That innate volatility may derive from the funding model or from the business sector in which the company operates.
A clash of cultures
When trying to dissect concepts such as the discount for illiquidity, there seem to be two distinct approaches – the computational disciplines and the behavioural sciences. In much of the literature the computational approach is in the ascendant. One computational approach argues that investments with no volatility should have no discount for illiquidity. The behavioural scientists recoil at this.
The Longstaff lookback option
Professor Longstaff attempted to describe the upper bound for the illiquidity discount by using option pricing theory. He has described this by imagining an investor who is blessed with perfect market timing, who can buy at the trough and sell at the peak of the market. For such a person the cost of not being able to trade can be computed by reference to the highest price spike that the investment achieved during the assumed period of illiquidity.
He has presented his findings in a complex formula with volatility and lockout period as inputs, all built on the formula for a normal distribution. This is known as the Longstaff lookback option. This, together with a detailed exposition of its use in practice, is available in a paper entitled, New Insight into Calculating Discounts for Lack of Marketability.
This paper computes the upper bounds for illiquidity as being 8.2%, 17.0% and 26.3% for a 1 year lockout with volatility of 10%, 20% and 30% respectively.
A possible way forward?
This is promoted as being a scientific means of reducing the speculation of the appropriate discount for lack of marketability. However, some are horrified at this thought and offer the following challenges.
- Under this approach an investment with no volatility has no discount, despite the fact that it cannot be realised for the lockout period. This cannot be readily supported, and is contradicted by empirical evidence, despite the theoretical arguments based on arbitrage.
- The approach does not apply a higher illiquidity discount when considering a control holding and a small minority holding in a private company, unless the assumed lockout period is extended for the latter.
- The marginal investor will have neutral market timing abilities; the investor with perfect market timing is a creature of the imagination who almost certainly does not exist. However if she does exist she would have no interest in trading in anything other than the most liquid markets in any event. She is not a market participant for the valuation of illiquid investments.
- The model has no regard for the investor who wishes to realise her investment rapidly for whatever reason: she may have recently been made redundant or have been faced with an unexpected large domestic expense. Whatever the cause, what she requires is to turn her investment into cash. She has no thoughts of arbitrage as a means of resolving the situation. She will therefore, almost certainly, have applied a lower value to any investment which did not allow a simple, clearly marked path to the exit door.
Searching the rubble
We have to ask if there is anything to salvage from the ruins of the Longstaff approach after such an onslaught. Perhaps surprisingly, there probably is. The innate sector volatility is one of the variables when thinking of illiquidity. The second variable in the model, the time period to realise, is also a relevant factor. However, there are demonstrably other variables.
In addition to volatility and time to sell, we can expect the discount for illiquidity to be in part, a function of:- differences in the hypothetical bid-offer spreads;
- the fear of faulty information being provided to the buyer;
- the likely costs of management and supervision if within a portfolio of investments;
- the relative size of the company concerned; and
- the relative liquidity of its balance.
No allowance in the capital asset pricing model (CAPM)
It is notable that the CAPM, derived as it is from modern portfolio theory (MPT), does not include an adjustment for relative liquidity. Any concept of relative illiquidity has been assumed out of existence, together with such troublesome variables such as transaction costs and bid-offer spreads.
Under MPT, markets are assumed to be perfectly liquid with no friction; it is also assumed that everyone can either borrow or lend at the risk free rate of return.
The small stock premium?
A small stock premium may help to account for this aspect of relative illiquidity. It is almost certainly the case that such an adjustment does include some illiquidity component. There are increasingly vocal challenges to the very existence of the small stock premium. However, if it does exist, there is a strong argument that it may reflect, at least in part, an illiquidity discount.
For the disciples of this view the application of a small stock adjustment and a liquidity adjustment may involve some double counting.
The costs of transacting and buyer’s remorse
Professor Damodaran has linked the illiquidity discount closely to the differentials in the costs of transacting. He has identified those costs as being:
- The direct costs of brokerage and other transaction costs (these must include due diligence);
- The bid-offer spread;
- The prospect of the transaction moving the market price;
- The opportunity costs whilst waiting to trade.
He uses a memorable phrase, buyer’s remorse, to explain one aspect of illiquidity and if a buyer regrets a purchase the costs of that regret for very liquid assets are modest. The more illiquid the asset, the greater is the cost of that buyer’s remorse.
As the costs of transacting in equities in the USA are higher than the costs of bond transactions, especially in the enormous market for US treasury bonds, there is a view that a part of the equity risk premium is effectively only compensation for those higher costs.
It must be the case that higher transaction charges should have an impact on the pricing of investments which cannot be freely traded in a liquid market. However that adjustment must be based upon perceptions of holding periods. If an investment is to be held for the ultra long term, such future costs may not have a material impact on pricing.
In the third article I will look at information asymmetry between buyer and seller and the impact that this may have upon value.
Andrew Strickland, Scrutton Bland
Valuation Group, October 2015