How asset price affects your alpha

Discussion in 'Options' started by TheBigShort, Feb 3, 2019.

  1. In dynamic hedging by NT, he states that alpha = theta/gamma = 1/2*variance*S.
    He also follows up by writing a table describing fair value of alpha per volatility.

    Would this not imply that selling options on higher priced assets and buying options on lower priced assets increase your alpha? I do not follow this as it would imply higher alpha for example selling SPX options vs SPY options.

    Lastly, he comments "an alpha that is lower than the fair value alpha for a short gamma position will result in long term losses". Is he implying that I could just scan for these low/high "rent ratio" options and have long term success?

    Reference is on pages 178:183 in Dynamic hedging
  2. I found this from the poster LongTheta on NP.

    One of the really useful tricks that I found in Taleb's Dynamic Hedging was his discussion of alpha = theta/gamma.

    If you take r = 0 for simplicity, it is easy to see that alpha = (S*vol)^2.

    That means that the higher the stock price, and the higher the vol, the higher theta will be relative to gamma. So if you are shorting options, and you wish to make get as much rent (theta) as possible for your risk (gamma), short the highest price, most volatile stocks. That will maximize your alpha.

    If you are longing options, you go for the lowest priced, least volatile stocks. Intuitively, the least volatile stocks are more likely to become more volatile, etc.

    Does anyone care to take a stab at explaining this better? How can increasing S generate higher returns for the risk you take? Can selling vol on high priced biotechs really be a better strategy than selling vol on low priced staples without considering historical vol etc...
  3. Hmmm. On the face of it, this is wrong. Firstly, if r = 0, then theta and gamma will have opposite signs. So you need a negative sign on the right hand side. Also the right hand side, I believe, is off by a factor of two. More like alpha = -0.5 * (S^2 * sigma^2)

    If Taleb wants to call theta over gamma "alpha," that is fine by me. But calling a quantity alpha doesn't make it an edge. Since theta is [usually] expressed in dollars, and gamma is bounded and effectively unitless, then of course an option with high IV, high priced underlying, will have a higher absolute ratio of theta to gamma. However claiming it is an edge is like saying you should sell the highest priced (in extrinsic value) options because they have the most premium.

    newwurldmn, TheBigShort and sle like this.
  4. Should his statement be ignored? He goes as far as providing a fair value table for alpha.
    I understand that a lot of his work is controversial but I can't see him saying something as ridiculous as "sell the highest priced options and buy the lowest"(which it sounds like). Do you have any idea of what he might have been trying to get at?

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  5. srinir


  6. I find Taleb nearly insufferable, so I hesitate to wade into his book to try to figure out what he is getting at. It would be easier to test the concept first, then if the idea seems to work on backtest, it might be worthwhile to try to figure out why it might work.

    The formula for "alpha fair value," from the table you posted, appears to be alpha-fair-value = Vol^2 * 14.0265. So what you can do is, for every Monday-after-third-Friday in the past, sort the nearest-to-atm calls on all active names for the upcoming monthly expiry by alpha / alpha-fair-value. Simulate a buy at close-mid on the lowest 5% and a sell at close-mid on the highest 5%. Hold until expiry. Repeat monthly to the present, and see if the simulated returns are significantly different from zero.

    If it works, start a hedge fund. Name it Empirica Redux.
    TheBigShort likes this.
  7. I don't think "bet against beta" or low vol anomaly is what Taleb is referencing here. Beta is linear in vol and low vol portfolios usually have a static (or static relative, as in sort portfolios) threshold. Taleb's alpha critical values (from the table) are linear in Var (quadratic in vol) and the threshhold (critical or fair value) is dynamic.

    What edge Taleb is attempting to exploit here is not obvious, at least not obvious to me.
    srinir likes this.
  8. ironchef


    I truly enjoyed reading all your posts sir.

    I do not understand the math, but please allow me to ask a few questions:

    1. If all the "greeks" are the same, for the same ATM strike, the premium should be proportional so there is no edge?

    2. All else being equal, higher IV provides higher premium but that doesn't mean higher profit unless the IV is "overpriced"? So how do I know if they are overpriced?

    3. But there may be a structural issue that the market often overpriced high price stocks with high IV during market turmoil and therefore there is an "edge" selling those?

    4. Perhaps his "fair value" is a frame of reference?
  9. ironchef


    I don't know, most of my gains during this bull market were BWB (Bet With Beta) instead of BAB.

    Intuitively, I think in an up market, I can get outsize return by using leverage. The US market has an up trend, so BAB on average over a long period will underperform???
  10. srinir


    That's not how it works. For a factor loading, you need to be long-short. In this case short high beta and long low beta and adjust for leverage.

    Most of the ETF's give half the loading (since long only). For argument sake, take your argument high beta out-performed in the up market. There is high beta ETF called SPHB. We can pretty much agree that we are in upmarket since 2012.

    Here are the results. Portfolio 1 is SPHB and Portfolio 2 is levered SPY. I adjusted the leverage, so that both of them have same standard deviation. SPY portfolio is almost twice bigger than SPHB

    Last edited: Feb 5, 2019
    #10     Feb 5, 2019