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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

1 Answer 1

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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.

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