Estimating the cost of illiquidity

Since I invest mostly in small or very small listed companies with limited liquidity I have for some time been thinking about how to incorporate the cost of this into valuations.

In a private placement the cost can be even higher. This came to the fore a couple of months ago when I invested in Elementica. There I relied on the good old gut and increased my discount rate a couple of % to account for the illiquidity.

Being a believer in combining learning(reading) with doing I was happy to come across a chapter on this in Aswath Damodarans Strategic Risk Taking (by the way, this book seems very much like an earlier, simplified, version of his Investment Valuation, which I’d recommend instead as a purchase).

The professor brings up four ways of adjusting the valuation for liquidity.

A post-valuation fixed percentage discount

Valuations come up in tax litigation and there standard practice has been to discount private firms 25-35 percent compared to public firms due to reduced liquidity. This figure comes from old studies on the discount for restricted stock offerings, where the same instrument is priced is open to two differently sized sets of investors. The stock market as a whole, and the owners of the company.

This figure seems too large, and the tax authorities have in some recent cases succesfully argued for smaller discounts based on.

Firm specific discount

Estimate a firm-specific discount considering a number of things

Liquidity of assets. If the assets of the company are very liquid it should not matter as much that the company itself isn’t since assets can be sold. This mostly applies to transactions where control of the company is transferred.Liquidity of assets

Financial health and cash flows. Financially healthy companies with positive cash flows need to be discounted less.

Possibility of IPO. If there is a substantial possibility of an IPO there is less need for an illiquidity discount.

Size of the firm. Larger firms should be discounted less.

Control component. Investing in a private firm is more attractive if a controlling stake is aquired. Thus a 51% stake can be substantially more valueable than a 49% stake.

To this list I would like to add another that I think matters: The number of owners.

Bid-ask spread as a proxy

The bid-ask spread can be used as a proxy for cost of liquidity. It is a lower bound, since even when the bid-ask spread is crossed there might only be a small volume there. Thus leading to additional costs in the form of opportunity cost of waiting to trade or more bid-ask spreads being crossed.

Two options: If traded, use the average historical bid-ask spread of the company you are valuing.

Alternatively, use a formula that statistically predicts the spread:

Spread = 0.145 – 0.0022 ln (annual revenues in $) – 0.015 (ERNN) -0.016(cash/firm value) – 0.11 (monthly trading volume/firm value)

where ERNN = 1 if earnings are negative and 0 if earnings are positive. This regression was done in 2000 so should be taken with a grain of salt.

Option-Based Discount

I’m not going into this one since in much detail. The basic idea is to value an option and use it as a proxy to cost of illiquidity.If for instance you are entering a private placement that will IPO or go bust in two years the cost of illiquidity can be viewed as an at-the-money put option with a two-year life.

To me this approach seems like a bad idea since option pricing models are notoriously bad at non-normal distributions with fat tail and event risks. Which is exactly the type of thing which is common for illiquid companies.

Conclusion

These are some options that can be used to explicitly estimate the cost of illqiuidity. If this approach is choosen care needs to be taken not to let the illiquidity also creep into other parts of the valuation, e.g. discount rates.

Obviously the cost of liquidity will vary across different investors. Those investing large amounts of money and trading frequently will be much more sensitive to liquidity than smaller investors using strategies that trade infrequently. Thus the adjustment for liquidity will need to be tailored to your own circumstances.

The cost of illiquidity is for individual investors mostly relevant in private companies and small caps.

Investing in small firms it easier to find information that has not reached the market. But the transaction costs are also higher. Broker costs are usually a minor part if small companies. Cost of spread + opportunity co going forwardst of not trading are substantial. Often people on message boards and forums of small companies equate their valuation to companies hundreds of times larger and believe the PE should be the same. The cost of illquidity is but one of many reasons this is not true (less auditing is another). pain in downturns.

My own approach has so far been to implicitly penalize companies with bad liquidity through higher discount rates. This is a very subjective way, and the change in discount rate is close to a pure guess. The mental models in this post should be useful to guess a little better.

Food for thought: Can there be value to illiquidity? If the illiquidity is complete, i.e. private placement = no prices. I would argue YES. It both prevents a twitchy trading finger and decreases the pain of a dwindling account balance.

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