# Portfolio return with changing assets over time

I need some feedback on a very basic question regarding the calculation of the portfolio return.

I have created an example of a portfolio with two assets and attempted to calculate the return: I've calculated the weighted asset returns and from there I would like to calculate the cumulative portfolio return (= the return of the portfolio from Jan 1 to Feb 28). I can't just multiply them (1+r1)*(1+r2)-1, right? The -10% return in January was when the portfolio's value was only \$1000 and the same relative decline in asset 1's value in February has a much smaller impact.

So do I simply weigh the returns according to the portfolio values? I've tried it and would appreciate some feedback on my calculation. Did I make a mistake? Is there an easier way to get the result?

## 1 Answer

If you calculate (1+r1)*(1+r2)-1 = 11.1435% that gives you the TWR (Time Weighted Return) which is one widely used measure of return. It treats all periods equally, no matter the assets involved.

I am not familiar with the calculation you do in B17 and C18.

If I compute the IRR (internal rate of return) for the cash flows [-1000,-20000,+25810] I get 21.65% per month, which is similar but not identical to your B20 value of 21.9%. The IRR takes into account the actual amounts invested, so is also referred to as a MWR (Money Weighted Return). TWR and MWR are the 2 main ways of computing returns on a portfolio. They do not give the same value.

If you want a money weighted method, I suggest the IRR.

• Thank you for explaining this to me. Did you use -20000 or -20900? – NoNameNo123 Jun 26 '19 at 14:11
• I used -20000. I am looking only at the cash inflows. In the second period 20000 of Asset 2 suddenly appeared which was not there before, so I assumed the fund received 20000 in cash from investors. For Asset 1 I assumed that nothing was sold or bought and the existing shares dropped in value to 900; so no external cash flow there. This is only an assumption and we would need to know actual inflow and outflows to compute the IRR. – Alex C Jun 26 '19 at 14:21