The mistake is the assumption that:
(x^r)+(y^r) is the same as (x+y)^r
i.e.
*/365 $ +/0.6 0.4 * 3 2 ^ %365
2.55099
*/365 $ (+/0.6 0.4 * 3 2) ^ %365
2.6
Devon McCormick wrote:
> Here's a real-life example I encountered recently. I've simplified the
> annual return
> numbers to 200% for stocks and 100% for bonds (*3 2, respectively) to make
> the
> math more easily checkable.
>
> I start with a series of daily returns for a stock and bond index:
>
> */stkret=. 365$3^%365 NB. Daily stock returns - triple over the year
> 3
> */bndret=. 365$2^%365 NB. Daily bond returns - double over the year
> 2
>
> I want to use the daily returns of a 60/40 stock/bond benchmark based on
> these
> index returns to calculate an annual return:
>
> NB. 60/40 stock/bond benchmark - naive calculation:
> */bmkret1=. (0.60*stkret)+0.40*bndret
> 2.5509869
> NB. is demonstrably wrong:
> 0.6 0.4 +/ . * 3 2
> 2.6
>
> NB. Alternate version (using cumulative returns) gives correct answer:
> {:bmkretcum=. (0.60**/\stkret)+0.40**/\bndret
> 2.6
>
> So, I've introduced a noticeable loss of precision simply by multiplying
> each series by a number less than one before accumulating the returns.
> This error is easy to make but harder to catch when using real return
> numbers
> if we don't have some independent calculation of the final result.
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