If you are a small investor you are probably building an investment portfolio by yourself. Some of you probably have never studied statistics and lacks the basic knowledge that allow you to make proper estimates on your potential return and risk.

Here I will tell you the 3 basic statistics that every investor needs to learn.

To make it easier for you to understand I will make a few examples on Excel so you can replicate it yourself. You will find the link to download the spreadsheet at the end of the article.

1. Compound interest calculation

This is a very basic concept and even beginners might already know what is this, but some might have some trouble on how to calculate it.

Let’s start with the theory. When you reinvest your profit, your total portfolio value will start to grow faster and faster as results of the compound effect. Imagine you can make 10% profit in one year from a $1000 investment. That will give you $100 profit . If you reinvest the profits and the next year you gain an additional 10%, your profit will be $110 instead of just $100.

What if you want to calculate your long term performance after 10 years where you always had 10% profits?
This can be calculated using exponentials. When you have 10% gains of your portfolio, it means your portfolio is worth 1.1 times your invested value. For instance, $1000 x 1.1 = $1100. More generally you takes the (percentage value / 100) + 1 x your initial investment. If the next year you made another 10% then your portfolio value would be $1000 x 1.1 x 1.1 = 1210 which is the same as $1000 x 1.1² = 1210. The exponential 1.1² stands for 10% gains every yeast of investment, in this case it is two years.
A similar concepts applies when you loose money. E.g. if your portfolio drops 50% in year 1 and 50% in year 2, your portfolio value will be $1000 x 0.5 x 0.5 = $250.

Excel example

We can make this more complicated and add recurrent deposits. For this calculation, we can create a spreadsheet in Excel.

Let’s consider this situation. You made periodic deposit over 10 years and your performance where varying every year. How to calculate you portfolio value after each year?

In this case the portfolio value will be given by the new deposit you made at the beginning of the year + previous portfolio value, times the annual return.

You can drag the formula for every year, and you will obtain your portfolio value after 10 years.

Now you might want to know your total performance, without considering the deposit. That can be calculated by multiplying the (annual returns + 1) -1, which can be done using the PRODUCT function in Excel.

That value will be different than the profit calculated from the total deposit and final portfolio value, because periodic deposit will alter the total profit of your portfolio. For instance, if you are gaining 50% from a $1000 initial deposit, your portfolio value will be $1500, but if you add an addition $1000, then your profits will be $500 over $2000 investment which is 25%. For this reason is you want to measure your performance if it more meaningful to calculate the performance using the product of your annual returns.

Finally, you might want to know what is the average annual return that you had over 10 years. A common mistake is to just calculate the average of your annual return. The right way of doing it is to use the inverse of the exponential operation I used above.

In this formula you take the total performance to the power of 1 divided the number of years.

You can try to play a bit with the values and formula to get familiar with these operations.

2. Expected return and standard deviation

This measure is useful to estimate how much you can expect when your portfolio is composed of multiple assets. Let’s use two popular stocks as example, Nvidia (NVDA) and Apple (AAPL).

The return is calculated as explained above. If your portfolio has a combination of the two you can calculate the return for each year just by multipling the yearly return of each stock by the fraction of the portfolio invested in each stock. E.g. if you have 40% NVDA and 60% AAPL you multiply NVDA return by 0.4 and AAPL return by 0.6.

You can notice that the return since 2010 of the combined portfolio is far different from the simple mean of NVDA and AAPL return.

Portfolio composition doesn’t only have an impact on the return, but also on the risk. Risk is usually proportional to the market volatility. Standard deviation a measure that indicates stock volatility. Briefly, it express how much each yearly return is distant from the mean. You can calculate standard deviation in Excel with STDEV.P function.

As you can notice the portfolio composed of both NVDA and AAPL has half of the standard deviation of NVDA, but almost the same return. A problem with standard deviation is that it is generally higher when the average return is high. To correct for this problem we can use the “Coefficient of variation” which is the standard deviation divided by the mean.

Now you can see that the NVDA+AAPL portfolio has the lowest coefficient of variation with a very high return.

If you are wondering how that’s possible check the next statistics.

3. Correlation

Correlation is a very important measure to help you reducing the risk of your investments. By investing in stocks that are not correlated to each other you can create a portfolio with high return and low risk as we have seen above.

Now I added another stock in the portfolio, Merck (MRK).

Here you can see that even by investing in AAPL you would had a year where you lose more than 6%. That’s not ideal if 2018 was the year you were planning to retire or to take your profits.

MRK performance where not even comparable to NVDA and AAPL and its coefficient of variation was actually high. However it still had a great benefit, it is negatively correlated with other stocks NVDA and AAPL. That means when AAPL goes up, MRK goes down, and vice versa.

You can calculate the level of correlation between two stocks with the function CORREL.

The correlation value ranges from -1 (negatively correlated) to +1 (positive correlation), 0 means that the stocks are not correlated.

You can visualize the correlation by plotting the yearly return in a scatter plot in Excel, and add a trend line.

As you can see, there is negative trend when comparing NVDA and AAPL with MRK. We can use this information to build a safer portfolio.

Here we have two portfolios, a more aggressive one with 40% NVDA, 40% AAPL, and 20% MRK, and a safer one with 30% NVDA, 30% AAPL, and 40% MRK. The first portfolio can give you 300% higher return compared to just investing in AAPL with just slightly higher risk. The second portfolio will have lower return, but lower volatility and most importantly every single year was profitable.

Conclusions and free Excel spreadsheet

I hope you found this article useful. As promised here is the link to the Excel file:

Have you find any mistake or you think there are other basic stats that every beginner investor should learn? Let me know in the comments.

Leave a Reply

Your email address will not be published. Required fields are marked *