Quick Statistics Question

[dcwriter2]

So an option on UVXY, a leveraged ETP on whatever it is -- index? futures? -- would be a what-order derivative? Fourth-order?

 

[quant1]

OP used xth-order derivatives and the title contained "statistics question" hence he was most likely referring to the technical derivatives terminology where even an etf that models spx is not considered a derivative. Vix, however, can be interpreted in this specific context as the derivative of spx as it is priced based on the implied volatility of specific spx index options. There is a high certainty that op refers to derivatives here as Greeks.

You can take d(NAV of ETF)/d(Underlying Index) to be the delta of an ETF to the underlying (just like a Greek).

In general I don't think that it is necessarily incorrect to think of ETFs (and especially ETNs) as derivatives (in the finance sense) and they have pretty well defined derivatives (in the math sense as above).

 

[quant1]

His use of second or third order derivatives is mathematically relevant. I'm not a "smart guy", I just don't use terminology I don't understand. Gamma is a second order derivative, delta is a first order derivative. This is common terminology in both math and finance. A derivative instrument is never referred to in its order.

Options are not only on stocks or indexes. An option is a contract that specifies the right, but not the obligation to buy or sell a specific unit of the underlying at (European) or at or before (American) it's expiration. You can trade options on anything as long as there is a market. We could even talk exotics like Bermudans if you'd like. In fact, insurance companies are basically option trading companies in the most broad definition.

The VIX is an index that tracks the implied volatility of the S&P. You may have an argument that the VIX (index) is a derivative, and it's futures are certainly derivatives.

By the way ETFs are not derivatives, smart guy. Let me repeat this to make it clear ETFs are not derivatives.

Go back into Hull and tell me where his definition defines a derivative as "any element that derives it's value from an underlying tradeable asset". A derivative INSTRUMENT derives its value from the performance of an underlying asset not its value. Specifically, derivatives have contract level specifications on the performance of the tradeable asset they are written on.

Are we going to call a mutual fund a derivative instrument now too? I'll concede leveraged ETFs may be able to considered a derivative in the loosest possible sense. But you are wrong in the general sense. What about hedge funds? Are they derivatives? How about trading spot gold? You'd be laughed at out of an interview for a banker job thinking like you do. Speaking of looking like a rookie - you don't even know what a derivative is. Pot calling the kettle black...hilarious.

How about you cut back on the insults when you have no idea what you're talking about.

Just wanted to add that I read that Reuters link. I get the whole "real wealth/asset" argument. But to be honest it feels very synthetic. In practice, owning an ETP has real exposure to the index that can be (nearly) perfectly offset by other ETPs with similar indices. There are real reasons that relationship to the index must hold. As we move into more statistical relationships I'd find "derivative" to be a bit too specific.

 

[GRULSTMRNN]

True, yes, I did not deny that. I just voiced what I think op may have meant.

You can take d(NAV of ETF)/d(Underlying Index) to be the delta of an ETF to the underlying (just like a Greek).

In general I don't think that it is necessarily incorrect to think of ETFs (and especially ETNs) as derivatives (in the finance sense) and they have pretty well defined derivatives (in the math sense as above).

 

[dcwriter2]

Not really what I'm looking for. Just whether I can say UVXY options are third or fourth order derivatives, in whatever sense, math, stat or financial.

 

[quant1]

Not really what I'm looking for. Just whether I can say UVXY options are third or fourth order derivatives, in whatever sense, math, stat or financial.

How about this? If we assume that saying UVXY is a "derivative" of the VIX index:

SPX components (stocks) ---> SPX index ---> SPX options ---> VIX index ---> UVXY (holds VX futures and potentially VIX swaps)

The "--->" operator is effectively "is related to".

 

[cafeole]

"A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset (like a security) or set of assets (like an index). Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes, and stocks." Investopedia.

ETFs are not contracts between two parties. If they were, then so are individual stocks.

 

[gaussian]

How about this? If we assume that saying UVXY is a "derivative" of the VIX index:

SPX components (stocks) ---> SPX index ---> SPX options ---> VIX index ---> UVXY (holds VX futures and potentially VIX swaps)

The "--->" operator is effectively "is related to".

The reason I'd allow UVXY to be considered a derivative is because the ETN derives its value from the value of a futures contract (the VIX). If it determined it's value directly from the IV of S&P options rather than through a derivative proxy, the waters get muddy again. I wouldn't call it's options an n-order derivative, I'd call them a derivative of a derivative. They mean the same thing mathematically, but in a financial sense a derivative of a derivative makes it far more clear.

The SPY isnt a derivative because it represents a basket of stocks. In particular with SPY it's definition makes this clear - The Trust seeks to achieve its investment objective by holding a portfolio of the common stocks that are included in the index (the “Portfolio”), with the weight of each stock in the Portfolio substantially corresponding to the weight of such stock in the index.

It's not deriving its value from anything. It's just a basket that seeks to track the S&P. Maybe if we continue to debate this, we can separate ETNs from ETFs which may help make things more clear.

 

[dcwriter2]

How about this? If we assume that saying UVXY is a "derivative" of the VIX index:

SPX components (stocks) ---> SPX index ---> SPX options ---> VIX index ---> UVXY (holds VX futures and potentially VIX swaps)

The "--->" operator is effectively "is related to".

Wow, so UVXY options are like a fourth-order derviative?

 

[.sigma]

SPY is a derivative of the S&P index.

$SPY does not "derive" its value from $SPX lol Its priced 1/10th the value. That's way different than a true derivative.

But the options on $SPY and $SPX derive their value from spot, thus being "derivatives"