Calculating Portfolio Return

Question

I am doing a research on the proper ways to calculate portfolio returns.

The condition: The underlying asset is physical gold bars. Just gold, purchased from 1 particular seller.

Currently i have two approaches. Consider the following:

trx_date gold_amount buy_unit_price total_amount

01/06 10gr $100 $1000

02/06 10gr $110 $1100

03/06 10gr $120 $1200

04/06 10gr $90 $900

Assumption: Today's sell price is $115

The first method would be calculating as follows:

1. I calculate all the money i've spent to purchase gold in the past i.e. ($1000 + $1100 + $1200 + $900 = $4200).

Then I find out the value of my gold using today's sell price i.e. ((10gr + 10gr + 10gr +10gr)* $1050 = $4600).

Finally, i calculate the return of my investment using the following formula

(present value - past value)/past value, i.e. (4600-4200)/4200 = 0.095

OR

I found this method here https://financetrain.com/how-to-calculate-portfolio-returns/

Which essentially taking into consideration the weight and the return of each time i "top up" my investment.

I would like to know which methodology is preferable and why ? (or perhaps there's a better approach to this).

Edit I tried both approaches and end up with similar result. Now i just need to find a justification why 1 methodology is preferable compare to the other.

Answer 1

It depends on what you're actually trying to measure. If you're trying to measure the performance of gold, then you could just look at the beginning and end prices of gold.

If you want to see how your decisions to buy and sell impacted your portfolio's return, then time-weighted return is a common (and easily calculable) measure. You basically take the return between each cash flow and take the geometric mean. That isolates the return based on your actions(e.g. did you buy low and sell high).

Another comparative measure is IRR. It gives you the equivalent constant rate of return over the time period - meaning at what constant rate could you have invested the money at the beginning and ended up with the same overall return. The two main drawbacks to IRR are that it can be hard to compute (it typically has to be solved for iteratively) and it can be influenced more heavily by larger cash flows. So if your purchases vary significantly in amount, then the returns after larger amounts are traded can dominate the IRR, where in TMR each time period is treated equally.