- Options: A Summary
- The Efficient Market Hypothesis
- Forecasting Volatility
- The Variance Premium
- Finding Trades with Positive Expected Value
- Strategies
- Confidence Level III
- Confidence Level II
- Confidence Level I
- Volatility Positions
- Directional Option Trading
- Directional Strategy Selection
- Trade Sizing
- Meta Risks
- Adjustments to BSM
- Rules of Thumb
- Rule of Five
- Rule of Three
- Execution

Trading is a process: find edge, structure the trade, control the risk. Repeat.

When looking for ideas it is important to focus on phenomena rather than parametrizations or models

# Options: A Summary

- BSM Spits out implied vol. The best way to think of implied vol is not as a predictor but simply as changing the fast moving various option prices into something slower moving
- It is a simplifying tool
- Success is largely about finding situation where vol is mispriced
- Hedging is intended to balance variance for transaction costs

# The Efficient Market Hypothesis

- Exceptions: Inefficiencies or Risk Premia
- Inefficiencies: temporary phenomena that last only until enough people notice them, or poorly priced risk premia
- Risk premia persists and can form the core of operations. But the profits will be less than the one off inefficiencies, which need aggressive action.

# Forecasting Volatility

- We can also distinguish trades at the tactical level (above is strategic): model driven or event driven
- Model Driven: we have a fair value or edge and always have an opinion. relative value.
- Event driven is a specific or unusual situation
- Examples in blackjack: card counting is a model, ace tracking is event driven
- Event driven are easily backtested in excel and can be very profitable. But may not often happen
- GARCH: Many tweaks, but basically says the same thing as always:
- best guess of vol for next N days is what it was the last N days
- ...taking into account clustering of vol (by weighing the more recent moves)
- ...and mean reverts in the long term (with a decay term)
**Bottom Line: Vol tomorrow will probably be close to what it was today. Vol in long term will probably be whatever the long term average has been.**- Best methods of predicting vol now use a variety of methods and weight htem
- The simple 30 day historical vol is actually the best single method...

# The Variance Premium

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**Why?**# Finding Trades with Positive Expected Value

## Strategies

### Confidence Level III

**Implied vol term structure as a predictor of vol (contango = lower)**- Options on fundamental factors (revisit if ever get into it)

### Confidence Level II

- Overnight effect: Index variance premium is (usually) realized overnight)
- FOMC and volatility: VIX futures rise into and selloff after FOMC meetings
- Buy futures two days before, sell before announcement
- at some time sell VIX futures, cover 45 minutes after
- Weekend effect: options decay more than expected over the weekend
- Vol of Vol Risk Premia: High VVIX = predictor of lower VIX

### Confidence Level I

# Volatility Positions

- It can be tempting to choose a shorter dated option when hedging. Don't do this.
- two options usually cost more than one longer dated.
- If the vol is in steep enough contango, MAY, make sense
**Selling OTM option structures give higher median returns and higher win rates but that can make it hard to distinguish between luck and genuine positive edge**- Highest vol premium in options that are short dated (1 week)
- Out of the money puts most premium, out of the money calls almost none

# Directional Option Trading

- BSM is risk nuetral
- You can add an estimate of drift and subjectively price options (better reflect the real world)
- Still include an interest rate. Stock appreciates by one rate and discounted by risk free
- "Best" or "optimal" is only with respect to a given criterion, trading decisions need to be based on more than just one criterion

# Directional Strategy Selection

- Overwriting: Strike determines how much edge is due to drift and how much to variance premium
- Short put spread is the classic conservative position
- Buying teenies makes sense
**Bullish risk reversals with a teeny (5d) put is his favorite position to get long:**- Potential for large wins
- takes advantage of skew premium
- Short implied skew trades are very difficult to make money on in practice
**Few rules in trading but here's one: Don't buy ratios (buy 1 sell 2)**- Variance and skew premia still most important even directionally
- single options have best correlation between profit and prediction
- spreads mitigate path dependency and create a stop - but too hard to do consistently (predict spot)

# Trade Sizing

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**Kelly Criterion should form the basis of sizing**- We can scale Kelly, and many do, but what if the edge is actually -ve?
- need to know variance of edge, and probability we are wrong. adjust bet downward based on how uncertain
- negative skewness also means we must adjust downward
- Scaling is ok, but the real best way to do this is to use Kelly with a percentage stop
- Keeps the best points of Kelly
- Stops all have costs
- Trailing stops worse than fixed stops. Both cost because small losers never get a chance to recover, and some would have
- Optimal Method: Split account into "safe" and "risky" ā> fully kelly bet on the risky portion
- Fixed split (not ideal)
- Trailing percentage stop ā> keep safe amount constant percentage below peak
- ex: start 20 risky 80 safe, double risky, now 40/80
- rebalance 80 safe to be 20% below 120, or 96
- new account is 96 safe 24 risky (77% and 23%, risky has grown as percentage)

# Meta Risks

- Real risks are things no one even has thought about (Madoff, theft, currency)

# Adjustments to BSM

- Stochastic interest rates not necessary (vol night high enough)
- Pricing Real options using BSM framework (these are options on actual physical things, not always traded)
- Find best correlated traded asset, and at least get an idea of value
**It wont be good, but do the best you can, accept the variance, and ask for enough edge**- Stochastic vols creates the convexity of the smile (vol gamma). Farther OTM options have convex payoffs to vol moves ā> worth more
- Correlation between vol and spot creates slope of the smile

# Rules of Thumb

### Rule of Five

- In a randomly sampled population, you can be 93% certain the median of a measure fall in between the range of 5 measurements (like vol periods)

### Rule of Three

- Probability something that never has been observed will happen: divide by length of time not seen and this gives you 95% upper limit
- so havent seen a presidential upset in first 30 elections, chance of next time = 3/30 = 10

# Execution

- Balance between paying too much or not making any trades whatsoever
- need to be aggressive when trading in direction of markets and patient when going against