I've recently started going through Axler carefully and doing the problems, a quarantine activity I guess, and have been enjoying it. I actually learned about this book on an older HN post.
It does have plenty of matrices. The main thing it really does is avoid determinants until the very end. The determinant is certainly something I remember learning as a kind of rote operation, without really understanding any intuition behind why you'd multiply and add these numbers in this particular way. I still feel lacking in "feel" here, which is why I suppose I'm going through Axler now.
The asset value underlying an ETF can be negative, but then the owner of the ETF will just have a worthless piece of paper. The ETF managers will have a problem on their hands regarding the negative amount, though.
In contrast, a futures contract is an agreement to make a future trade, so it can keep going against you past 0. If you are able to take physical delivery, your worst-case scenario is that you pay the money you said you would, and you get your oil. But if you are a casual day-trader type, you probably don't have the ability to take physical, so you may be in trouble (over a barrel, literally).
I agree with you about the dangers of ETFs and about knowledgeability. I didn't mean to advocate for ETFs on an absolute basis, just to make a relative statement about them vs. futures.
I'm not recommending USO or oil itself as an investment, and I agree that you will be paying money to the ETF manager if you get involved in it.
But I don't agree that USO is _more_ dangerous for a casual trader to trade than oil futures, for the reasons I mentioned.
Removing the overall fluctuations of the oil market, the relative problem with ETFs is that they bleed away value over time. That's a real issue, but I wouldn't compare that to juggling a live hand grenade.
Edit: you did not say it was more dangerous, my mistake. I do think that ETFs are less dangerous, for the reasons I mentioned.
There are ETFs that track oil futures (basically like a stock, but backed by oil instead of a company). It's been a while since I've looked at any of this, but I think USO is still the most prominent.
There are plenty of things to watch out for with these ETFs. You pay ongoing expense fees. And ETFs, especially those that aren't just holding containers for assets, can have subtleties in their prospectuses that cause their value to fluctuate in counterintuitive ways. There's still a lot to be cautious about.
However, compared to the actual futures, they're more suitable for casual investors, for reasons such as what we see here. They can't go below 0 and don't necessarily involve margin. And the ETF will typically deal with things like rolling the futures position ahead of expiry.
I don't know that this is regional so much as colloquial vs. formal. In the US people recognize that the subjunctive is technically correct and use it in formal writing. But it's very common to violate this rule in speech, so much so that to my ears it sounds less "wrong" than "informal."
As far as musicians go, you can find examples of people on both sides of the pond using or not using the subjunctive. Beyoncé sings "If I were a boy," while Thom Yorke sings "I wish I was special."
Based on my experience learning Czech (not native at all, just interested):
- it's typically listed as a separate letter when writing out the alphabet
- but in practice it's typed out as "c h" and not as a single character
- it occupies its own place in Czech standard alphabetical order, my English-Czech dictionary has all the "ch" words after "h" (so interestingly in order to do a proper sort programmatically you need to possibly look 2 characters ahead)
Since last Friday I've been making my Zoom virtual background a daily rotation of artwork. It's been a fun and educational experience for me (I'm no art expert, just a casual fan of museums) and I think my friends and co-workers have enjoyed it. When you're mostly stuck at home all day it's nice to have a daily "new" to look forward to.
I've been recording my choices and when this is over I'll have a little "Zoom Museum" as a kind of artistic memorial of the pandemic.
This link is a great source for new art, so thank you OP!
I think the part that you have correctly included that people forget or elide is that it's the probability under a specific null hypothesis. So it's a function of what you have chosen for that - normal distributions, a certain parameter value of 0, etc. So this means that a) it's not the probability you'd see in the real world under repeated performance b) it's not the probability under other reasonable null hypotheses. Like maybe under the hypothesis parameter = 0 you get an improbably large p-value, but under parameter = 0.1, or with different assumed underlying distributions, you wouldn't see something so extreme.
I'd guess that the original writer understands this, and that Gelman is only pointing it out because casual readers sometimes don't mentally retain the full baggage that the p-value carries.
It does have plenty of matrices. The main thing it really does is avoid determinants until the very end. The determinant is certainly something I remember learning as a kind of rote operation, without really understanding any intuition behind why you'd multiply and add these numbers in this particular way. I still feel lacking in "feel" here, which is why I suppose I'm going through Axler now.