Compounding Interest

[rgtc]

Hi guys!

I am working on a portofolio of assets and wanted to know if the way I compound interest is correct: I start with monthly prices (closing price at end of each month) and then I calculate the return for each month.

Asset 1 (A1): Weight in the portfolio: 50%: End of Month 1 Price: 100; End of Month 2 Price: 110; End of Month 3 Price: 120;
Asset 2 (A2): Weight 50%: End of Month 1 Price: 50; End of Month 2 Price: 60; End of Month 3 Price: 70;

This means that if I invest 100 dollars I will have:
$50 A1+ $50 A2 at the end of first month;
50*(1.1)=55$ A1 and 60*(1.2)=72$ A2 at the end of second month;
55*(1.096)=60.005$ A1 and 72*(1.167)=84.024$ A2 at the end of third month and so on...

Is this the correct way to compound interests in a portfolio and to calculate the performance of the money invested? I am asking because if I compound returns like this, on long time frames the value of the assets really skyrockets! Is this really the power of compound interest, or am I making some mistakes?

I hope you can help me, thank you in advance!

 

[JeffM]

It’s late, and I am sleepy. I’ll look again at this thread in the morning, but a few preliminaries.

First, when you are talking about returns of 100% in a month, you have completely misunderstood what the power of compounding means. Suppose you realize post-tax profit of 3% annually. Sort of measly, right. But will it take you 33 years to double your money? No. It will take only 23, about 30% less than intuition suggests. What the power of compounding tells you is that what is important is not just average annual return, but also the time you let returns earn more returns. Thinking about returns of 100% per month is ridiculous. Over something like 140 years, the average ANNUAL return in the US stock market has been about 8%.

Second, your example is flawed. You said that in the first month asset 1 went from 50 to 100, but you show it as still 50 at the end of month 1. Which is it?

Third, you are making way too much work for yourself. Divide the aggregate market value of your portfolio at the end of the most recent period by the aggregate market value of your portfolio at the end of the immediately preceding period, subtract 1, and multiply by 100. That is the percentage return for the period. WARNING If your period is not a year, then this is obviously not an annual return.

 

[rgtc]

Hi Jeff, Thanks for the answer.

1) I know that these returns are not sustainable, and I used them just to make my question clearer. They obviously do not represent real stock prices

2) Asset 1 went from 100 to 110 in the first month, meaning that the percentage return is: (110-100)/100=0.1 and therefore the 50$ allocated to Asset 1 should become 50*(1+0.1)=55$ at the end of the first month. I don't understand where is the flaw

3) Cool. This means that I have being doing things correctly, right? I do: (FINAL VALUE - INITIAL VALUE/ INITIAL VALUE) and I come up with the percentage returns for earch month, which is the same as what you said. Then I do: PRINCIPAL*(1+PERCENTAGE RETURN) = RESULTING VALUE (during the first month the principal is 50 for both assets) to calculate the value of the holding after each month. The resulting value of the holding during the last month becomes the principal the next month and so on... I only would like to know if what I do is correct

Thanks

 

[JeffM]

The flaw was in your fourth paragraph, where you showed asset 1 at 50 at the end of month 1 instead of 100. That error may have propagated throughout the paragraph.

Yes, [MATH]\dfrac{x - y}{y} = \dfrac{x}{y} - 1[/MATH] ALWAYS.

The second form is easier to compute on a hand calculator (and less prone to error) because you enter y only once. But mathematically it is six of one or a half dozen of the other.

The main point I wanted to make is that working with weights is extra work. To calculate portfolio returns you can work with aggregate values. Far less likely to screw anything up.

 

[rgtc]

Ok got it. Thank you very much!