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*

## 3 comments:

Professor,

It sounds scientific, yes infact we need to factor in liquidity factor in portfolio optimization problem. But i don't see (at least on the top of mind) any compatible liquidity measure which can be factored in as a mere constraint in the optimization problem without restating the complete problem. Can you suggest any such measure which helps me here??

i guess risks related to illiquid assets from the price-movement perspective can be factored.. i guess ill throw a poison type random variable in the mixture.. definitely the optimization/control problem will change.. irl.. i think, nobody uses quadratic programming..its too elementary and applies to text-books ,strictly

My point is not that you do a full fledged optimization. It is that illiquid asset classes look far better on a historical risk/return table than they really are. In fact, I have seen proponents of alternative asset classes use their historical risk/return numbers to push investors to invest more in them. That was the story used to push private equity and hedge funds to endowments in 2006 and 2007. Last week, I read an article suggesting that investors invest in fine wine, because it offered a great risk/return trade off. My only response was that if it did not work out, you could at least drink away your sorrows.

Post a Comment