Return Smoothing - Why Illiquid Assets Look Safer Than They Are

By EC Assets Research Team, Alternatives Research · Published 29 October 2026

Return Smoothing: Return smoothing is the spreading of an asset's true gains and losses over several reporting periods, because its value is appraised, modelled or marked by hand rather than observed in a market. Smoothed returns are autocorrelated, understate volatility and beta, and inflate Sharpe ratios, without any single reported number being wrong.

What Return Smoothing Is

Return smoothing is what happens to a return series when the prices feeding it are estimated rather than observed. An office building, a private loan or a stake in an unlisted company has no daily quote. Its value is appraised, modelled or marked by the manager, and estimates of this kind change later and less than the value they describe. Each reported return becomes a blend of the current period's true return and the returns of earlier periods.

The effect on the statistics is systematic. Smoothed returns are positively autocorrelated, their volatility is too low, their beta and correlation with listed markets are too low, and the Sharpe ratio computed from them is too high. Nothing needs to be misreported for this to happen: every individual mark can be defensible and the aggregate still misleading.

Geltner (1993) analysed the mechanism in appraisal-based property indices. Getmansky, Lo and Makarov (2004) applied it to hedge funds and concluded that illiquidity exposure and smoothed returns are the most likely explanation for the strong serial correlation in reported fund performance.

How It Works

The Getmansky-Lo-Makarov model writes the reported return as a weighted average of current and past true returns:

$$R^{o}t = \theta_0 R_t + \theta_1 R{t-1} + \dots + \theta_k R_{t-k}, \qquad \sum_j \theta_j = 1$$

Because the weights sum to one, the mean is unchanged: every true return is eventually reported in full. What changes is the variance. If true returns are uncorrelated with volatility σ, the reported volatility is

$$\sigma^{o} = \sigma \sqrt{\textstyle\sum_j \theta_j^2}$$

and the sum of squared weights is below one unless all the weight sits in the current period. The lag-one autocorrelation of the reported series is the overlap between successive weights, Σ θ_j × θ_(j+1) divided by Σ θ_j².

The same logic explains the other distortions. A regression of reported returns on same-period market returns captures only θ0 of the true beta; the rest arrives in later months, which is why summing the betas on lagged market returns, the Dimson (1979) correction, recovers it. Asness, Krail and Liew (2001) found that hedge funds in aggregate carry significantly more market exposure than same-month regressions suggest once lagged betas are added.

Worked Example

A strategy has true monthly returns with a mean of 0.5 percent above cash and a volatility of 3 percent, uncorrelated over time. Its true annual volatility is 3 × √12 = 10.4 percent and its true Sharpe ratio 6 / 10.4 = 0.58. Its holdings are marked so that each month's true return is reported 50 percent in that month, 30 percent in the next and 20 percent in the one after.

Reported Sharpe ratios annualise the monthly figure by √12, the usual convention, which assumes uncorrelated returns.

For the 50-30-20 profile, the reported monthly volatility is 3 × √0.38 = 1.85 percent, which annualises by √12 to 6.4 percent. The reported Sharpe ratio is 6 / 6.4 = 0.94 rather than 0.58, and the reported returns have autocorrelations of 0.55 at one month and 0.26 at two. An equity beta of 0.6 appears as 0.3 in a same-month regression; adding the betas on one- and two-month lagged market returns, 0.18 and 0.12, restores the full 0.6.

The autocorrelations are also the repair. Lo (2002) shows that √12 annualisation holds only for uncorrelated returns. Including the covariance terms, the annual variance is 12 × 0.38 + 2 × (11 × 0.21 + 10 × 0.10) = 11.18 monthly variances instead of 12 × 0.38 = 4.56, an annual volatility of 10.0 percent and nearly all of the true 10.4. The remainder belongs to returns earned late in the year that are reported in the next.

Shocks are delayed rather than absorbed. A true loss of 20 percent in one month, with nothing else happening, is reported as -10, -6 and -4 percent. The worst reported month is half the true one; the three-month loss adds up to the same 20 percent.

When It Applies (and Limitations)

Wherever prices are estimated. Direct real estate, private equity, private credit, infrastructure and hedge funds holding thinly traded securities all show it. Liquid strategies marked to exchange prices show little, and their autocorrelation is close to zero.

Not all autocorrelation is smoothing. Some reflects genuine persistence in the underlying returns rather than in the marks. The model attributes all serial correlation to the reporting process, and in those cases the correction overstates the true risk.

The weights are estimated too. The θ values come from the reported series itself, usually from a short history, and they shift when valuation policy, auditors or market conditions change. Unsmoothed volatility is an estimate with a wide error band, not a measurement.

It works in both directions. The lag that hides a fall also delays the recovery. Over a full cycle reported and true cumulative returns converge; the distortion lies in the path and in every statistic computed from it.

Why It Matters for Institutional Investors

It distorts allocation. Mean-variance optimisers favour assets with a high return per unit of measured risk. Fed smoothed private-market statistics, they allocate more to those assets than their true risk justifies, and the low measured correlations add a diversification benefit that partly does not exist. The first-order correction across asset families is set out under alternative assets.

It produces the denominator effect. When listed markets fall and private marks lag, private holdings briefly rise as a share of the portfolio, can breach allocation limits and force sales or slow new commitments at the worst moment.

It disguises liquidity risk. A smooth series suggests an asset that can be sold at its mark at any time. The autocorrelation says otherwise: the mark is a lagging estimate, and the price available to a forced seller, the central concern of liquidity management, can be well below it.

References

1. Getmansky, M., Lo, A. W., & Makarov, I. (2004). An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns. Journal of Financial Economics, 74(3), 529-609.
2. Geltner, D. (1993). Estimating Market Values from Appraised Values without Assuming an Efficient Market. Journal of Real Estate Research, 8(3), 325-345.
3. Dimson, E. (1979). Risk Measurement When Shares Are Subject to Infrequent Trading. Journal of Financial Economics, 7(2), 197-226.
4. Asness, C., Krail, R., & Liew, J. (2001). Do Hedge Funds Hedge? Journal of Portfolio Management, 28(1), 6-19.
5. Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36-52.