Investing General Discussion

Gurgeh said:

So, if I have to invest on a 6 faced dice or a 20 faced dice, the amount I'm ready to pay for that investment doesn't depend on the expected value ? The results of the rolls are irrevelant to what i'm willing to bet.

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Only if you're betting long enough to actually achieve the expected value. If you are making a single bet your variance is very high and that definitely matters.

Gurgeh said:

If I'm picking a random stock from the dow jones (with the proper probability) the expected value of that strategy is the same as the expected value of the dow jones.

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No, it absolutely is not. Picking a single stock at random from a distribution you are virtually guaranteed not to achieve the distribution mean. In the case of the die roll you are literally guaranteed, since the roll is discrete.

You are confusing the theoretical value of a strategy with a single incident of implementing it and its attendant variance.

Gurgeh said:

You might argue that it is not the same once I actually picked one at random

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Yes. The hypothetical ex-ante return is not the ex-post return that you will actually experience. You are confusing the two in a dangerous way.

Gurgeh said:

but the strategy of picking a stock at random has the same expected value as the dow jones.

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Until the instant you actually DO it.

Gurgeh said:

The variance is not the same, but if you invest twice a month for a few years this isn't even an issue.

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I'd be shocked if this were true. There are a huge number of degrees of freedom in the stock market.You'd need a massive portfolio (ie, an index fund) to really flatten your variance. It's not the same as rolling dice.

Gurgeh said:

If you want to invest on the dow jones, getting two dozens of stocks from the DJ is going to be good enough, on average (or expected value) you'll get the same, and it seems that you're even getting a lower variance ...

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This is because you don't understand expected values, means, variance or how to interpret them.

I love when someone mentions Game Theory and then people start arguing statistics and probability.

Khane said:

I love when someone mentions Game Theory and then people start arguing statistics and probability.

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Well you need to at the least have basic knowledge of all 3 to understand finance a little bit.

wormie said:

If an expected value of a random stock from an index is the same as the expected value of the index doesn't this mean that all stocks in the index must have the same expected value? Plz no more.

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So I'm going to explain what they did in the research the forbes article mentionned : (it's not exactly that but it's close enough to understand how it involves probabilities, statistics and game theory, well it's not exactly game theory as there is only 1 player, but the vocabulary is taken from the game theory)

The author decided to compare investing strategy using real market data of the past, so you want to compare 2 strategy, buying and ETF, buying at random. So they're going to estimate the expected value and the variance of both strategies.

You pick a bunch of point in times, decide of a lenght of the investment (say 8 years)
So you apply both strategy, every day starting jan 1970 to jan 2011 :
You pick random stocks jan 1 1970, see what they are worth jan 1 1978 (something like you invest $100, you allocate each $1 at random on a stock of the index)
You buy an ETF jan 1 1970 and see what it is worth jan 1 1978

So you have a strategy, and a sample of the results this strategy yield, using that sample you estimate the expected value and variance using the empirical mean and the empirical variance.
With this you have an estimate of the expected value and variance of both strategies (using 12000ish samples x number of indexes they used)

And apparently they found out that way that picking at random outperformed (not much in expected value, but more in variance) all other strategies.

Honestly it shouldn't come as a shock that picking at random is better than following the index, there is no particular reason that the index is the optimal allocation of stocks, and it's not too hard to imagine a few reasons why it would be a bad one)

Sanrith Descartes said:

Gurgeh I suppose I should ask, is this some investing theory crafting you are doing or do you actually invest your hard earned $$ with die rolls? I'm gonna guess I already know the answer but want to confirm.

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I'm not actually rolling dice, but I don't look much, or at all into the companies I buy. I need x% of industry, y% of services, z% of financials, etc.. I realised not too long ago that there wasn't much thought in what I was doing and it had been working decently well (i.e. slightly better than the index over the last 8 years). I never tried to outsmart professionnal investors, and always assumed that whatever effort I would make, they'd beat me and extract a part of my potential gains. And since I remembered my games theory lessons and the uninformed player strategy vs an informed player, I decided it wasn't worth trying to make much sense. And now there are articles showing that it isn't a bad approach after all.

And that was using data from the past, with the increase use of ETF, it would probably mean that in the future that allocation is going to get worse and worse (as the weighting isn't optimal, and everyone is buying the same porfolios), so I guess in a market in which most people use ETF, you're increasingly likely to beat them by playing at random.

My point is rather that, ETF aren't all that usefull, there is plenty of litterature saying that you can buy 20 stocks based on the scrabble value of the company and get your average 8% with a variance comparable or inferior to an ETF.

Seriously. Post proof of your returns over the past year, 5 years, whatever. There is absolutely zero evidence in any of your posts. The only thing resembling any ownage of a stance or position lies within,

"I realised not too long ago that there wasn't much thought in what I was doing and it had been working decently well (i.e. slightly better than the index over the last 8 years). I never tried to outsmart professionnal investors, and always assumed that whatever effort I would make, they'd beat me and extract a part of my potential gains. And since I remembered my games theory lessons and the uninformed player strategy vs an informed player, I decided it wasn't worth trying to make much sense. And now there are articles showing that it isn't a bad approach after all."

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What the fuck is that?

Post your fucking returns. I will happily post mine. I'm following the S&P for the past few years. I'm at like 15% this year. If your investments beat it, post them and fucking beat it.

I'm not going to beat S&P500 with CAC40 stocks ! But still, I'm nearly 2% above cac40 with 69.61% of directly owned stocks, and 30% of ETF (about 2/3rd of them being Korea/Japan/Russia)

I've got 15 stocks and 6 different ETF, but I'm not following the weighting of the cac40, only 4.87% of financials, vs nearly 10% in the CAC40, 0% of health related stock vs 10%, more industry and consumer good... but in the end the match is fairly close regardless.

Anyway it's sure not proving anything, the paper behind that article Computer Simulation Suggests That The Best Investment Strategy Is A Random One is actually making the comparison with a much larger sample than 1...

wormie said:

“Our simple simulation will perform a comparative analysis of the performance of different trading strategies: our traders will have to predict, day by day, if the market will go up (’bullish’ trend) or down (’bearish’ trend).”

Just fyi

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What's more, although some of the "traditional"' strategies showed better performance in a particular stock indiex, none performed better over the four indicies. (...)
But the authors did find one big advantage of a random strategy. Counterintuitively, the random investing strategy was much less volatile than the others. In other words, while on a given day, the strategy might not gain as much as another, it wouldn't lose as much, either. The swings were much more manageable. That means, they conclude, "the random strategy is less risky than the considered standard trading strategies, while the average performance is almost identical."

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They also compared the random strategy to index.

And there is this one, that you can replicate at home with R

1. Medium values of the Sortino ratios don’t differ significantly between ETF investing and random portfolio management.
2. Buy & hold the market is better than random choices of assets. Probably buy the market at the right time is a good approach for passive investing.
3. Some of the assets have better performance, but you should have a deeper analysis to investing in. This variant will differ little from the development of its own trading strategy, and it’s another way to invest.

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This table contains an aggregate result (result variable).

Result of simulation
As you see, we don’t have a significant difference between the Sortino ratios of ETF and random portfolios. Median of p-value of our experiment is quite high.

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They're godamn using 2 to 50 random stocks... And the difference isn't much.

wormie said:

300 portfolios

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they're using a 300 samples of 2 to 50 random stocks picks, yeah, indeed. I'm not quite sure what's your point.

LachiusTZ said:

So... Not going to post your investments?

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So, whoever has the biggest dick is right ? I'm not posting the absolute value of my investments and I posted enough information about it.

wormie said:

They are 300 portfolios of at least 2 random stocks picked out of ~400 possible choices. The average trend of these all of these portfolios does not say anything about each individual portfolio which is what your strategy is. You aren't picking 300 portfolios, you are picking 1.

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Which is why they're comparing the quartiles and median of the return of ETF and random stocks ? You realise that an ETF is also random, right ? So they're also taking a 300-sample of ETFs returns.