On 1st of January I had a total of 120 dollars invested in a scheme. I made further deposits (as per table below) and have a final figure of $620 on June 10th. How do I work out my percentage gain from January 1st to June 10th inclusive of the deposits made?
On
Well, consider an average-daily-deposit-withdrawal-balance of the year-to-date but, of course, year-to-date starts over at the end of each year. Then the software that I develop results in 27.35% . However the software projects the balance averaging as to year-end and that reduces shocks from large deposits or withdrawals.
Or for viewpoint, just average the given balances as they are:
120 for 35 days, 370 for 66 days, and 500 for 58 days.
Then the average balance is 360.125. The percentage gain is 120 / 360.125 or 33.32% .
I can very nearly match the software by projecting the current average balance to the future year-end like this:
120 for 365 days, 250 for 330 days, and 130 for 264 days.
Then the average balance projected to the future year-end is 440.05 . The percentage gain projected to the future year-end is 120 / 440.05 or 27.27%.
In either case I may be a day or two off in the calendar day counting.
Since I didn't stop at the first paragraph, I had to edit for a couple of days.
And here is a link to a modified-Dietz:
There are actually multiple return calculations.
Time Weighted Return: This is used if we precisely know the returns of each period. When the cashflows come in, they happen at the join between the different periods. This is the standard calculation used by professional money managers that have daily accounting of their investment returns.
Returns for each period are calculated independently $\frac {B - F - A}{A}$
$B$ is the ending balance $F$ is the cash flow $A$ is the beginning balance
Cash flows come in on the end of period dates.
If the flows are credited at beginning of period, returns for each period are $\frac {B -F - A}{A+F}$
The periodic returns are geometrically linked.
$(1 + \frac {400-250 - 120}{120})(1+\frac {580-130-400}{400})(1+\frac{620-580}{580})\\ \left(1+\frac {30}{120}\right)\left(1+\frac{50}{400}\right)\left(1+\frac{40}{580}\right)-1\\ \left(\frac {150}{120}\right)\left(\frac{450}{400}\right)\left(\frac{620}{580}\right)-1$
https://en.wikipedia.org/wiki/Time-weighted_return
Modified Dietz:
Modified Dietz is a simple interest rate of return, for investment portfolios with intermediate cash flows and no intermediate valuation:
$\frac {B-A-F}{A + \sum_\limits{t= 1}^T W_tF_t}$
$F$ is the total flow
$F_t$ are the cash flows received at time $t.$
$W_i$ is a time weighting factor for each cash flow.
Deposit $\$120$ on day 0, (invested for 160 days)
$\$250$ on day 35 (invested for 125 days)
$\$130$ on day 101 (invested for 59 days)
$\frac {620-120-250-130}{120 + 250\frac {125}{160}+130\frac{59}{160}} = 0.33\%$
https://en.wikipedia.org/wiki/Modified_Dietz_method
Another calculation is the dollar weighted return.
This method also ignores the intermediate marks to market, and plugs all of the cash flows into the IRR formula and solves for a discount rate such that the future value equals the future value.
$\sum_\limits{t = 1}^T F_t(1+r)^t = FV\\ 120 (1+r)^{\frac{160}{365}}+ 250(1+r)^{\frac{125}{365}}+130(1+r)^{\frac{59}{365}} = 620$
You may see this written with present values instead of future values.
$\sum_\limits{t = 1}^T \frac{t_i}{(1+r)^t_i} = \frac{FV}{(1+r)^T}$
We cannot solve for $r$ algebraically, but we can use numerical estimates to find
$r = 95.1\%$
This is an annualized return for $r$ vs. a holding period return for the other methods.
https://breakingdownfinance.com/finance-topics/finance-basics/dollar-weighted-return/