#### Asset Valuation & selection in Illiquid Markets via aswathdamodaran

In my last post, I looked at how the asset allocation decision can be altered by differences in liquidity across asset classes, with the unsurprising conclusion that investors who desire liquidity should tilt their portfolios towards more liquid asset classes. Assuming that you have made the right asset allocation judgment, how does illiquidity affect your choices of assets within each class? In other words, if you have decided to invest 40% of your portfolio in stocks, how does illiquidity affect which stocks you buy?

To select assets within each asset class, you can either value each one on its fundamentals (intrinsic valuation), compare its pricing to how similar assets are priced (relative valuation) or price it as an option (contingent claim valuation). In each case, illiquidity can affect value.

a. *Intrinsic Valuation*: There are many different intrinsic valuation approaches but they all share a common theme. The value of an asset is a function of its expected cash flows, growth and risk. In discounted cash flow valuation, for instance, the expected cash flows discounted back at a risk adjusted discount rate yields a risk-adjusted value. In conventional valuation, the expected cash flows are unbiased estimates of what the asset will generate each period and the risk adjustment is for non-diversifiable market risk (with equity) and for default risk (with debt). Nowhere in this process is illiquidity considered explicitly. Not surprisingly, we tend to over value illiquid assets.

So, how do you bring illiquidity into intrinsic valuation? There are two choices. The first is to estimate the risk adjusted value, using the conventional approach, and to then reduce this value by an *illiquidity discount*. That discount can be estimated by looking at on how the market prices illiquid assets. For instance, studies have looked at restricted stock (stock issued by publicly traded companies that cannot be traded by investors for one year after the issue), pre-IPO transactions (where co-owners sell their stake in the months prior to an announced IPO) and companies with multiple classes of shares traded on different venues (with different liquidity characteristics). These studies generally yield large discounts (25-50%) for illiquid assets and private company appraisers have generally used these studies to back up the use of similar discounts when valuing non-traded businesses. Perhaps, this approach can be extended to publicly traded companies.

The second is to adjust the discount rate for illiquidity, pushing it up for illiquid companies. The illiquidity premium added to the discount rate is usually estimated by looking at the past. In its crudest form, you can assume that the premium that small cap companies or venture capitalists have earned over the market (about 3-4% on an annual basis over the last few decades) is due to illiquidity and add that number on to the cost of equity of any “illiquid” company. In its more sophisticated version, the adjustment to the discount rate can be linked to a measure of illiquidity on the company – its turnover ratio, trading volume or the bid-ask spread. One study concludes that every 1% increase in the bid-ask spread pushes up the discount rate by 0.25%. Thus, the cost of equity for a stock with a beta of 1.20 and a bid-ask spread of $0.50 (on a stock price of $ 10), with a riskfree rate of 4% and an equity risk premium of 6% is:

Cost of equity = 4% + 1.20 (6%) + 0.25% (.5/10) = 12.45%

With both approaches, the value will decrease with illiquidity.

b. *Relative Valuation*: In its most common form, relative valuation involves screening the market for cheap companies, with one screen for pricing (low PE, low price to book, , low EV/EBITDA) and one or more for desirable fundamentals (high growth, low risk, high ROE). If you ignore illiquidity, your cheap stock portfolio will end up with a lot of illiquid stocks. The simplest way to incorporate illiquidity is to add it as a screen. Thus, in addition to screening for high growth and low risk, you could also screen for high liquidity (high float, high turnover ratios, low bid-ask spreads, high trading volume etc.). The tightness of the liquidity screen can then be varied to fit your liquidity needs as an investor.

c. *Contingent Claim Valuation*: All option pricing models are built on two principles: replication (where a portfolio of the underlying asset and a riskfree investment is created to have the same cash flows as the option) and preventing arbitrage (the replicating portfolio and the option have to trade at the same price) . Both principles require liquidity: you be able to trade the option, the underlying asset and the riskfree asset in any quantity and at no cost. Illiquidity in any one of these markets will throw a wrench into the process and cause the option pricing models to yield incorrect values, with the imprecision increasing with illiquidity. So, what are your choices for bringing illiquidity into the process? You can try to modify the models to incorporate illiquidity explicitly but option pricing models are complicated enough already and this adds an additional layer of complication. Alternatively, you can adjust the inputs into the option pricing model. My choice would be the underlying asset value (S): using a lower value for illiquid underlying assets will reduce the value of call options on those assets.

In summary, no matter which approach you use, illiquidity is not a neutral factor. The investments you make within each asset class will reflect both the illiquidity of the investment and your own liquidity needs (and preferences) as an investor.

*I have a paper on the effects of illiquidity on financial theory, where I examine the effects of liquidity on valuation in more detail:*

*http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1729408*