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.

Basic Concepts of Econometrics

Econometrics is the "trendy term" for the application mathematics and statistics to economic data. It includes time series analysis and regression analysis.

What happens when you square volatility? Why is this important in derivatives pricing?

When you square a volatility you get a smaller number in units of volatility squared. The square of volatility appears in the expressions d1 and d2 in the Black-Scholes pricing formulas for European puts and calls.

For example, the square of 5% is 0.25%. The square of 9% (this looks like an FX vol) is 0.81%. From something small, we get something very small.

Commodity Contracts

CME Feed Cattle Futures: contract size = 50,000 pounds. Pricing units: cents per pound.
Contract months: Jan, Mar, Apr, May, Aug, Sep, Oct, Nov.

Cocoa Futures (Liffe exchange; part of the NYX): units of 10 tonnes. Pricing units: £ per tonne.
Contract months: March. May, July, September, December.
A tonne here means a metric tonne of 1000 kilograms. (as opposed to short tons and long tonnes).

Apart from the quantitative side, there is some jargon needed to understand the trading and settlement procedures surrounding cocoa: firstly what is cocoa? It refers to cocoa beans, which are whole seeds of the cocoa tree. A bean cluster refers to two or more beans joined together unable to be split by reasonable hand pressure.  

More "Exotic" Greeks in Convertibles

When contemplating the more exotic greeks relating to convertibles, you want to think about dividend and credit risk.

Phi (Dividend Risk)

Sensitivity of CB value to a change in dividends (or rather the dividend yield). The relationship between fair value and dividend yield is an inverse one.

CB value (simplified equation) = [PV of the CB's income - PV of stock dividend over the expected life of the security].

If you're long CB, you're long an option on stock, so without holding the stock you're not getting dividends. This can be a huge opportunity cost, thus dividend risk can be significant.

If I underestimate dividends, then I overestimate the value of the Convertible Bond.

Omicron (Credit Risk)

Sensitivity of the bond to change in credit spread. This can be the most important sensitivity measure for an OTM convertible. It's really, really important to know the omicron risk of your CB position and even more so for your portfolio as a whole.

This is particularly true for low-grade issues.

Generally speaking, as credit spreads narrow - this is good for the convertible's value. As credit spreads widen, this reduces the value of the convertible.

Greeks Needed for Convertible Arbitrage Purposes

DELTA (By that I mean the Continuous-Time Delta)

ANALYTIC DEFINTION- change in CB price for a given change in the Underlying Stock price.
MEANING - equity sensitivity for a CB.Tells the arbitrageur how many shares to SHORT against a long bond position.
CALCULATION - It's taken as N(d1) discounted by the stock's dividend yield.

NUMERIC RANGE OF DELTA:
* Approaches one as CB moves deep-in-the-money.
* Approaches zero as the stock price falls.

MORE ABOUT DELTA:
What we've talked about is the continuous-time delta. Suppose you expect to rebalance the hedge for every 5% move in the stock price - so you can calculate the change in value for a down move  and for an up move, average them, and that's your delta. It's still one number - but you factor in any asymmetric behaviours.

GAMMA

Sensitivity of delta to changes in Stock Price. A higher gamma implied the convertible's hedge must be rebalanced more frequently.

The interesting thing about gamma is it's variation with moneyness. Gamma is low for deep-in-the-money convertibles and for a far-out-the-money convertible. ATM CBs have the highest gammas.

Break-even Inflation - What it Means for Investors

You may have seen charts of the "break-even inflation" rate (% yield versus maturity) and wondered - what is this inflation rate represent?

Why does it vary with maturity, and maturity of what kind of product? What does it mean to say the B/E inflation rate in the US for April 2014 is 2%?

The Vanguard Group (an asset management firm) have published a tutorial on break-even inflation, and how it's derived, and how it's relevant to investment selection. It explains that B/E Inflation = Comparable Fixed Rate - Inflation-Linked Real Yield.

If BEI = 2%, then if average inflation is more than 2%, the inflation-linked investment will outperform the fixed rate investment.

The DVO1, or Delta, of a Bond

The DVO1, Bond Duration or "Delta" of a bond, describes how the bond price changes to a change in yield.

LTCM - A Case Study in Leverage

LTCM were known for their relative value bets but also for leverage: controlling $100bn in positions from $4.8bn in assets. (That's 20x leverage). However, leverage alone is meaningless without considering the volatility of the underlying assets. For example, many commonly available options products have 20x leverage built-in.

Straddle Calendar

One of their favorite trades was playing the long term volatility vs. short term volatility in the swaptions market via straddles.

With the Straddle Calendar, you are playing the term structure of volatility, not just instantaneous term structure of volatility, but how it evolves.

Worked Example of Straddle Calendar

Suppose the term structure of volatility is upward sloping.

Straddle Calendar Strategies

This did not work when short term vol surged due to the Russian crisis.

This trade requires a view on how the swaption volatility term structure will evolve.

The Basic of Option Leverage and Logarithmic Delta

Options leverage, also known as lambda, is the percentage change in the options price divided by the percentage change in the underlying spot price.

It can be shown that leverage of a call is (delta lnC / delta ln S). Alternatively, it is also delta multiplied by S over C, i.e. ratio of underlying price to call price. Lambda is also known as logarithmic delta.

It would be interesting to compare the leverage of different options, how it varies with moneyness and how it varies with asset class. Is there convexity in leverage?

Eric Benhamou's paper is a good introduction to option leverage.

As a trader, it is interesting to calculate leverage for each of your positions.