Efficient Frontier and Leverage.

Research
1

All,

Riccardo is reportedly adding some options for using a correlation matrix and ETFs. As I understand it, he has a finance degree but does not choose to participate in any discussions about diversification in this forum.

I definitely understand that. Likewise, Hem has not chosen to post recently. Marc is gone. We are told there is an AI expert somewhere at P123. No word about his interest in this topic.

The important questions on this topic are quite simple. It is finding the best answer for any single member at P123 that is hard. I do not mean to imply that the answers are easy (just the questions). This has all been trivialized at P123.[color=firebrick] The P123 forum is at best a competition as to who has the biggest…uh, returns. Won by the person who can find the best cherry-picked, overfitted or anecdotal example. Nothing more can be expected of P123 at this time with regard to mainstream considerations in finance.[/color]

I still think 2 question matter: 1) Is it possible to get increased returns with decreased volatility by using mean-variance optimization (perhaps with some leverage)?

I seem to recall there may have been a Nobel Prize for some ideas on this. And there are some newer ideas.

Question 2) that may not apply to everyone: If you are at or near retirement are you willing to give up some return (if necessary) in order ensue that you will not run out of money with a large drawdown and be able to continue to withdraw a minimum amount to live on each year until you die. Thinking you may not be in love with the idea of generating new income mowing lawns when you are 85 years old if there is an unexpectantly large drawdown.

[color=firebrick]The Kelly Criterion addresses a third (separate) question if one decides to use at lot of leverage: How much leverage is safe and will give you the highest returns?[/color] Again, I do not think these questions are particularly difficult to understand nor do I think they are unimportant for everyone at P123.

There is an article by Pimco (referenced) and post that attempts to put some of this together into one theory: A Bond Fund’s View on Risk. Some have said this is too complex for P123 members. If what Yuval says is true in this regard, maybe Riccardo will help at some point.

Maybe we can hope for something from Riccardo on this in a bit. In the meantime we have Portfolio Visualizer, other sites and Python libraries to help with these questions.

Here is something like the assets one would find in the security-market-line as a start. But this is not really a topic for discussion at P123.

More realistically, maybe we will get an overfitted backtest from one of the members (or staff) that will be represented as the final word on this (no Nobel Prize or even a finance degree required): I leave the floor to whomever wishes to think an overfitted in-sample backtest is the final word on this. Riccardo and Hem are welcome to reply also but I think I would die holding my breath waiting–in which case this would all be academic anyway. And BTW, I am not looking to mow lawns when I am 85 years old either. But that could just be me.

If you are an [color=firebrick]“optimistic”[/color] investment advisor no need to worry about any of this of course.

Best,

Jim

Efficient Frontier.jpg
Efficient Frontier.jpg2544×1286 189 KB

2

Jim,

As mentioned in my email,

Nice screenshot about the efficient frontier, it saids it all.

Regards
James

3

Thanks for linking the paper.

The Kelly criteria which says that if one makes more money from each trade and/or have a greater number of positive trades then they should hold bigger & less positions. Sounds simple but not that simple to implement effectively. The equation requires one to predict the probability of a win (W) and the amount one wins vs loses in advance (R). These variables, W and R, will change over time and this could be rapid as seen by the recent volatility. In addition to variability in R and W there also will be difficulty determining the time frame over which R and W are measured. Exhibit 1 from the paper shows that the Kelly criteria will excel over time but it also mentions that it would take 227 years to have a 90% confidence that the Kelly strategy will outperform a fixed strategy. In the less than 227 years one could have a portfolio “wipe out” from holding concentrated positions during a crash. In conclusion, it appears that some concentration/leverage could be useful but we don’t have the tools here to determine the optimum amount.

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Hi Scott,

I just want to say I agree with your conclusions about the Kelly criterion.

Let me add to your reasons. The Kelly criterion can be summarized as edge/odds. And in fact the Pimco paper says you should use the “continuous” edge/odds.

So the Kelly criterion falls apart for most of us for the reason a lot of strategies fall apart: Past results do not predict future returns. In other words the edge (future returns) is never fully assured–especially not “continuously” as market conditions change. I don’t mean to imply that this is the only problem the Kelly criterions has limiting its usefulness for stocks.

I could imagine that some advanced traders using pairs trading for example might be able to move beyond the limitations you and I have here at P123.

But I agree with you and the above is just one of the additional reasons I have for agreeing with you.

Plus, you don’t need it unless you are using a lot of leverage or use a single high-beta port (no diversity) with little edge (or little or no alpha). But why would anyone need to know the Kelly criterion to understand that is a problem?

Best,

Jim