All of Adam Bull's Comments + Replies

No, it's just causation without correlation; correlation is defined to be the aggregate effect.

yes, but I am posing the WHY question. In this case it is just an averaging effect not a feedback controller.

I wouldn't read too much into that quote, it seems pretty misleading to me. There are essentially two statistical paradigms, frequentism and Bayesianism, which you probably already know about.

The third item is referring to the likelihood principle, a philosophical position which states that inference should be based only on the likelihood. There are a small number of techniques in both frequentism and Bayesianism which have this property, but in general it's pretty restrictive, and I don't know of any practitioners who take it seriously.

You'll notice the f... (read more)

(Still not financial advice.)

Well, Kelly is optimal if you have infinite time, or logarithmic utility. In practice we all have finite time, and many of us are more risk-averse. Plus, as you mentioned earlier, Kelly is only optimal if you know the payoff distribution, which you don't.

I'm not saying leverage can't be a useful addition to a portfolio; just that there are also reasonable concerns about it. Yes, a leveraged mix of equities and bonds has done pretty well the past forty years. But the thirty before that, it was a disaster. Sure, the macroeconomic regime was different then; but in a world of negative interest rates, are you sure it won't change again?

Nope. We are not trying to avoid all risk. We're trying to get exposed to risk so we can get paid for it. The right side is uncomfortable. [] Taking on the risk of bonds crashing, in the appropriate amount, so we can get paid for it, is exactly the point of adding leveraged bonds to a risk premium portfolio. If it weren't risky, there wouldn't be a risk premium for holding it. People on the margins have been forecasting the end of the bond bull market for years. If you had listened to them then, you'd have given up the returns up till now. If you play the game long enough, risks will eventually bite you. You will have drawdowns. Don't Bet the Farm. But the market pays you extra for it. You'll still eventually come out ahead if you size your exposure appropriately.

(This is not financial advice.)

I'm not sure the linked article shows it to be false, exactly. If you look at the first graph, you can see that over 135 years of US data, 1x leverage returns about 4% annually, and 2x leverage about 5%, with double the risk. That's pretty bad, unless you're desperate for risk.

Now, that plot doesn't include dividends, which are an important part of the calculation. And using different countries or time periods will give different results, as they demonstrate later on. Still, if you're discussing a type of investment the SEC s... (read more)

Leveraging up, on its own, is never going to improve your Sharpe ratio. But you can use leverage to get a better return if your portfolio is below your risk tolerance, at least until you hit the optimal bet size. Volatility does have bad effects on leverage, which is why my somewhat safer system [] reduces the leverage for an asset when its vol is high, even below 1x, if necessary, by holding cash. The Kelly strategy means there is always an optimal amount of leverage, and it's unlikely to be exactly 1x.

Most Western countries levy some form of CGT; to avoid it, you'd need to move to a low-tax jurisdiction like Switzerland or Singapore. It's certainly possible for founders and investors to do that, but it's a pretty big life change.

Moving from one US state to another, on the other hand, is pretty easy.

In the simplest case where the errors are Gaussian, this would probably be covered by standard regression lower bounds? You'd show that exponentials and sigmoids can be made close in L² over a restricted domain, then deduce it requires many samples / low noise to distinguish them.

Or as Aaro says above, maybe better to parametrise the sigmoid, and take the Fisher information of the turning point parameter.