This article is the English translation of the original in Danish that was published in August 2025 in Finans/Invest. You can download the original here.
This article analyzes the theoretical and practical trade-off between the illiquidity premium and the rebalancing premium in institutional portfolios. While illiquid assets have historically offered attractive excess returns, their non-tradability limits the investor’s ability to rebalance systematically – and thus achieve the rebalancing premium, which can be significant, especially in volatile and low-correlated markets. On the other hand, the presence of illiquid assets introduces a possible counterbalance to the so-called volatility drag – the fact that high volatility reduces the geometric return of the portfolio. Through a combination of theoretical review, simulated portfolio examples and practical implications, it is illustrated how investors can balance the opposing considerations of liquidity, flexibility and return.
Introduction
As institutional investors have increasingly allocated capital to illiquid asset classes such as private equity, infrastructure and private credit, there has been increased debate about the advantages and disadvantages of these investments. As shown in Figure 1, the share has increased from 13% in 2016 to over 18% in 2023, and it is credit, infrastructure and private equity in particular that have increased, while hedge funds and agriculture today play a smaller role.
Figure 1: Development in allocation to Alternative Investments in Danish pension funds
The discussion includes, among other things, their impact on the overall portfolio risk and return, and the question of whether limited liquidity can be a disadvantage, as illiquid assets reduce investors’ ability to carry out ongoing rebalancing – a discipline that in itself can be a source of excess returns in volatile but liquid markets. Rebalancing as such is not a new phenomenon, but rather a widespread practice used to adjust portfolios back to the strategic asset allocation when asset weightings shift as a result of market movements and the natural development of the portfolio. However, the fact that rebalancing can be a source of extra returns is often not in focus.
The rebalancing premium is the excess return that potentially arises when an investor continuously sells relatively expensive assets and buys relatively cheap assets through regular rebalancing, due to the volatility and lack of correlation of the assets.
On the other hand, there is a relatively broad consensus that illiquid assets have historically provided an excess return compared to listed assets. This is also evident from Figure 2, which shows the indexed development in a number of alternative and traditional asset classes.
Figure 2: Indexed development in a number of alternative and traditional asset classes
This excess return is often called an “illiquidity premium” – an excess return that compensates for the absence of ongoing trading and price transparency. It is obvious that this excess return is in reality a combination of a complexity premium and an expression of the skill of the investors, since it is probably not possible to achieve the premium simply by buying arbitrary unlisted assets. Nevertheless, the term “illiquidity premium” is widely used in the literature as well as in this article for the sake of simplicity as a collective term for the excess return associated with illiquid investments.
In addition, the presence of illiquid assets introduces a possible counterbalance to the so-called volatility drag – the fact that high volatility reduces the geometric return of the portfolio. Many illiquid asset classes exhibit low reported volatility, which is often due to smoothing due to model-based valuation, but at the same time, several of these asset classes potentially offer real diversification benefits that reduce the overall variance of the portfolio.
These three opposing effects / premiums – the rebalancing premium, the illiquidity premium and the volatility drag – are more thoroughly defined and discussed in later sections. They complicate the assessment of the optimal ratio between liquid and illiquid investments and raise a central portfolio theory question: Is there a theoretically optimal allocation to illiquid assets that allows for the harvesting of both the illiquidity premium and the rebalancing premium – or does one premium dominate the other?
The purpose of this article is to analyze the theoretical and practical trade-off between the illiquidity premium and the rebalancing premium in institutional portfolios. The article also discusses how volatility drag may argue for including illiquid assets in a well-diversified portfolio – despite their limited rebalancing – as the diversification benefit increases the long-term geometric return, even if the arithmetic return is held unchanged.
Through a combination of theoretical review, simulated portfolio examples and practical implications, it is illustrated how investors can balance the opposing considerations of liquidity, flexibility and return.
The analysis shows that while realizing the rebalancing premium may appear attractive, a diversified portfolio with exposure to illiquid assets may be even more advantageous – both due to the higher expected return (the illiquidity premium) and due to the reduced volatility drag thanks to the diversification gain, leading to higher final wealth.
Theoretical framework
To analyze the possible trade-off between illiquidity premium and rebalancing premium, a conceptual clarification of the two premiums and their underlying mechanisms is required. In addition, the concept of volatility drag and its importance for portfolio construction is included, as it has direct relevance for understanding the role of illiquid assets in a diversified portfolio.
Illiquidity premium
The illiquidity premium refers to the expected excess return that investors require to tie up capital in assets with low marketability and limited price transparency. Classical theories (Amihud and Mendelson, 1986) relate liquidity to transaction costs and price spreads, but for alternative investments – such as private equity and infrastructure – liquidity risk is rather associated with, among other things, long investment horizons, lock-up periods and lack of mark-to-market valuation.
Empirically, there is evidence that illiquid asset classes have delivered higher returns than their liquid counterparts, even after adjusting for market risk (Harris et al., 2012; Brown & Kaplan 2019; Brown et al., 2025). However, it is worth noting that the premium cannot necessarily be attributed to illiquidity – at least not alone. Among others, Rasmussen (2023) argues that the excess return primarily stems from higher leverage and tax advantages. Rode (2021), on the other hand, argues that the coincidence of complex structures, information asymmetry and active ownership means that the real return depends to a large extent on investors’ ability to identify and exploit attractive investments – which suggests that the premium can be partly characterized as a skill-dependent return component, which is called the complexity premium. The concept is also used in other research papers later (Timm et al., 2024). Nevertheless, for the sake of simplicity, the term “illiquidity premium” is used in this article as a collective term for the historically observed excess return on investment in unlisted, illiquid assets.
Volatility drag and geometric returns
Volatility drag describes how volatility “eats” away at the total return because the realized geometric return over several periods becomes lower than the arithmetic mean. This happens because losses drag more negatively than corresponding gains drag positively when you multiply returns together rather than adding them together. The higher the volatility, the greater the drag and thus the higher the volatility, the lower the realized return over time, all else being equal.
You can approximate volatility drag with this formula:
According to Kitces (2017), this formula provides a close approximation in practice.
This relationship has important implications for portfolio composition: A reduction in the portfolio’s overall volatility – e.g. through diversification – can in itself increase the long-term geometric return, all else being equal.
Volatility drag is particularly relevant for long-term investors because the geometric return determines how much wealth actually grows over time. A portfolio composition with lower volatility can therefore lead to higher final wealth, even if the average return is the same.
As can be seen from Table 1, the accumulated return falls from 5% to 4.5% at a 10% volatility. This corresponds to a 24%-point lower return over a 20-year horizon or a 122%-point lower return over a 40-year horizon. By reducing volatility from 10% to 5%, the return is only 6.2% points and 32.8% points lower, although the expected return is kept unchanged.
Table 1: Example calculation of volatility drag
Illiquid assets, which are typically reported to have low volatility and low correlation to listed markets, can therefore reduce the portfolio’s overall variance and thereby mitigate the effect of volatility drag. However, it is important to distinguish between real risk reduction and artificial smoothing. Certain illiquid asset classes (e.g. infrastructure and private equity) use valuation models that result in smoother return paths than corresponding liquid assets. Volatility drag is therefore reduced measuredly, but not necessarily financially. However, if the asset also contributes to real diversification – e.g. via exposure to alternative risk premiums – it can contribute positively to the portfolio’s long-term return and risk profile and reduce volatility drag and thus increase the realized return.
Rebalancing premium
The rebalancing premium describes the potential gain that an investor can make by systematically restoring the original portfolio allocation when asset classes deviate from their target weights due to price fluctuations. The idea is particularly relevant in portfolios with volatile but not perfectly correlated assets. By selling relatively more expensive (rising) assets and buying relatively cheaper (falling) assets, the investor can “buy low and sell high” in a systematic process. Rebalancing is not in itself new to institutional investors, as portfolios are usually only allowed to deviate to a certain extent from the strategic asset allocation in order to comply with risk limits. Rebalancing is thus already used, mostly with a focus on risk management. The focus of this analysis, however, is on the return generation through rebalancing.
William Bernstein (1996) popularized the concept as a key advantage of constant-mix strategies, where rebalancing not only reduces risk but can also make a positive contribution to geometric returns.
Bernstein writes that the average annual returns on stocks and bonds between 1926 and 1994 were 10.19% and 5.51%, respectively, giving an arithmetic average return of 7.85% for a 50/50 mix, which is however a theoretical figure, as one must either rebalance or keep a buy & hold portfolio, which has given significantly different returns. An annual rebalancing of this portfolio to maintain a constant 50/50 mix would have given a return of 8.34%, which implies a rebalancing premium of 0.49%. However, Bernstein also notes that if one had placed equal amounts of money in stocks and bonds on January 1, 1926 and had not rebalanced, the return would have been 9.17%. This is because the significantly higher stock return overshadows the bond return over the 69-year period studied; in the last 40 years of the period, the non-rebalanced portfolio consists of more than 90% stocks. Thus, the higher return of the non-rebalanced portfolio comes at the expense of a much higher risk than the rebalanced one.
The annual, statistically expected rebalancing premium of a two-asset portfolio can be estimated by this formula:
Where W = weight of asset 1 and asset 2, 𝝈 = volatility of asset 1 and asset 2, and 𝜌 = correlation coefficient between asset 1 and asset 2.
As Table 2 shows, the higher the volatility of the assets and the lower their correlation with each other, the greater the gain. In practice, however, it is difficult to find asset pairs that have both very high volatility and a negative correlation. An obvious place to look is the commodity markets: Prices of commodities from completely different sectors (e.g. agricultural commodities vs. industrial metals) can have low correlation, while volatility is generally high. Finally, it is important to remember that volatility drag also increases with volatility, so the actual net premium (geometric return) decreases when volatility becomes very high.
Table 2: Rebalancing premium as a function of correlation and volatility
At least in theory, it is possible to generate a return solely from the rebalancing premium, even though the assets have a realized return of zero individually. This is illustrated in Table 3, which shows the return for two assets, a buy & hold strategy, and a rebalancing strategy. By selling a little of Asset B and buying Asset A after year 1, a return of 1.01 kr. is generated, even though the accumulated return of both the individual assets individually and a buy & hold strategy is zero.
Table 3: Example of the rebalancing premium
The size of the realized rebalancing premium depends in the real world on several factors, including:
• Volatility of the asset classes involved
• The correlation structure between them
• Rebalancing frequency and method (time-based vs. threshold-based)
• Transaction costs and tax considerations
Several articles have been written on rebalancing frequency and method, with partly contradictory results. Berstein (1996) found that no single rebalancing period dominates. Monthly rebalancing was best in three cases, quarterly in four, and annual in three. In contrast, Arnott and Lovell (1993) found that regular monthly rebalancing returns dominated less active approaches, while Smith and Desormeau (2006) found that for many of the model portfolios studied, deferring rebalancing for up to four years was better than a monthly or quarterly rebalancing policy.
But regardless of the frequency, there is empirical evidence that even with moderate positive correlation and moderate volatility, the rebalancing premium can over time constitute an important source of return improvement – provided that the portfolio consists of liquid assets that allow for rebalancing.
This aspect becomes particularly relevant in the discussion of illiquid investments: When a larger share of the portfolio is tied up in assets that cannot be rebalanced on an ongoing basis – such as private equity, real estate or infrastructure – the potential to reap the rebalancing premium is reduced. This creates a potential conflict between allocation to illiquid asset classes and the ability to rebalance efficiently.
However, the rebalancing premium is not risk-free: For the rebalancing premium to arise in practice, it is required not only that the asset classes exhibit return rotation over time, but also that their long-term returns are roughly comparable. If one asset class systematically outperforms the other, rebalancing will in the long run reduce the portfolio’s total return. In practice, this often – but not necessarily – involves some degree of mean reversion.
In markets with long-term trends and a lack of return rotation, rebalancing can also lead to lower returns, as was the case during the 2008 financial crisis, cf. Figure 3, where a rebalancing strategy continued to buy stocks in a falling market and thus experienced greater losses than a passive buy & hold strategy. As a result, the return profile of a rebalancing strategy is typically characterized by a concave structure.
Figure 3: Development of a 50% stocks / 50% bonds portfolio during the Financial Crisis
On the other hand, it was an advantage to rebalance during the Covid-19 crisis, which was quickly over and an investor who rebalanced at the end of March 2020 had beaten a buy & hold investor – at least before transaction costs, cf. Figure 4.
Figure 4: Development of a 50% stocks / 50% bonds portfolio during the Covid-19 crisis
This suggests that convex buy and hold strategies provide better returns in markets with a long-term upward (or downward) trend, while concave rebalancing strategies provide better returns in volatile but stagnant markets.
Trade-off between illiquidity and rebalancing premium
The illiquidity premium and the rebalancing premium represent two valuable but potentially conflicting sources of excess return in a portfolio. The illiquidity premium rewards investors for tying up capital in assets with limited liquidity, while the rebalancing premium is created through ongoing portfolio rebalancing, which requires liquid markets. This section examines how these premiums can conflict and illustrates the issue through simulations.
Mechanical conflict between premiums
The fundamental reason for the conflict is the portfolio’s liquidity needs and opportunities. Rebalancing requires that an investor can continuously buy and sell assets to restore the desired weighting. Illiquid assets limit this flexibility, as they typically cannot be sold at market price or on short notice. This reduces the investor’s ability to reap the rebalancing premium when the share of illiquid assets increases.
A high share of illiquid assets can increase the portfolio’s expected return via the illiquidity premium, but at the same time reduce the overall risk adjustment of the return. This is because reduced rebalancing freedom and lower liquidity can increase the portfolio’s risk and reduce the contribution of the rebalancing premium, which is an important source of excess return in volatile but liquid markets.
Optimal portfolio composition is therefore about balancing the desire to reap the illiquidity premium with the need to maintain flexibility and exploit the rebalancing premium.
Simulated portfolio example
To illustrate this trade-off, one can simulate a portfolio consisting of both liquid and illiquid asset classes. To make the input parameters unbiased, I have chosen to base the analysis on return expectations from the Danish Council for Return Expectations.
Table 4 and Table 5 show the input parameters used for the analysis, which are taken from the Danish Council for Return Expectations.
Table 4: Expected return and risk
Table 5: Correlation matrix
The simulation compares two portfolios: One portfolio consisting of 50% stocks and 50% bonds (the rebalancing premium is highest with a 50:50 weighting) and one portfolio with 70% liquid assets (35% stocks and 35% bonds to again maximize the rebalancing premium) and 30% illiquid assets (private equity, real estate & infrastructure), which is a proposal for a realistic allocation. Rebalancing is only possible here on the part invested in liquid assets, i.e. on 70% of the portfolio. The total rebalancing premium is reduced proportionally to the share of illiquid assets. Expected total return is calculated as (expected return + rebalancing premium * (1 – share of illiquid assets)). Sharpe Ratio is calculated as (expected total return / volatility).
See Table 6, the rebalancing premium estimated using Bernstein’s formula is – as expected – largest for the portfolio without illiquid assets. For the portfolio with illiquid assets, the rebalancing premium is scaled by 70% to take into account that only 70% of the portfolio can be rebalanced on an ongoing basis. In contrast, the total return is largest for the portfolio with illiquid assets, which is due to a reallocation from bonds with lower expected returns to illiquid assets with higher expected returns. This increases the expected return by 0.45% points (excess return of 3% points x 15% weight). At the same time, the risk in the form of standard deviation decreases, resulting in a higher Sharpe Ratio, as illiquid assets have a lower standard deviation than stocks and at the same time offer attractive diversification properties. This suggests that illiquid assets in appropriate amounts can improve the portfolio’s risk-adjusted performance.
Table 6: Results of the analysis
The above results are expected returns measured for a single period. Over several periods, volatility drag will apply, which will pull down the geometric return. And the higher the standard deviation, the higher the volatility drag, i.e. largest for the portfolio without illiquid assets. The estimate for volatility drag based on the aforementioned formula is 0.49% and 0.37%, respectively, which means that the expected geometric return for the portfolio including illiquid assets is 0.42%-points p.a. higher than for the portfolio without illiquid assets. That is, in a geometric world (which is the real world in which the pension funds’ customers live) the portfolio is even more advantageous than in an arithmetic world.
By varying the proportion of illiquid assets and measuring the portfolio’s total return, volatility and Sharpe Ratio, the effect of reduced rebalancing freedom and diversification can be quantified. Simulations show that the Sharpe Ratio is highest at 44% allocated to illiquid assets, cf. Figure 5. It is important to note that this is not a free optimization, as the ratio between stocks and bonds is kept constant to maximize the rebalancing premium. Thus, only the proportion of the liquid block and the illiquid block, respectively, can vary.
Figure 5: Sharpe Ratio as a function of the proportion of illiquid assets
Of course, this result depends on the chosen input parameters in the form of expected return, risk and correlation from the Danish Return Expectations Council, which are advantageous for illiquid assets. In addition, the optimal portfolio composition also depends on the investor’s liquidity needs, investment horizon and risk tolerance. Although a 44% allocation to illiquid assets is high, and higher than what many institutional investors can bear due to liquidity constraints, it is not unprecedented in the Danish pension industry. Especially among the occupational pension companies, there are several with over 30% allocated to unlisted investments, and a single example with around 40%.
Conclusion
This article has analyzed the theoretical and practical trade-off between illiquidity premium, rebalancing premium and volatility drag in institutional portfolios. While illiquid assets have historically offered attractive excess returns, their non-tradability limits the investor’s ability to rebalance systematically – and thus achieve the rebalancing premium, which can be significant, especially in volatile and low-correlated markets.
Through simulation based on input parameters from the Danish Return Expectations Council, it has been shown that the portfolio’s risk-adjusted return can be improved up to a certain point by including illiquid assets, but that this gain gradually erodes when the proportion becomes too large, which may be due to the reduction in the rebalancing premium and lack of diversification. This indicates that there is a non-trivial optimal allocation between liquid and illiquid asset classes and the opposing considerations of liquidity, flexibility and return. The optimal proportion also depends on the investor’s investment horizon, liquidity needs and governance structure.
The analysis has also shown that adding illiquid assets can reduce the portfolio’s volatility drag and thus improve the geometric return – all other things being equal. However, this effect must be interpreted with caution, as it is often partly technically conditioned by artificially low volatility (e.g. valuation methods), which does not reduce volatility drag in reality. But it can also be real due to other, alternative risk premiums and thus a real diversification benefit. Since the analysis is based on expected returns and standard deviations from the Danish Return Expectations Council, which takes the smoothing into account, the results must be assumed to be robust.
The analysis indicates that investors do not need to fear giving up too much of the rebalancing premium, as both the improved portfolio characteristics and the higher expected return more than compensate for it. The results are of course dependent on illiquid assets also contributing in the future with both the illiquidity premium and low correlations to traditional asset classes, and that the volatilities of stocks and bonds and their mutual correlation are not significantly different from the input parameters. Higher volatility and lower correlation will, all else being equal, increase the rebalancing premium. However, it is important to point out again that the optimal portfolio composition – in addition to capital market assumptions – also depends on the investor’s liquidity needs, investment horizon and risk tolerance.
The rebalancing premium can be quite significant, especially for assets with high volatility and low correlation, which may argue for a dedicated “volatility harvesting” mandate within volatile markets. On the other hand, the rebalancing premium between stocks and bonds is not large enough to argue for a lower share of illiquid assets, as the illiquidity premium is larger than the rebalancing premium. The conclusion must therefore be that it is not a question of either the illiquidity premium or the rebalancing premium – but of balancing the two in a holistic portfolio strategy.
Literature
Amihud, Yakov and Mendelson, Haim, 1986: Asset pricing and the bid-ask spread, Journal of Financial Economics, vol. 17, issue 2, 223-249
Arnott, Robert D. and Lovell, Robert M., 1993: Rebalancing: Why? When? How Often?, The Journal of Investing, vol. 2, issue 1
Bernstein, W. J. (1996). The Rebalancing Bonus, Efficient Frontier, http://www.efficientfrontier.com/ef/996/rebal.htm
Brown, G. W. and Kaplan, S. N., 2019: Have Private Equity Returns Really Declined?
https://uncipc.org/index.php/publication/have-private-equity-returns-really-declined/
Brown, G.W., Lundblad, C. and Volckmann, W., 2025: Risk-Adjusted Performance of Private Funds: What Do We Know?
https://uncipc.org/index.php/publication/risk-adjusted-white-paper/
Harris, R.S., Jenkinson, T. & Kaplan, S.N., 2012: Private Equity Performance: What Do We Know?, NBER Working Paper
https://www.nber.org/papers/w17874
Kitces, Michael, 2017: Volatility Drag And Its Impact On (Arithmetic) Investment Returns In Monte Carlo Analysis,
https://www.kitces.com/blog/volatility-drag-variance-drain-mean-arithmetic-vs-geometric-average-investment-returns/
Rasmussen, Claus H., 2023: Alternative investeringer: Gearing, skat og risiko – en diskussion, Finans/Invest – nr. 2/2023
Rode, Nils, 2021: The complexity premium: what is it and how does it work?, https://www.schroders.com/en-lu/lu/professional/insights/the-complexity-premium-what-is-it-and-how-does-it-work/
Rådet for Afkastforventninger, 2025: Langsigtede afkastforventninger, www.afkastforventninger.dk
Smith, David and Desormeau, William, 2006: Optimal Rebalancing Frequency for Bond-Stock Portfolios,
https://www.researchgate.net/publication/260019094_Optimal_Rebalancing_Frequency_for_Stock-Bond_Portfolios
Timm, Sina, Lickes, Marc, Vu, Huy, Künzli, Leandro, 2024: Return Attribution in Direct Lending
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5056319