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An error has also crept into the presentation of the time-weighted return TWR.
The two-month yield r2 is obtained by multiplying the interest factor of the first month a by that of the second month b and then subtracting 1:
a = 1050/1000 = 1,05
b = 3150/3050 = 1,032787
r2 = ab - 1 = 8.4426%
Thanks for the tip, Christian! The formulas have now been corrected 🙂
Hello Eric, that looks good now!
Only in the case of the simple return does the text not really fit the calculation. The latter is correct in principle, except that the minus one is missing.
r2 = 3150/(1000 + 2000) - 1 = 5%
In the description, however, it should somehow read like this:
The sum of all incoming payments minus the sum of all outgoing payments equals the cash flow total.
With this and the final value, the simple return for two months is then calculated as:
r2 = (terminal value - cash flow total) / cash flow total
Or remodelled:
r2 = terminal value/cash flow total - 1
The simple return per month r is then calculated as follows:
r = root(1 + r2) - 1 = root(1.05) - 1 = 2.47%
And of course the incoming and outgoing payments are included in the cash flow total in the simple return (only the timing is not).
Best regards, Christian
The calculation of the money-weighted return MWR is unfortunately presented incorrectly.
The equation to be solved is:
1000 + 2000/(1+r) = 3150/(1+r)^2
Or in the variant obtained by multiplying by (1+r)^2:
1000 (1+r)^2 + 2000 (1+r) = 3150
Both lead to the solution:
r = 3.7155%
In Excel or Calc, the same value r is obtained using the function for the internal rate of return IKV:
r = IKV({1000;2000;-3150})
And r is not the return for the two-month period, but the return for one period, i.e. for one month.
The return r2 for the two-month period is calculated as follows:
r2 = (1+r)^2 - 1 = 7.569%