Interaction between opaqueness and illiquidity in an investor’s portfolio
Accounting & Finance / 24 September 2015
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Professor of Finance
Grigory Vilkov is a Professor in the Department of Finance at Frankfurt School of Finance & Management and the Academic Director of the Master of Finance. Grigory's research topics include the use of derivative instruments and option-implied information in asset pricing and portfolio management, and general equilibrium modeling with frictions.

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by Adrian Buss (INSEAD – Finance), Raman Uppal (EDHEC Business School; Centre for Economic Policy Research) and Grigory Vilkov (Frankfurt School of Finance & Management; Research Center SAFE)
Traditional models of portfolio choice and asset pricing assume that assets are liquid and can be traded without cost. While this is a reasonable assumption for government securities and publicly traded stocks of large companies, there are substantial costs for trading alternative asset classes, such as private equity, stocks of smaller companies, hedge funds, and real-estate funds. Evidence shows that institutional real estate transaction costs are often above 3%, the bid-ask spreads for smaller firms can be 10%, and costs of private equity transactions can exceed even 10%, and, consequently, the interval between trades in these assets can span long periods. Even within liquid asset classes, subclasses can be highly illiquid, e.g., stocks in pink-sheet OTC markets may not trade for a week, and municipal bonds typically trade twice per year.
These alternative assets typically do not have long histories and regularly observed market values, and the returns from investing in these assets are less transparent than the returns from public equity. Knowing that investors’ expectations are influenced by their personal experience even in transparent markets, we allow investors’ experience to play a crucial role in forming expectations for alternative asset classes. The empirical findings regarding the importance of personal experience are mirrored by the following quote from Albert Einstein: “The only source of knowledge is experience.”
The interaction between opaqueness and illiquidity raises fundamental questions about asset allocation, asset pricing and their dynamics. How does the interaction between opaqueness and illiquidity affect an investor’s portfolio? Should inexperienced investors hold alternative assets at all, and how should they revise their portfolios over time as they gain experience but face substantial transaction costs? What risks arise because of illiquidity and investors’ inexperience? What are the consequences for asset prices and risk premia and their evolution over time? 
Our key results are as follows. When one asset is opaque, the inexperienced investor recognizes the estimation risk inherent in this asset, and so she optimally reduces her initial holdings of this asset. This is accompanied by an increase in the holding of the liquid equity index, and, driven by the desire for precautionary savings, a substantial increase in holdings of the bond. On the other hand, because of market clearing, the experienced investor’s initial holdings of the alternative asset increase with its opacity. Consequently, neither investor holds the fully diversified market portfolio. As investors gain experience, they increase their investment in alternative assets. These asset-allocation characteristics are consistent with the empirically observed behavior of institutional investors: private (Ivy League) endowment funds have increased their target allocation for alternative assets over the last decades as they acquired (positive) experience and, nowadays, strongly overweight alternative assets in their portfolios. In contrast, relatively inexperienced endowment funds invest only marginally in alternative assets. A consequence of this asset allocation in our model is that the volatility of the inexperienced investor’s consumption growth is lower than that of the experienced investor. However, in exchange for “insuring” the inexperienced investor, the experienced investor earns a higher expected return on her wealth. In line with this, empirical research shows that endowment funds that entered earlier into alternative assets achieved higher returns and attribute this success to the importance of experience in interpreting ambiguous data.
Surprisingly, because of the interaction between inexperience and illiquidity, the inexperienced investor’s optimal initial holdings of the alternative asset can be larger with illiquidity. The intuition for this is that ideally the investor would like to start with a low holding of the alternative asset and increase this position over time as she gains experience. However, this would generate substantial trading costs. Accordingly, inexperienced investors that are new to an alternative asset class trade off the higher risk of initial over-investment versus the cost of future rebalancing. If the transaction cost dominates, it is optimal for such investors to reduce the portfolio tilt away from the alternative asset, and thus, hold more initially. Transaction costs also induce portfolio inertia. Consequently, in the presence of transaction costs, the inexperienced investor could end up holding a majority of the alternative asset over time even if she is more pessimistic about its growth rate than the experienced investor. This effect is driven by prior beliefs and the reluctance to change portfolio holdings in the presence of transaction costs.
As expected, transaction costs for trading the alternative asset reduce its turnover. This also triggers a decrease in bond turnover because the bond is used to finance trade in the alternative asset. However, the turnover of the liquid risky asset increases because it is used as a substitute for trading the alternative asset. This “spillover” effect can be so significant that the inexperienced investor’s holdings in the liquid risky asset track perfectly the dividend dynamics of the alternative asset, introducing excess correlation and leading to more volatile holdings in the liquid equity index.
With transaction costs for the alternative asset, its price drops and this is mirrored by an increase in its expected return and also its volatility. For a transaction cost of 5%, we find an average price discount of more than 4% and a maximum discount of more than 12%, consistent with empirical data. The price discount also implies a sizable increase in expected returns, in line with empirical evidence. Contrary to intuition, the illiquidity discount is stronger for moderate transaction costs than for full illiquidity. That is, the price discount is larger in a setting where investors incur a cost for trading the asset, compared to a setting where trade is precluded exogenously. Because the bond and the equity index serve as substitutes to the alternative asset, their prices increase in the transaction costs for the alternative asset.
Read the original paper.