# Asset allocation for illiquid markets

In my last post, I argued that illiquidity is not a minor problem restricted to a few stocks. In fact, it can affect all stocks, at least during some time periods, with its effect varying across stocks. I also noted that much of financial theory is built around the presumption that markets are liquid.

So, how would financial theory and practice change, if illiquidity is explicitly incorporated into the process? Let's start with the first step in investments, asset allocation, where you decide how much of your overall wealth you will invest in different asset classes - treasuries, corporate bonds, stocks, real estate, collectibles. In fact, defining asset classes loosely, private equity, hedge funds and mortgage backed securities can be considered new entrants in the game, vying for portfolio dollars.

In the classic mean variance framework, the optimum asset allocation mix is the one that maximizes expected returns, given a risk constraint. Thus, you feed in the expected returns and standard deviations of different asset classes, in conjunction with their covariances with each other, and let optimization work its magic. Here is the catch. The average returns, standard deviations and correlations all come from historical data. With illiquid asset classes, standard deviations tend to be under estimated (for a completely illiquid asset, there will be no trading and the standard deviation will be zero) and the covariances consequently will be misestimated. In fact, the least liquid asset classes often look like they offer the best risk/return tradeoffs, if you don't control for illiquidity. Plugging these values into the optimization framework will generate weights that are too high for the illiquid asset classes, for the typical investor. In the last decade, especially, this has led many endowment funds to over invest in real estate, private equity and hedge funds, categories notoriously over exposed to the vagaries of illiquidity.

So, how would you bring illiquidity into the mix and what are the consequences? There are two routes you can follow. In the first, you adjust the expected returns of illiquid asset classes downwards to reflect the expected cost of illiquidity. That would make these asset classes less desirable and counter act the underestimation of standard deviations. The other is to restate the optimization problem thus: Maximize expected return subject to the constraints that risk be below a "stated" level and that liquidity be greater than a specified constraint.

With both approaches, the "right" asset allocation mix will vary across investors. Investors who desire or need more liquidity will tilt their portfolios towards more liquid asset classes (large market cap stocks, highly rated corporate bonds) . Investors who value liquidity less may actually gain by tilting their portfolios away from more liquid asset classes towards less liquid ones (real assets, small cap and low priced stocks, low rated corporate bonds).*I have a paper on the effects of illiquidity on financial theory, where I look at asset allocation in more detail:**http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1729408*