Converting an Annual Target Return to a Daily Target

Summary

The document addresses how to translate an annual target excess return stated in basis points into an equivalent daily target over a 252-day year. It rejects both taking the annual number to a fractional power directly and simply dividing the basis-point figure by the number of days, because returns compound and basis points represent a fraction of principal.

The proposed procedure first converts the annual basis-point target into a decimal return, takes the 252nd root of one plus that return, subtracts one to obtain the daily compounded return, and converts the result back to basis points. The answer gives an approximate daily figure for the example in the question. This conversion assumes a constant compounded daily rate across the stated number of periods; realized returns can vary, and arithmetic averaging or different day-count conventions may call for other calculations.

Key ideas

• Convert a basis-point target to a decimal return before calculating its periodic equivalent.
• For a compounded annual target, take the period root of one plus the annual return, then subtract one.
• Convert the resulting periodic decimal return back into basis points for comparison.
• The calculation assumes compounding over the stated number of periods at a constant rate.

Tags

# De-annualizing a target alpha return


# De-annualizing a target alpha return












apologies if this is not the correct place for this type of question, but I just want to confirm if the following de-annualization is correct.

if a manager states that he will earn 200 bps of target excess returns over a year. How much daily target excess returns would be expected?

i believe that the de-annualization should be 200 ^ (1/252), but a colleague said that it should be 200 * 1/252. Which method is the most correct approach?

## Answer by vonjd (score 1, accepted)

https://quant.stackexchange.com/a/16709

It is neither: Because returns are growth rates that have to be compounded and basis points are percentage points divided by $100$ you do the following:

$$10000\ (\sqrt[252]{\frac{200}{10000}+1}-1)\approx 0.7858\ bp$$

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