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Unsmoothning returns(Ang)


New Member
Hi David
In BT the below para is mentioned
"Unsmoothing affects only risk estimates and not expected returns: Smoothing of returns or the mean estimates require only the first and last price observation but in smoothing of risks, all the risks are counted and spread over several periods. Thus unsmoothing changes only the volatility estimates and not the return estimates. "
However in schweser it's mentioned that unsmoothning returns affects risk and return estimates and could have a dramatic effect on returns

could you please clarify


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @saurabhpal49 I think it hinges on whether we are talking about expected return (a typical first moment view) or minimum return during a period (which is really a dispersion measure and, as such, it should not surprise us the unsmoothing impacts this as it impacts volatility).

Here is Ang (the source, page 421-22):
"The unsmoothing process has several important properties:
1. Unsmoothing affects only risk estimates and not expected returns. Intuitively, estimates of the mean require only the first and last price observation (with dividends take “total prices,” which count reinvested dividends).12 Smoothing spreads the shocks over several periods, but it still counts all the shocks. In Figure 13.2, we can see that the first and last observations are unchanged by infrequent sampling; thus unsmoothing changes only the volatility estimates.

2. Unsmoothing has no effect if the observed returns are uncorrelated. In many cases, reported illiquid asset returns are autocorrelated because illiquid asset values are appraised. The appraisal process induces smoothing because appraisers use, as they should, both the most recent and comparable sales (which are transactions) together with past appraised values (which are estimated, or perceived, values). The artificial smoothness from the appraisal process has pushed many in real estate to develop pure transactions-based, rather than appraisal-based indexes. Autocorrelation also results from more shady aspects of subjective valuation procedures—the reluctance of managers to mark to market in down markets.

In many cases, we expect the true illiquid asset returns to be autocorrelated as well.14 Illiquid asset markets—like real estate, private equity, timber plantations, and infrastructure—are markets where information is not available to all participants, information does not spread rapidly, and capital cannot be immediately deployed into new investments. Informationally inefficient markets with slow-moving capital are characterized by persistent returns.

3. Unsmoothing is an art ..."

I think schweser's comment comes from subsequent chapters. Notice the difference. The above statement refers to expected returns (and, really, returns as we normally think of them; i.e., first moment or point-to-point). This paragraph refers to the minimum return(s) during a quarter which is really a measure of dispersion (annotation is mine):
"Unsmoothing produces a dramatic effect. The minimum reported return during the real estate downturn in the early 1990s is –5.3% during the quarter ending December 1991. The corresponding [i.e., minimum during the quarter] unsmoothed return is –22.6%. During the financial crisis, NCREIF returns reached a low of –8.3% in December 2008. The unsmoothed [again, the "low during the period" so this is really a view on dispersion rather than expected return] return during this quarter is –36.3%. The volatility of the raw NCREIF returns is 2.25% per quarter, whereas the volatility of the unsmoothed returns is 6.26% per quarter. This approximates the volatility of stock returns, which is around 7.5% per quarter. Correlation (and hence beta) estimates are also affected by unsmoothing: the correlation of raw NCREIF returns with the S&P 500 is 9.2% and this rises to 15.8% once the unsmoothing correction is applied."