How Much Extra Return Should You Demand For Illiquidity?

In some corners of asset management, marketers are offering to lock up your money to “save you from yourself”. These Samaritans don’t want you to succumb to behavioral biases and overtrading. I’m fine if private funds want to argue that the best opportunities are illiquid (I don’t have to believe them but I’m ok with them making this argument). But don’t tell me your lockups are doing me a favor. Don’t act like you shouldn’t be giving me a discount for tying up my money.

Should You Care About Liquidity Even If You Are Talking About Money You Don’t Need For A Long Time

Perhaps you are one of these people who doesn’t want to put their hands on the wheel. You are self-aware enough to know you’d chop yourself to pieces in the market. First, I commend this level of self-awareness but you still deserve a discount all else equal (I know it never is).

Why?

First of all, your needs or preferences don’t set the marginal price. Don’t be so vain, not everything is about you ūüé∂. The price of illiquid investments are set by those who do care about liquidity even if you don’t. You inherit that discount the same way you get power windows for free nowadays. You get that even if you think you’d be better off with the physical exercise of cranking your own windows.

The second reason why illiquidity deserves a discount or liquidity deserves a premium is liquidity itself is an option. Any argument that says liquidity is bad, whether for behavioral or any other reason, needs to address the value of that option.

Uh oh. Are we going to need to price some abstract option?

Fortunately, no. We can build the intuition from option theory to demonstrate that liquidity is not only valuable, but quantifiably so. It gets better. We can also point to another approach that demonstrates the measurable value of liquidity without pricing options. The best part is its driven by the same underlying logic that makes the option approach work.

Before we start thinking about the value of liquidity, let me start with why I started thinking about this question.

3 things I’ve come across recently have made wonder about how big a liquidity premium is warranted.

1. “Networks of confidence

I was listening to @Jesse_Livermore on the Invest Like The Best podcast.

I’ll paraphrase:

High valuations are increasingly dependent on liquidity or what he terms “networks of confidence”. He refers back to prior work that shows how you’d need a healthy discount to intrinsic to buy an asset you couldn’t sell.

On Twitter, he later posed a cool thought experiment where you price an asset that has no fundamental risk but unpredictable, perhaps zero liquidity in the future. The only thing you can rely on is its unchanging (even in real terms) dividend.

Look through the thread and you will not be able to unsee how little thought we put into pricing liquidity.

2. Illiquid vs Liquid Bonds

I came across this article about US Government EE bonds which showed how a feature of these treasury-issued bonds is, if held for 20 years, you are guaranteed 2x your money back.¬†That means your worst case is you earn a 3.5% CAGR nominally. The catch: they don’t trade in an open market. Compare that to liquid 20 year US treasuries at about 1.5% yield. [Let’s set aside the fact that one can only buy $10k worth of EE bonds per year.]

There is a 2% per year difference in yield if you held both to maturity! That sounds big. But is it? This comparison is a perfect example of why we’d really like to be able to quantify the value of liquidity.

3. Insurance products

I know someone who is considering jamming a bunch of savings into an insurance product that “guarantees” around 3.5% per year if held for about 25 years. I don’t want to turn this into a post about insurance, I have enough brain damage from the email threads I’m privy to. The larger point is there are products where you can earn more yield for sacrificing liquidity even after after adjusting for the credit risk and the actuarial features of these products. (PSA: If you are interested in getting technical about insurance my buddy @RajivRebello covers it from the institutional side. In other words, he understands the math and levers in ways you cannot pry out of retail brokers.)

Hopefully I have convinced you that a) liquidity is worth a premium and b) we are faced with real-life comparisons that beg us to price it.

How big should the liquidity premium be?

As I alluded earlier, there are 2 frameworks in which I have started to think about this. Let’s start with the approach I found personally more intuitive (although I suspect most of you will find the second approach more natural).

The Liquidity-Is-An-Option Replication Approach

First, what’s the obvious advantage of liquidity?

You can cut risk.

The fact that a market is willing to show you a bid for your investment at all times has a real theoretical value. That may sound abstract but the entire options market is actually built upon that idea. Let’s see how.

Go back to the untradeable EE bond vs the 20 year treasury. The nominal EE bond has a nominally guaranteed CAGR of 3.5% if held to maturity. But it’s real return is not guaranteed. In real terms, you can technically lose 100%. In contrast, the liquid treasury bond can be sold. If you placed a stop order on it, you can create one of those hockey stick payoff diagrams where the most you can lose is your stop price.

So…you have created an option. This was the entire basis of portfolio insurance.

[reader recoils ūü§ģ]

I know, I know.

1987 ruined the term portfolio insurance. But the reality is some version of it is done every time a market maker sells an option and delta hedges it. The market maker is trying to dynamically replicate the option they have sold. They are “manufacturing” a long option.¬†The market maker hopes the accumulation of losses due to negative gamma (buying high and selling low) is less than the premium they collected up front for the option.

The key here is to recognize that the ability to “manufacture” an option by trading is possible because of liquidity.

Sure, there are caveats. The “manufactured” option fails in the presence of gaps. It’s not as valuable as “hard” or contractual optionality. 1987, in fact, makes my point…the constraint on theory is liquidity. Liquidity is valuable in itself because it sustains options. And options are good.

[aside: options are valuable because they allow you to fine tune risk. Slice & dice the expressions of your desired exposure or lack of exposure. Equity is an option. Capital structures allocate options according to what shape of risk people are willing to take. Some investors require insurance. Some investors only equity, while others may prefer debt. And there are some debt holders who want CDS, another type of option that can be relative-value arbitraged against vanilla options]

Back to the bonds…

So we can think of a liquid bond as having an option to sell that the EE bond does not.

Liquid bond = EE bond + Option

What’s that option worth? Pricing the option (if we assume the market is continuous) will be an exercise in portfolio insurance-esque replication.

The recipe will look something like this:

1. Pick some theoretical strike price (ie maybe a desired stop price)

2. Estimate what option is worth

3. Add it to the cost of an EE bond that guarantees 3.5% for 20 yrs.

Compare the portfolio comprising a 3.5% EE bond + this theoretical option  to a portfolio which simply holds the 1.5% treasury and you are taking a big step toward quantifying the value of liquidity!

That identity one more time:

Liquid bond = EE bond + Option

What is the main driver of the option’s value?

Volatility.

The premium we are willing to pay for liquidity depends on volatility. The higher the volatility the more the liquidity option is worth and the larger the gap should be between a liquid and illiquid price. 

It’s interesting to consider in light of recent valuations. The more volatile the future is, the bigger the discount we should ascribe to illiquid assets. Today, with implied vols relatively elevated, private investing should be worth less if all else is equal. (I expect private managers to claim that all the alpha is in private markets which is an argument they are entitled to)

To restate the main point of the liquidity-as-an-option replication approach:

Increased volatility raises the value of liquidity because it raises the value of the option embedded in the ability to trade.

I mentioned there’s a second framework for valuing the premium we can ascribe to liquidity.

Rebalancing premium

The ability to rebalance your portfolio is valuable.

Here’s an intuitive demonstration:

Markets take a dive. Pretend 1/2 your wealth was in stocks and 1/2 in your home. If homes were down more than stocks, you could sell stocks & upgrade your home while restoring a 50/50 allocation.

In Lessons From Coin Flip Investing, I showed how rebalancing between a coin flipping investment and a positive expectancy investment enhances performance. Specifically, rebalancing pushes your geometric return up towards the expected arithmetic return (remember geometric returns are lower than arithmetic because of volatility drain). You earn a “premium” for rebalancing.

There are 2 main drivers of the rebalancing premium.

  • Volatility¬†

    The size of¬† the premium is a direct function of volatility since the drain is half the variance. This should be satisfying — the option replication framework also said that volatility increases the value of liquidity.

  • Correlation

    A full explanation would be out of scope here. Instead, I direct you to
    @breakingthemark and his blog. His recent post, The Great Age of Rebalancing Begins, shows how lower fees/spreads provide unprecedented opportunity to capture “Shannon’s Demon” — the underlying concept behind rebalancing premium first identified by Claude Shannon.¬†

Key Takeaways

  • Liquidity-As-An-Option and rebalancing premium are 2 ways to price the value of liquidity
  • Both methods agree — the greater the volatility, the more liquidity is worth.
  • You should get a better deal for accepting less liquidity

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