I often get asked about how to invest in the stock market. Not surprisingly, this has been a common topic in my classes. Brazil is experiencing a big change in its financial scenario. Historically, fixed income instruments paid a large premium over the stock market and that is no longer the case. Interest rates are low, without the pressure from inflation. This means a more sustainable scenario for low-interest rates in the future. Without the premium in the fixed income market, people turn to the stock market.

We can separate investors according to their horizon. Traders try to profit in the short term, usually within a day, and long-term investors buy a stock without the intent to sell it in the near future. This type of investment strategy is called BH (*buy and hold*). At the extreme, you buy a stock and hold it forever. The most famous spokesperson of BH is Warren Buffet, among many others.

Investing in the long run works for me because it doesn’t require much of my time. You just need to keep up with the quarterly and yearly financial reports of companies. You can easily do it as a side activity, parallel to your main job. You don’t need a lot of brain power to do it either, but it does require knowledge of accounting practices to understand all printed material released by companies.

I read many books before starting to invest and one of the most interesting tables I’ve found portrays the relationship between investment horizon and profitability. The idea is that the more time you hold a stock or index, higher the chance of a profit. The table, originally from Taleb’s *Fooled by Randomness*, is as follows.

My problem with the table is that it seems pretty off. My experience tells me that a 67% chance of positive return every month seems exaggerated. If that was the case, making money in the stock market would be easy. Digging deeper, I found out that the data behind the table is simulated and, therefore, doesn’t really give good an estimate about the improvement in the probability of profits as a function of the investment horizon.

As you probably suspect, I decided to tackle the problem using real data and R. I wrote a simple function that will grab data, simulate investments of different horizons many times and plot the results. Let’s try it for the SP500 index:

```
source('fct_invest_horizon.R')
my.ticker <- '^GSPC' # ticker from yahoo finance
max.horizon = 255*50 # 50 years
first.date <- '1950-01-01'
last.date <- Sys.Date()
n.points <- 50 # number of points in figure
rf.year <- 0 # risk free return (or inflation)
l.out <- get.figs.invest.horizon(ticker.in = my.ticker,
first.date = first.date,
last.date = last.date,
max.horizon = max.horizon,
n.points = n.points,
rf.year = rf.year)
```

```
## Warning: `data_frame()` is deprecated, use `tibble()`.
## This warning is displayed once per session.
```

`print(l.out$p1)`

`print(l.out$p2)`

As the investment horizon increases, the chances of a positive return increases. This result suggests that, if you invest for more than 13 years, it is very unlikely that you’ll see a negative return. When looking at the distribution of total returns by the horizon, we find that it increases significantly with time. Someone that invested for 50 years is likely to receive a 2500% return on the investment.

With input input `rf.year`

we can also set a desired rate of return. Let’s try it with 5% return per year, with is pretty standard for financial markets.

```
my.ticker <- '^GSPC' # ticker from yahoo finance
max.horizon = 255*50 # 50 years
first.date <- '1950-01-01'
last.date <- Sys.Date()
n.points <- 50 # number of points in figure
rf.year <- 0.05 # risk free return (or inflation) - yearly
l.out <- get.figs.invest.horizon(ticker.in = my.ticker,
first.date = first.date,
last.date = last.date,
max.horizon = max.horizon,
n.points = n.points,
rf.year = rf.year)
print(l.out$p1)
```

As expected, the curve of probabilities has a lower slope, meaning that you need more time investing in the SP500 index to guarantee a return of more than 5% a year.

Now, let’s try the same setup for Berkshire stock (BRK-A). This is Buffet’s company and looking at its share price we can have a good understanding of how successful Buffet has been as a BH (*buy and hold*) investor.

```
my.ticker <- 'BRK-A' # ticker from yahoo finance
max.horizon = 255*25 # 50 years
first.date <- '1980-01-01'
last.date <- Sys.Date()
n.points <- 50 # number of points in figure
rf.year <- 0.05 # risk free return (or inflation) - yearly
l.out <- get.figs.invest.horizon(ticker.in = my.ticker,
first.date = first.date,
last.date = last.date,
max.horizon = max.horizon,
n.points = n.points,
rf.year = rf.year)
print(l.out$p1)
```

`print(l.out$p2)`

Well, needless to say that, historically, Buffet has done very well in his investments! If you bought the stock and kept it for more 1 year, there is a 70% chance that you got a profit.

I hope this post convinced you to start investing. The results are clear, its better to start as early as possible.