Translating an Annual Benchmark Premium into Monthly Returns

Summary

The document considers how to convert a private equity benchmark expressed as an equity index plus an annual premium into monthly benchmark returns. It contrasts adding a monthly equivalent spread with compounding the index return and premium, highlighting that these conventions can produce different results. It does not establish a universal market convention.

The author describes an operational choice: distribute a spread across months so each calendar year’s compounded benchmark return equals that year’s index return plus the stated premium. This makes calendar-year results align with the quoted benchmark, but the monthly spread varies between years. The approach also creates a timing problem: applying it partway through a year would require revising earlier monthly spreads to preserve the annual target. The account offers a practical workaround and its limitation, rather than a general standard for all reporting periods.

Key ideas

• An annual index premium can be translated into monthly returns using more than one convention.
• Adding a monthly spread and compounding the benchmark with a premium are distinct methods.
• The described approach targets the annual premium at the calendar-year level.
• That method requires different monthly spreads across years and cannot be applied cleanly midyear without revising prior months.

Tags

# How would one define MSCI World Index + 3% or S&P 500 + 3%?


# How would one define MSCI World Index + 3% or S&P 500 + 3%?












Sometimes private equity-benchmarks contain an illiquidity premium. This is then reflected in something like "MSCI World Index + 3%".

Is there a conventional way of calculating this number for monthly returns? For example, these would be three possibilities:

- Monthly benchmark return = MSCI return + 103%^(1/12) - 100%

- Monthly benchmark return = MSCI return + 3%/12

- Monthly benchmark return = (100% + MSCI return) * 103%^(1/12) - 100%

And I can possibly think of more. Is there some convention?

## Answer by Řídící (score 1)

https://quant.stackexchange.com/a/81161

OP here. What I have done is to add the same spread to each month in the same calendar year, such that the calendar year return equals MSCI return + 3%. This means different monthly spreads in different calendar years. (And hope for the best for non-calendar years.) Ugly, but at least the calendar years don't surprise anyone.

Edit: One problem: you can't do this midway a current calendar year. (Or every month you'd have to retrospectively change the spreads of the previous months in this calender year.) :(

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.