2 Decades of SPX Vols

Despite that this is only up to 2011, it gives a pretty feel for SPX vol term structure and is a beautiful work of art from Artemis Capital Management.

Volatility at World's End: Two Decades of Movement

Easy portfolio setup for a 2.37 Sharpe Ratio

The CBOE VARB-X (Volatility Arbitrage) Strategy Benchmark has reached a Sharpe ratio of 2.37-- significantly greater than the Sharpe Ratio for the S&P 500 for the same time period, as seen in the below graph.

* Technically it is more of a statistical arbitrage, since it's an unhedged bet, though with a very positive expectation.

Some basic relative performance stats for the period:

Average Annual Return Standard Deviation      VARB-X 19.00% 6.40%              SPX 8.30% 10.30%

It is simple to replicate, by following the setup described in the Strategy Benchmark Paper.

1) Keep 80% of the portfolio cash.
2) Short and hold Variance Futures, roll with each expiration.

Ways to avoid the volatility spikes (drawdowns)

1) Apply a volatility filter
2) Use volatility forecasts for position size adjustment. You can do this in Excel, or off a 3rd party such as NYU V-Lab

Gamma/Theta Relationship for FX Options

I approach expected option PnL (Profit & Loss) from a holistic approach. Similar to the former post on Expected PnL, i.e. E(PnL) of delta hedged stock options (link), here is the basic estimate for the 24hour E(PnL) for delta neutral FX Options:

Source: Foreign Exchange Derivatives: Advanced Hedging and Trading Techniques
(You're welcome)

Given the following variable definitions:

Sigma: Average Realized Volatility for the life of the trade
S: Underlying FX spot value
Gamma: Option Gamma
r(d): Domestic risk free rate
r(f): Foreign risk free rate
Delta: Option delta
Theta: Option Theta
V: Value of Options (straddles, strangles, etc.)

So how do we use this?

Estimate a RANGE of the coming day's estimated realized vol, and you would find the rough break-even, most-likely points of E(PnL).

What's the deal with Barrier Options?

Barrier options offer several interesting benefits to professional traders with increased cost-effectiveness and complex hedging needs, and they can be statically replicated with vanilla options. Today we look at the basic payoff structure of an “up-and-out Call”, and replication with vanilla options so to avoid OTC transactions.

Payoff structure of an Up-and-Out Call Option
Examples are from Static Options Replication by Derman, Ergene, and Kani.

Given that

Underlying	100
Strike	100
Barrier	120
Rebate	0
Time to Expiration	1 Year
Dividend Yield	5%
Expected Volatility	25%
Risk-Free Rate	10%

We get the following option values

Up-and-Out Call	0.656
Vanilla Call	0.114

Payoff diagram

Replication with vanilla options

The key to replication is about matching theoretical payoffs at various future underlying values so that the portfolio behaves like the barrier option. See the Goldman Sachs Research Note for detailed notes. I will leave the replication for the example Up-and-Out Call here,

Quantity	Strike	Expiration	Values
0.16253	120	2	0.0001
0.25477	120	4	0.018
0.44057	120	6	0.106
0.93082	120	8	0.455
2.79028	120	10	2.175
-6.51351	120	12	-7.14
1	100	12	6.67
		Total Cost	2.284

High Liquidity ~ High Efficiency (not good for trading)

Financial products of very high liquidity are often unfavorable by professional traders, mainly due to increased price efficiency. I am going to point out a few ideas on why this may be so from personal experience. I may be wrong, and would welcome any contrasting ideas, as long as we all end up learning something contributing to larger trading profits going forward.

Benefits from high liquidity

High liquidity implies lower transaction costs for exchange participants who engage in purely liquidity-taking executions. This segment of participants includes the following segments:

1)      New traders, often with no positive expected alpha

2)      Buy & hold funds, with no positive expected alpha

3)      Short & hold funds, with no expected alpha in the short term

4)      Pure/Statistical Arbitrageurs, who generate almost purely alpha, and depend on multiple executions simultaneously.

* OTC (Over The Counter) products such as spot FX, CFDs, or CDS do not always offer lower transaction costs despite high liquidity.

So having high liquidity is great, right? Let’s see how that might not be the case.

Liquidity and level of competition

Exchange traded products of high liquidity usually indicates an increased number of smarter, significantly capitalized competition who specialize in liquidity provision and short term alpha. This group of participants is usually institutional in nature, full of very smart analysts and traders working to squeeze every penny out of any inefficiency available.

A more efficient market system is undesirable for less capitalized professional, private traders. Using poker as an analogy, you are expected to make more money playing against newbies than a table full of pros.

Low to mid liquidity conditions, opportunities

From my experience with exchange traded derivatives, a lot of “easier” money making opportunities tend to arise in periods of low liquidity. Here are some examples of opportunities available only in periods, products of relatively low liquidity:

1) Liquidity Provision: Make the market, and get that wider bid/offer spreads from careless, desperate traders who close their eyes, hit the market, and hope for the best. Some exchanges offer a rebate for liquidity provision orders, as a bonus.

2) Pure arbitrage: Different derivative contracts of identical underlying products get out of line against fair values more easily with respect to supply and demand.

3) More “honest” momentum: Easier-to-read tape and orderbook balance for intraday trading success.  

Many other forms of price inefficiency exist in low, mid liquidity exchange traded products, it only takes a bit of digging to find them. Basically, low liquidity ~ more exploitable inefficiencies. It may be counter intuitive, but makes sense right?

Why I avoid web based analysis content

Just came across the story of Andy Zaky, the internet-educated investment advisor at seeking-alpha, who led a good number of investors down a road of heavy losses off the AAPL dip. While some may choose to crucify Zaky, his followers were largely victims of their personal resistance toward critical thinking.

*I personally avoid web content similar to that of seeking-alpha.

Reality of most Internet analysis content

The fact remains, those who make a living off analysis do so because up to this point, they have not been able to make more off actual trading. I have met traders/fund managers with more experience who really have little idea of how to make money trading since most of their income is generated off management fees.

Be diligent

No matter how economically comprehensive a forecast may appear, sound, or feel, it is necessary to do your own research about the actual valuations, potential big player interventions, etc. There is no way around it.

Karen the (Incredibly Successful) Option Writer Interview

CBOE Skew Index

The implied skew index provides a point of reference for the S&P500 implied volatility smile.

Ever wonder if the far out-of-the-money (OTM) puts are relatively cheap or expensive with respect to at-the-money (ATM) options? Or how accurate it is at forecasting actual skewness of future SPX returns? Historical Skew Index Data is now freely available to answer these questions.

Here is a glimpse of the implied skew along with Realized Skew of SPX returns since 2001.