optimization, genetic optimizations, non-convex optimizations, principal component analysis, statistical/Bayesian optimization, and a thousand fancy libraries. From my point of view, optimization will help improve a strategy by 10–20%; however, it won’t lead to a profitable strategy in the first place. If a strategy is bad, no optimization will help. Focus on deductive analysis and feature engineering — in simple terms, making sense out of the inputs and data. - Better data, better features, “Data is the oil of the digital world,”
- Fast feedback is a must
Competing with big players, especially in the HFT realm, is probably a bad idea (like I explained above). Going the opposite — holding trades for days, months, and years — also is not ideal. For me, the sweet spot is a holding time of 5 to 60 minutes. If I can’t test a strategy in 2 weeks with statistical significance (meaning more than 100 trades), I’m not investing my time in it. To test a strategy with a multi-day (and longer) holding period, I’d need months to validate, and this is not what I’m interested in.
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The truth is, simple statistics, Monte Carlo simulation and a little bit of Python is all you need. Simple assumptions well simulated and validated can spot over-priced and under-priced bids and asks, that’s it. The fancy models are good for your ego and general understanding. In markets, a CS 101 probability and statistics is good enough for a profitable strategy.
Important questions you must ask yourself before using a Trading Strategy:- Does it outperform a benchmark?
- Does it have a high enough Sharpe ratio?
- Does it have a small enough drawdown and short enough draw-down duration?
- Does the backtest suffer from survivorship bias?
- Does the strategy lose steam in recent years compared to its earlier years?
- Does the strategy have its own “niche” that protects it from intense competition from large institutional money managers?
- Things to take care in Back-Testing:
Data: Split/dividend adjustments, noise in daily high/low, and survivorship bias.
Performance measurement: Annualized Sharpe ratio and maximum draw-down.
Look-ahead bias: Using unobtainable future information for past trading decisions.
Data-snooping bias: Using too many parameters to fit historical data, and avoiding it using large enough sample, out-of-sample testing, and sensitivity analysis.
Transaction cost: Impact of transaction costs on performance.
Strategy refinement: Common ways to make small variations on the strategy to optimize performance.
How we can implement RISK-Management Using Programming?:
- Calculating the Kelly criterion is relatively simple and relies on two basic components: your trading strategy’s win percentage probability and its win to loss ratio.
The win percentage probability is the probability that a trade will have a positive return. The win to loss ratio is equal to your total trading profits divided by your total trading losses.
These will help you arrive at a number called the Kelly percentage. This gives you a guide to what percentage of your trading account is the maximum amount you should risk on any given trade.
The formula for the Kelly percentage looks like this:
Kelly % = W — [(1 — W) / R]
Kelly % = Kelly percentage
W = Win percentage probability (total number of winning trades/total number of trades)
R = Win to loss ratio (total amount gained by winning trades/total amount lost by losing trades)