What is Trading? What is Risk Management?

Trading (and trade in general) in its true fundamental form is not about mathematics at all, not even one iota, but is basically about buying and selling, profit and loss. To calculate profit and loss, a knowledge of basic arithmetic is sufficient.

Its fundamental principle is to buy low and sell high, and not necessarily in that order. The complex mathematics of pricing and hedging is no more and no less than finding ways to achieve the above principle.

The truth about trading is exemplified in many excellent books. Reminisces of a Stock Operator has a number of trading strategies that work when the volatility is low.

However, allied with Trading is the role of Risk Management, which are more about how you can manage your trading activity in a mathematical way so that you can trade robustly regardless of external conditions.

The Realized Variance of Easter Eggs

The payoff of a variance swap is quite a different affair depending on who you are in the buying and selling process. Suppose I am a nasty speculator who thinks the spot market for Easter Eggs is going to go crazy and wants to be long realized variance on Easter Eggs. I don't care about Easter Eggs, I don't consume Easter Eggs, I just watch the prices like a hawk and see that things are going crazy.

Lots of people are buying and selling Easter Eggs and no-one, absolutely no-one, can agree a price. Why? The cost of cocoa, the cost of milk, the cost of sugar are all fluctuating wildly according to strange models like e=mc-squared.

Does Dispersion Trading Really Work?

If you are Long Dispersion you are Long Volatility and Short Correlation

Trading dispersion is basically the same as trading correlation, whereby you are trading an aggregate against it's components. After trading volatility, skew and term structure you may have gotten bored and need a new technique - this technique is dispersion trading.

Being long dispersion is tantamount to being short correlation but also long volatility as assuming ceteris paribus, if the volatility of the components goes up, the investor profits.

Long Dispersion Refers to "The Long Volatility Setup"

Dispersion is really a special case of volatility trading, whereby you offset a position in the volatility of a basket of stocks (or other assets) against the volatility of the basket itself.  Specifically, you short the basket volatility and buy up volatilities of the components. So when volatility increases in the components, the loss on the short will be outweighed by the gain on the components.

Stronger the Negative Correlation the Lower the Basket Volatility, So More Profit

The greater the inverse correlation of the components, the more the volatilities of the components will offset each other and bring down the corresponding basket volatility, so the basket itself moves less than the components.

Risks of Holding Reverse Convertibles

Reverse Convertibles are Basically Bonds with Long Delta and Short Volatility Features

A reverse convertible is basically a bond with an enhanced yield, "manufactured" by the sale of a (typically) ATM put option.

They can be Made "Exotic"

Reverse Cons can be "exoticised" by selling an "exotic" option instead of the vanilla put. For example, a down-and-in put can be specified.

Reverse Convertible As A First Step to More Complex Products

The "reverse con" is also a useful building block in structures of greater sophistry, such as the autocallable.

Why Investors who Invest in Reverse Convertibles are Considered Bullish on the Underlying

An investor in the structure is considered "bullish" since the sale of the ATM put makes the investor inherently long delta (recall that to be long delta, you can be long futures, long a call or short a put).

Why Investors who Invest in Reverse Convertibles are Considered Bearish on Volatility

As an investor, you have also sold volatility (in technical terms, you are short gamma, and short vega) through the sale of the put option.

The Most Basic "Exotic" Reverse Convertible (The "Knock-In" Reverse Convertible)

The most basic "exotic" reverse convertible is the "knock-in" reverse convertible, whereby the "bond" is enhanced by selling a down-and-in put option.  The option kicks in when spot drops below a certain level.

Realized Volatility Boosting Effect of Short Squeezes

As markets fall, short sellers become more active. As stop-losses tend to be tight, as soon as these stops are breached, the market retaliates with upside moves. This boosts realized volatility.

Spot-Vol Correlation as a Reason for Skew

Not all option markets exhibit skew (in the conventional sense). Many currency pairs are not skewed in the same way that equity index options exhibit skew, and are sometimes said to exhibit "reverse skew".  Here skew refers to the tendency of low strike options to have higher implied volatilities than high strike options. This is partly, or perhaps entirely, depending on your view, due to spot-vol correlation. As spot falls, realized volatility increases. Implied volatility generally rises with realized volatility, so a lower spot price should mean "otherwise equivalent" (say ATMF) options should be priced with higher volatility. The option seller wants protection (or, looked at from another angle, compensation) from the negative spot-vol correlation on the downside.

Prethinking Derivatives

Derivatives mathematics is intuitive to a derivatives trader, just as the rules of poker are intuitive to the professional poker player.  This is because the trader (ideally) has done a great deal of pre-thinking of the underlying mathematics of derivatives such that the behaviours and relationships are second-nature.