Calculating rate of return

[Punker]

Assume you had a portfolio where you made a monthly deposit. Say you started at 0 and deposited $100/month for 6 months, then $300/month for 6 more months. At the end, you've deposited $600+$1800= $2400. You check your account and the portfolio is now worth $2600. How would you calculate rate of return?

I swear, its not a homework question. I am just trying to see how my guy is doing.

[squiffy]

This is the type of question I have had. I actually took a Finance Theory class in law school, but don't remember covering a problem like this.

It's obviously easy if you have only one deposit. The multiple deposits make it more complicated.

Three possible approaches.

First, just make several simplified calculations. They won't be precise, but may be close enough for government work. For example, take the total profit and divide by the total amount invested and adjust so that you get an annual rate. This will be clearly incorrect, but is a rough guide. You will always be undercalculating the actual return because the recent deposits have not really had much time to work.

Second, you can ignore the return for the most recent deposits and only calculate return for deposits held six months or longer. So say you have actually deposited 2600. But you will only calculate return on money held for 6 months and profit thereone.

Third, calculate a separate return for each deposit.

By making multiple calculations, you tend to get pieces of the big picture. Like photographing an elephant from 10 different directions.

We can discuss this more. It's hard to discuss by posts. Wish we had a class we were all taking.

I face this same problem when I invest in stocks and make multiple purchases over time.

Say you buy 1000 shares of NOK on Sept. 1. And after one month they have appreciated 1%.

Your actual return is 1% in 30 days. And your actual profit is say $500. I think that these are the most important figures.

Many programs like quicken translate this into an effective annual rate. But this is really artificial and potentially unhelpful.

IF the stocks keep appreciating at 1% a month (that's a big if), then your annual rate is 1% a month for 12 months or 12% per annum. But do you see how that is probably an artificial overestimate of your true return? The only way to know your true annual return is to wait one year, then see how much those stocks have gone up, or gone down. You might end up losing money over 12 months!!!!!

So the most accurate would be.

I deposited $100 on Jan. 1. Over 6 months it earned x%.

Another problem, is that it is hard to figure out what proportion of the interest was earned by each $100 deposit. You can figure it out. But it's really not worth your time.

So easiest is to say, as of Sept. 1, I have deposited $2600 and since Jan. 1 I have earned $100 in interest, which is so much % of the 2300 which has been actively earning interest.

Just try to record factually, each month, what is happening to the money. Then analyze it.

The most meaningful adjustment would be to temporarily ignore those deposits which are so recent that they have earned no interest.

I hope there is a math major out there with a better answer. But my college roommate was a summa cum laude math major and he seems to be perplexed by this same issue.

[squiffy]

So, assuming the entire 2400 has been earning interest. (The last $300 deposit only for 1 month)

200 profit / 2400 invested = about 8.3% but not per annum.

I think the key to keep in mind is that you are doing better than 8.3% per annum because 8.3% per annum would mean that you put the entire 2400 in on Jan 1 and kept it there for 12 months.

Here, 1 $300 deposit was only there 1 month, 1 $300 deposit was only there 2 months, 1 $300 deposit was only there 3 months, etc.

Again, it may NOT be helpful or realistic to translate this earning into any other kind of per annum analysis, because as I illustrated with the stock, that would be speculative.

Who knows what will happen to the last $300 deposit over 12 months.

So I would keep it simple and stick to the basic facts.

You deposited $2400 over the course of 1 year. At the end, you have $200 more than when you started.

So you have actually made 8.3% on the money invested. Though not per annum. You can recalculate at the end of each month or year. As long as you are consistent in your calculations, you can follow roughly how you are doing.

The good thing about a stock purchase is that it is easier to figure out how EACH purchase is doing, because you have a purchase price and the number of shares, and you can compare to the current market price.

So last year, I made about 12-15 separate purchases of NOK. Some purchases were at say $12 and the stock went up to say $16.

Other purchases wer at 16.50 and the stock was underwater.

So I did separate calculations for each purchase. Some purchases were profitable and some were not.

And I also did a grant total, lumping together all the purchases and coming up with a profit percentage. And I used the earliest purchase date.

So, I started buying in Jan. and kept buying through Dec.
At the end I had $45,000 more than I had in Jan.

SO that is NOT a per annum profit because some of the purchases had only been held for 1-2 months. But just for the purpose of rough calculations, it was somewhat akin to a giant single purchase in Jan.

[squiffy]

If you leave off the last $300 deposit, which has only been there 1 month, you have a rate of about

200 / 2100 = 9.5%

If you leave off the last two $300 deposits, which have only been there 2 months and 1 month respectively,

200/ 1800 = 11%

So your true rate is probably closer to 9 or 10% or so on the money that has been in there long enough to make the biggest difference on the earnings or interest rate.

[midas]

You need to calculate an internal rate of return-IRR. I used Excel's XIRR function and assumed you put the money in your account on the 15th of each month and had $2600 on the 30th of the last month.

Excel says your account had a return of 23.31%. Which even though I'm rusty at this, sounds right.

[Punker]

Thanks midas...the XIRR function in excel is exactly what I was looking for.