# Calculating return on ISA

I'm based in the UK and trying to calculate how much I've made in my ISA. Below is a mock-up of the monthly investments and how I calculate my returns where I take the current price divided by the price at which the investment is bought. This table ignores fees and other costs for the sake of simplicity.

`Unrealised Return % = Current Price / Price`

`Unrealised Return = Cost * Current Price / Price`

Period Buy/Sell Quantity Price Cost Current Price Unrealised Return % Unrealised Return
1 Buy 100 £1.00 £100 £1.20 20% £20.00
2 Buy 90.91 £1.1 £100 £1.20 9.09% £9.09
3 Buy 90.01 £1.11 £100 £1.20 8.11% £8.11
4 Buy 105.26 £0.95 £100 £1.20 26.32 £26.32
5 Buy 95.24 £1.05 £100 £1.20 14.29% £14.29
6 Sell 93.46 £1.07 £100 £1.20
7 Buy 90.91 £1.1 £100 £1.20

By summing the Unrealised Return column gives the total amount of "profit" and that works fine up until period 5.

Now that I have a sell in period 6, I'm unsure how to calculate my return. My question is this method correct? How do you account for a sell?

Thanks

Calculating the time-weighted return.

"Suppose that the portfolio is valued immediately after each external flow."

`M0` to `M7` show the accumulating value of the investment. `C0` to `C7` are the cash flows.

``````M0 = C0 = 100

C1 = 100
M1 = (M0/1*1.1 + C1) = 210

C2 = 100
M2 = (M1/1.1*1.11 + C2) = 311.909

C3 = 100
M3 = (M2/1.11*0.95 + C3) = 366.949

C4 = 100
M4 = (M3/0.95*1.05 + C4) = 505.575

C5 = -100
M5 = (M4/1.05*1.07 + C5) = 415.205

C6 = 100
M6 = (M5/1.07*1.1 + C6) = 526.847

C7 = 0
M7 = (M6/1.1*1.2 + C7) = 574.742
``````

The final value of the investment is £574.74

``````twr = (M1 - C1)/M0*(M2 - C2)/M1*(M3 - C3)/M2*(M4 - C4)/M3*
(M5 - C5)/M4*(M6 - C6)/M5*(M7 - C7)/M6 - 1 = 0.2
``````

The time-weighted return is 20% over the whole time-span of the investment.

Note the time-weighted return is a measure of investment performance independent of the amounts invested, and so could be calculated from the returns alone, e.g.

``````twr = (1.1/1)*(1.11/1.1)*(0.95/1.11)*(1.05/0.95)*
(1.07/1.05)*(1.1/1.07)*(1.2/1.1) - 1 = 0.2
``````

and of course, simply initial price to final: `£1.20/£1.00 - 1 = 20%`

However if you have fees they would be combined with the cash flows in the longer version.