If you have an investment, the % return over a period is simply:

return = (Vnow - Vstart)/Vstart * 100%

so by way of example... invest 1000 6mo ago, so the portfolio looks like:

return is (1180 - 1000)/1000 *100 = 18%

But what if you have several investments starting at different times? Do you pretend they all started at the same time? eg

return = (Σ Vnow - Σ Vstart)/ Σ Vstart *100%

or what?

again, example previous investment + new one started in month 3, individually have returns of 18% and 12%, but what's the actual return?



Using the above approach gives (2300 - 2000)/2000 *100 = 15% which is intuitively correct but I can't help feeling there's some other way to combine these investment returns....

Thoughts?

 

The calculation you want to use depends on the question(s) you want to answer.
I think the solution you might be looking for is to annualize your rate of return. So if you made 18% in six months, you'd call that a 36% ARR, annualized rate of return. A gain of 12% in 3 months is a 48%ARR. You can get the average ARR by summing the weighted contributions from each investment.

Another way to look at an investment choice is to compare it to an alternative investment, such as an index on the broader market. For every investment, you can compare how it's doing compared to how that same money would have done if invested in the S&P500, Russel 5000, that sort of thing. You have to be careful to determine how dividends are handled in those benchmarks. Some ignore dividends, some reinvest them.

The standard metric for financial portfolio analysis is to determine the risk-adjusted rate of return. Anyone can get a higher return by accepting a higher risk. Unfortunately the correction for risk level is far more work. Most lay people don't bother.

 

Using the above approach gives (2300 - 2000)/2000 *100 = 15% which is intuitively correct but I can't help feeling there's some other way to combine these investment returns....

Thoughts?

I prefer to use annualized ROI https://www.investopedia.com/articles/basics/10/guide-to-calculating-roi.asp

 

Anywho, the ARR of 18% over 6 months is 39%, because 1.18^2 = 1.39. The ARR of 12% over 3 months is 57%.

 

If you have an investment, the % return over a period is simply:

return = (Vnow - Vstart)/Vstart * 100%

so by way of example... invest 1000 6mo ago, so the portfolio looks like:
View attachment 310119
return is (1180 - 1000)/1000 *100 = 18%

But what if you have several investments starting at different times? Do you pretend they all started at the same time? eg

return = (Σ Vnow - Σ Vstart)/ Σ Vstart *100%

or what?

again, example previous investment + new one started in month 3, individually have returns of 18% and 12%, but what's the actual return?

View attachment 310120

Using the above approach gives (2300 - 2000)/2000 *100 = 15% which is intuitively correct but I can't help feeling there's some other way to combine these investment returns....

Thoughts?

There are a number of ways of doing it, depending on exactly what question it is you are trying to answer.

Notice that your first investment had an annualized (simple interest) ROI of 36% while the second had 48%.

Also, the data that you showed really reflects investment periods of just five months and two months, respectively. But I'm going with the stated six month and three month periods.

Taking the total gain and dividing it by the total invested can make sense in some circumstances, but only if you don't care about how long the money was tied up. This approach also makes it hard to compare your return to whatever alternatives you might have chosen instead.

The approach I find most meaningful is to determine the rate of return that would be needed on a single investment that would produce the same end result for the given transactions into and out of it.

This is pretty easy to do if we use an equivalent investment that uses simple interest, R, per year.

You made two investments into this hypothetical instrument. $1000 for 0.5 year and $1000 for 0.25 year. Thus the amount at the end would be:

$1000*R*(0.5 yr) + $1000*R*(0.25 yr) = $180 + $120 = $300

Solving for R gets us

R = 40% APR

Note that this is comfortable between the 36% and 48% for the individual investments, which makes sense. It also favors the longer term investment, which also makes sense.

So, using this result, how much profit did you make?

You had a total of $2000 invested for an average of 4.5 months at an APR of 40%.

$2000 * 40%/yr * (4.5/12) yr = $300

 

Irving
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@Irving

I just got something in the mail that makes for a useful example of the approach I described -- as well as highlights how insidious the offers that companies push at us can be.

I have a business credit card that has just made changes to the terms of one of their programs in which you can make a large purchase and choose to pay it over time by creating a fee-based plan for it. The terms are pretty simple. Instead of getting charged interest (they make repeated use of terms like "no interest" and "interest-free"), you pay "just a fixed monthly fee" of 1.72% of the original purchase amount.

So a question one might (or really should) ask is, "What is the effective interest rate I'm being charged on this plan?" It is tempting to just take the 1.72% and multiply it by 12 to get 20.64%, which should have us shaking in our boots on it's own, but the reality is far worse.

While the answer depends very slightly on how long the plan lasts, to illustrate the method, let's use a one year plan. To simplify things, we will use assume that the year is divided into twelve equal months (mortgages almost always do this, while revolving plans generally use a daily periodic rate, but the difference for our purposes is extremely minor).

The amount of the purchase doesn't matter, but for convenience we will use $1000. The monthly fee is therefore $17.20 and the required monthly payment is $100.53. After twelve such payments, the residual balance is $0.04 (which would be added to the final payment due).

To determine the effective APR of this plan, we set up a parallel schedule of payments in which, instead of this fixed monthly fee, we assess a monthly interest charge at a fixed APR and apply the same $100.53 payment amount each month. We then adjust the APR until the residual balance at end of the repayment period is as close as we can get it to the fixed-fee plan. Those results are shown below:

	$1,000.00​	Purchase
	1.72%​	Monthly Fee Rate		36.14%​	APR
	$17.20​	Monthly Fee
	12​	Plan months
	$100.53​	Monthly Payment
	Balance	Fee	Payment		Balance	Interest	Payment
0​	$1,000.00​	$17.20​	$100.53​		$1,000.00​	$30.12​	$100.53​
1​	$916.67​	$17.20​	$100.53​		$929.59​	$28.00​	$100.53​
2​	$833.34​	$17.20​	$100.53​		$857.06​	$25.81​	$100.53​
3​	$750.01​	$17.20​	$100.53​		$782.34​	$23.56​	$100.53​
4​	$666.68​	$17.20​	$100.53​		$705.37​	$21.24​	$100.53​
5​	$583.35​	$17.20​	$100.53​		$626.08​	$18.86​	$100.53​
6​	$500.02​	$17.20​	$100.53​		$544.41​	$16.40​	$100.53​
7​	$416.69​	$17.20​	$100.53​		$460.28​	$13.86​	$100.53​
8​	$333.36​	$17.20​	$100.53​		$373.61​	$11.25​	$100.53​
9​	$250.03​	$17.20​	$100.53​		$284.33​	$8.56​	$100.53​
10​	$166.70​	$17.20​	$100.53​		$192.36​	$5.79​	$100.53​
11​	$83.37​	$17.20​	$100.53​		$97.62​	$2.94​	$100.53​
12​	$0.04​	​	​		$0.03​	​	​

As you can see, this 12-month plan is equivalent to being charged 36.14% APR on this purchase, a rate that is considerably higher than the actual interest rate on this card (which, IIRC, is about 17% -- I don't care because I refuse to pay a penny in interest on credit cards and so they are paid in full every month). It's even markedly higher than the default rate that applies to accounts that are past due, which is something like 28.9%.