Work related problem regarding weighted averages and percentages

I'm not exactly sure if this is a weighted average problem but here goes.
Theres a financial portfolio amounting to 419900$. Its profit yield from inception to date is 3.2067% which equals to 13465$.

After a new client entered with 20000 the new portfolio is worth 439900$.
How should we proceed with calculating the new yield from inception to date?
The problem appears because from now on, yields are calculated against the 439900 portfolio but the 3.2067% yield is based on the 419900 portfolio.
How can I adjust the 3.2067% yield according to new profits without implying that the portfolio was worth 439900$ since its inception?

Crossover said:

[There's] a financial portfolio amounting to [$419,900].

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Is this the current value, or the initial investment amount?

Crossover said:

Its profit yield from inception to date is 3.2067% which equals to [$13,465].

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This amount is 3.2067% of the previous amount, so I would guess that the previous amount was the original investment amount.

Crossover said:

After a new client entered with 20000 the new portfolio is worth [$439,900].

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What do you mean here by "worth"? Are the profits being withdrawn from the account, so the account only ever contains the actual amounts invested?

Crossover said:

How should we proceed with calculating the new yield from inception to date?

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If this is actually from your employment, try asking whoever is the finance guy (or somebody who works in the finance department) to explain whatever work-related thing it is that you're looking at.

419,900 is the initial capital and the yield has been being calculated against this figure.

439,900 is the "adjusted" initial capital after the new client entered.

So let me explain where the calculation problem arises.

Let's say the portfolio recorded a $1000 profit today. That's after the new client entered.
Were I to calculate the new total yield % by adding $1000 to the existing 13465$ of profits and divide it by 419,900 then this would not reflect the entrance of the new client and would end up with a yield % higher than the actual.
If on the other hand I added $1000 to the existing $13465 and divide by 439,900 this would lower the overall yield and would indicate a performance drop on the portfolio that doesn't exist in reality.

My question is,
Is there a way to combine the previous profit against the previous size of the portfolio and today's (and future) profits against the new size of the portfolio and come up with a number that reflects the real performance of the portfolio ?

Well its not the yield after one year neither it is an average yield.
It's the yield since the portfolio was created i.e. the current profit divided by the initial 419,900 capital which has remained fixed until this new client added 20,000.

Crossover said:

I'm not exactly sure if this is a weighted average problem but here goes.
Theres a financial portfolio amounting to 419900$. Its profit yield from inception to date is 3.2067% which equals to 13465$.

After a new client entered with 20000 the new portfolio is worth 439900$.
How should we proceed with calculating the new yield from inception to date?
The problem appears because from now on, yields are calculated against the 439900 portfolio but the 3.2067% yield is based on the 419900 portfolio.
How can I adjust the 3.2067% yield according to new profits without implying that the portfolio was worth 439900$ since its inception?

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Here's how I would go about it assuming I retained earnings, i.e. compound interest:
(1) You invested P₁ at time zero and held it for a period of n₁. Your present value at time n₁ is P₁ x^n₁ where x=1+i and i is the average rate of return over some period n=n₁+n₂.
(2) You now invest P₂ at time n1 and hold it for a period of n₂. Your present value at time n (=n₁+n₂) is (P₁ x^n₁ + P₂) x^n₂ or your present value at time n is
PV = P₁ x^n₁+n₂ + P₂ x^n₂

This can obviously be generalized to
PV = \(\displaystyle \Sigma\, P_j x^{m_j}\)
where PV is the present value, i.e. the time you want the average interest quote, x = 1+i, and P_j is the investment held for time m_j. Note that m₁ = n₁ + n₂ + n₃ + ... + n_L where L is the total number of periods and m₁ is the total length of time, i.e. since inception. Also note that this is generally going to require some sort of iterative technique to find x (and hence i).

@Denis

It looks like you are using the rule of three. However this simply applies the 3.20% yield to the new size of the portfolio.
I need this calculation for a spreadsheet that first calculates the current profit and then divides it by the initial investment to come up with the yield of said investment since its inception.
As long as the the size of the portfolio was fixed at 419900 this was easy.
Now that the size increased, the denominator increases and thus the yield decreases.
By using the rule of three the yield of 3.20% corresponds to a higher profit than the actual one so this is not useful.

Crossover said:

I'm not exactly sure if this is a weighted average problem but here goes.
Theres a financial portfolio amounting to 419900$. Its profit yield from inception to date is 3.2067% which equals to 13465$.

After a new client entered with 20000 the new portfolio is worth 439900$.
How should we proceed with calculating the new yield from inception to date?
The problem appears because from now on, yields are calculated against the 439900 portfolio but the 3.2067% yield is based on the 419900 portfolio.
How can I adjust the 3.2067% yield according to new profits without implying that the portfolio was worth 439900$ since its inception?

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The way you calculated average profit yield 3.2067% (= 13465/419900) is profit/dollar invested - no time component.

So the new average should be calculated the same way!!

Denis said:

Right...though I never heard it by that name!
With the info you're giving us, nothing else can be calculated...

Your problem as it is stated is a bit like:
5 guys with shovels are digging a hole, now at 15 feet deep.
A 6th guy is hired: what is now the digging rate?

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Excellent example - free get-out-of-the-corner card is here!!!

@Denis

I am not American or Canadian for that matter. I was taught that this specific method was called rule of three at 7th Grade when we were introduced toequations https://en.wikipedia.org/wiki/Cross-multiplication#Rule_of_Three and even though the link says it's taught in French secondary education it's probably not the only country to teach it that way since I'm not French either.
It utilizes the specific relation you mention whenever 1 out of the 4 values is unknown.Not exactly seeing how it is misleading, unless you find non-US terminology misleading that is.
It's not even a wrong term though.

Funny as it sounds your analogy is good for my problem.

Crossover said:

I'm not exactly sure if this is a weighted average problem but here goes.
Theres a financial portfolio amounting to 419900$. Its profit yield from inception to date is 3.2067% which equals to 13465$.

After a new client entered with 20000 the new portfolio is worth 439900$.
How should we proceed with calculating the new yield from inception to date?
The problem appears because from now on, yields are calculated against the 439900 portfolio but the 3.2067% yield is based on the 419900 portfolio.
How can I adjust the 3.2067% yield according to new profits without implying that the portfolio was worth 439900$ since its inception?

Click to expand...

Going through Google, the average yield seems to be total earnings divided by average balance. So suppose you had 50000 at the beginning of the term [since inception], added 25000 half way through the term and the total interest was 2000. The average balance is (L*50000+(L/2)*25000)/L = 62500 where L is the length of time since inception. Thus average yield is 2000/62500=0.032 or 3.2%. So the answer to your question appears to be 'Yes, it is a weighted average problem. The balance used for the yield calculation is the weighted average of the amounts deposited/invested.'