Worthwhile Canadian Initiative

Liquidity and risk: liquidity as the value of an option to sell at the market price

Is this a risk crisis or a liquidity crisis? What's the difference?

We can define "risk" and "liquidity" any way we like, but some definitions are more useful than others. A useful definition would explain why "risky" assets need high yields to make people willing to hold them, and why "illiquid" assets need high yields to make people willing to hold them. And useful definitions of "risk" and "liquidity" would allowed us to distinguish the two.

Here's my distinction between risk and liquidity:

The value of an asset can be decomposed into two parts: the value of the stream of dividends (where redemption counts as a final dividend) to the owner of the asset; and the value of the right (or option) to sell the asset at any time at the market price. We should use "risk" to talk about the effect of uncertainly on the value of the stream of dividends; and use "liquidity" to talk about the value of the right to sell the asset. The value of liquidity is the value of an option to sell at the market price whenever I choose to exercise that option.

"The Bank of Canada should peg the TSE 300" - revisited

"The Bank of Canada should peg the TSE-300" is the title of a Carleton Economics Department working paper I wrote in 1992. (Sorry, but no web version available; this was in the olden days when all we had was paper, and when the TSX was the TSE.) Given the recent turmoil in financial markets, and the renewed interest in having central banks look at asset prices, I was wondering whether to resurrect this paper, but dithered. Now Roger Farmer has beaten me to it. Mark Thoma posted it on his blog, and Tyler Cowen on his.

The reactions in the comments are mostly either unfavourable, or incredulous. I thought I would write a few words in defence of the idea, and then say why I no longer support it.

Trading volume, liquidity crises, Carl Menger, and "off-the-run" bonds

An asset which becomes less liquid (the costs of trading it increase) will be traded less frequently. If an asset is traded less frequently, it will become even less liquid.....

An asset which becomes more liquid (the costs of trading it decrease) will be traded more frequently. If an asset is traded more frequently, it will become even more liquid.....

Why did Liquidity Fall? How does Illiquidity affect asset values?

In a previous post, I argued that assets became less liquid in the last couple of months, and that the fall in liquidity might have been a major cause of the fall in asset values. So, why did liquidity fall?

There's a literature based on a model of informed traders, uninformed traders, and "noise" traders (better called "liquidity traders"). Robert Waldmann knows that literature better than I do, and has a post, similar to mine, in which he also offers an explanation of the fall in liquidity.

Here's my own very simple model of liquidity. It explains why a small initial shock to asset values could have a much larger effect on equilibrium asset values by making assets less liquid.

Liquidity, Time Preference, Brad DeLong, and the missing $20 trillion

Brad DeLong has an excellent short essay on the financial crisis. Read it.

I disagree with one part of it:

Liquidity Discount: The cash flowing to capital arrives in the present rather than the future, and people prefer — to varying degrees at different times — the bird in the hand to the one in the bush that will arrive in hand next year. Fluctuations in this liquidity discount are yet a fourth source of fluctuations in global capital wealth.

That's not liquidity; that's time preference. Liquidity can explain the missing $20 trillion, even if time preference can't.

Welfare costs of the business cycle and the equity premium

In many ways, Robert Lucas' famous estimate of the welfare costs of the business cycle is a restatement of the equity premium puzzle. If you take a standard model in which consumer preferences are time-separable, iso-elastic and have 'plausible' levels of risk aversion, then the fluctuations in marginal utility associated with unanticipated movements in consumption generate welfare losses that are much too small to justify either a high risk premium for stocks or the degree to which macroeconomic policy analysts have been preoccupied with the business cycle.

So if you were able to come up with a model that can explain the equity premium, there's a pretty good chance that it'll generate estimates for the welfare costs of the business cycle that are much larger than what Lucas calculates. And there are at least two theoretical approaches that reach just that conclusion.

Flawed discounting of the Stern report

Max Wilkinson has a go in the Financial Times, complete with an over-the-top headline: Stern's report is based on flawed figures. The issue is Stern's choice of using a discount rate of 2-3% a year to discount the future costs of global warming:

[T]he actual figure used by Sir Nicholas seems to have been between 2 and 3 per cent, less than half the rate that the UK Treasury now uses for assessing large capital projects and much lower than the private sector would expect...

A higher discount rate, predicated on a high economic growth rate and more in line with commercial realities, would discount future costs so that they appear much smaller to today’s consumers and taxpayers. It would make the costs of global warming in 100 years’ time appear small or even negligible in present-day terms.

As far as I can tell, pretty much every structural macroeconomic model makes use of a rate of around 3% to discount future utility. Since there are many reasons to think that an even lower rate is appropriate for an analysis of climate change, it's probably quite sensible to consider slightly lower values as well.

As far as the arithmetic goes, Wilkinson has a point: a higher discount rate would indeed significantly affect the present-value calculations. But there's no earthly reason to think that the proper discount rate is the one used to discount the returns from a capital investment project. The return on those sorts of investments incorporate a risk premium over and above the rate at which the investor discounts future utility. For most investments, that risk premium is positive, since their payoffs are generally positively correlated with movements in consumption. But since the benefits of of addressing climate change are unlikely to have any particular correlation to movements in consumption (i.e., the business cycle), the appropriate risk premium for discounting the benefits of slowing global warming is approximately zero.