Shares: owning a piece of a company
When you buy a share you own a small part of a business. If the company grows and earns more, the share tends to become more valuable, and some companies also pay part of their profit to shareholders as a dividend.
The price moves every day as buyers and sellers change their minds. Over short periods that movement can be large and has little to do with how the business is really doing.
Funds: many companies in one purchase
A fund pools money from many investors and buys a collection of shares. One purchase gives you a slice of all of them. An ETF (exchange-traded fund) is a fund you buy and sell through a broker just like a share.
Funds charge a yearly fee, shown as a percentage. Small differences matter over decades, so it is worth checking.
Indices: a list with rules
An index is a list of companies picked by a rule. The S&P 500 is roughly the 500 largest companies listed in the US. The FTSE 100 is the 100 largest on the London Stock Exchange.
An index is a measuring stick, not a product. When people say they bought the S&P 500, they mean they bought a fund that copies it. That kind of fund is called an index fund or tracker.
A custom index is the same idea with your own rule, for example the 20 largest computer-chip companies with no single one above 10%. On Arithmos we call the result a portfolio, because that is what you end up holding.
Portfolios: your mix
A portfolio is everything you hold, or a mix you are planning to hold: which investments, and what percentage of your money goes into each. Ten companies at 10% each is a portfolio. So is one global fund at 100%.
How the money is split is called the weighting. Equal weighting puts the same amount in each company. Weighting by size puts more into bigger companies, which is how most well-known indices work.
Risk: why spreading out matters
If all your money is in one company and it has a bad year, so do you. Holding many companies across different industries and countries is called diversification, and it is the main protection ordinary investors have.
A portfolio built around one theme, such as AI or clean energy, is less spread out than a broad global fund. Many people keep themes to a smaller part of their investments for that reason.
Where Arithmos fits
Arithmos is a research tool. You describe what you want to invest in, and it suggests a portfolio: a list of companies, how much of each, and the reason for every pick. It then replays that mix against real past prices so you can see how it would have behaved.
Arithmos does not hold your money, place trades or give personal advice. If you decide to invest, you do it yourself through your own broker.
Three ways to invest
There is no single right route. Many people combine them, and plenty decide a broad global fund is all they need.
- 1
Buy individual shares
Pick one or more companies and buy their shares through a broker or investing app.
- Good for
- Simple to understand. You own exactly what you chose.
- Watch out for
- If you only hold a few companies, one bad result can do real damage. Picking winners is hard, even for professionals.
- 2
Buy a ready-made fund
A fund (often an ETF) holds dozens of companies in one purchase.
- Good for
- Instant spread across many companies, with very little effort.
- Watch out for
- You get what the fund provider chose, including companies you may not want. Themed funds usually charge more than broad trackers, so check the yearly fee and the top ten holdings. Which funds you can buy depends on where you live.
- 3
Build your own portfolio
Choose your own mix of companies and how much of each, then buy them through your broker. This is what Arithmos helps with: describe the mix in a sentence and it builds and tests one for you to consider.
- Good for
- You decide exactly what is in and what is out, and you can see the reason for every company.
- Watch out for
- More to look after than a fund. Buying many separate shares can cost more in dealing fees, and a tested result is a simulation, not a promise.
The risks
- The value of investments can go down as well as up, and you may get back less than you put in.
- Past performance, real or simulated, does not tell you what will happen next.
- Tax rules depend on your country and circumstances and can change.
Try it yourself
The quickest way to understand a portfolio is to look at one. Here is how to turn this guide into something you can inspect.
- 1
Start from the idea
The button below opens the builder with this guide's idea already typed in. Change any part of it: the number of companies, the countries, the limit per company.
- 2
Read the reason for every company
You get a list of companies, how much of each, and a plain-English reason for each pick. If one looks wrong to you, you can ask for it to be changed.
- 3
Look at the bad years, not just the good ones
The portfolio is replayed against real past prices. Check the biggest fall along the way, and ask yourself whether you could have sat through it.
- 4
Decide for yourself
If you want to act on it, you buy the shares yourself through your own broker. Arithmos never holds your money or places trades.
“The 30 biggest companies in the world, with bigger companies getting a bigger share and no company over 8%.”
Browsing portfolios other people have published is free. See pricing for what building your own includes. A tested result is a simulation using past prices. It is not a forecast and not a recommendation.
Common questions
What is the difference between an index and a portfolio?
An index is a list of companies chosen by a rule, used as a measuring stick. A portfolio is what you actually hold or plan to hold. If you buy every company in an index in the same proportions, your portfolio copies that index.
Is an index fund the same as an index?
No. The index is the list. An index fund is a product, run by a fund company, that buys the companies on the list so you can invest in all of them at once.
How much money do I need to start investing?
Many brokers and investing apps let you start with small amounts and buy fractions of a share. What matters more is that it is money you will not need for several years.
Does Arithmos invest my money for me?
No. Arithmos builds and tests portfolio ideas. It never holds your money or places trades. You choose whether to act on anything, using your own broker.
