## Perfect diversification means no asset can be dropped from (rather than added to) a portfolio

A common belief: adding extra asset to a portfolio will automatically reduce the portfolio risk. We provide a counter-example resorting only to the simplest algebra and explain why this erroneous belief is so common.

## Why I am skeptical about investing in “global trends”

Investing in a "globaly demanded" product or service seems (at first glance) to be a nice idea. However, it may be (too) dangerous: not all global trends turn into profit and even if they do, you need to get in early since most of global trends (even genuine) turn into bubbles and do burst.

## Stripping down the robo-advisors: sparrow-brains inside

Summary:

• Robo-advisors promise the risk profiling in a few easy steps, which is unrealistic both from mathematical and behavioral points of view.
• The "optimal" portfolios are usually based on Markowitz-like models, which are inapplicable in practice due to their extreme numerical sensitivity to the market parameters estimation errors.
• Robo-advisors lure investors with low management fees but minimizing fees and maximizing the wealth is not the same. Moreover, the compound costs are not so small in the long term.
• A positive side: Robo-advisers do not (yet) foist toxic financial products upon you.

## Numeracy for Traders- Lesson 1 – Fractions

Fractions is a topic from elementary mathematics but surprisingly even some Ph.Ds in math have problems with them. After this lesson you will be able to read pie diagrams, calculate portfolio weights and weighted average returns. This lesson does not substitute systematic learning but helps you to recall fractions and demonstrates their usage in trading context.

## Mystery and misery of the martingale betting system: why it will not make you rich

Summary:

• The martingale strategy asymptotically implies infinite capital or infinitely divisible stake. In reality you have a limited capital and there is a lower (in casino also an upper) bound of the stake.
• In a fair game (with 50/50 chance of profit and loss) the probability of profit after a series of losses is still 50% (because the outcomes of bets or trades are independent from each other).
• Typically, if you win then your profits are moderate but if you lose, the losses are severe (you can lose your capital just after a small series of unlucky bets).
• If you make pretty many bets, you might make a good profit but the probability to make profit at all decreases with the number of bets. Losses stays severe.

## Binary Options: you may earn in a short term but eventually you WILL lose

Summary:

• Gambling with binary options you either lose 100% or earn about 90% of your stake. The win lose/ratio of 90/100 = 0.9 is worse than by the European roulette (36/37 = 0.973) and even by American roulette (36/38 = 0.947).
• A trade takes just a couple of minutes, which allows (and implicitly encourages) you to commit a lot of trades. Due to the law of large numbers and negative odds, the more you trade, the more you lose.
• Don't trust numerous "success stories" in Internet. Virtually all of them are fake and they are just a marketing trick of brokers or those who earn with brokers' affiliate programs.