Sunday, 19 February 2012

Thoughts on the Illiquidity Premium

Originally I intended to write a short article on the matching premium under Solvency 2. Unfortunately my draft turned in to a long and meandering rant which I've now consigned to the bin. Instead I'll restrict myself to a couple of paragraphs, preferably with bullet points.

The concept variously called the liquidity premium, the illiquidity premium or the matching premium is well known inside that section of the actuarial population involved in annuity writing, and unheard of elsewhere. The theory is that annuity writers can estimate their future  liability cash ows to a high degree of accuracy, and can buy bonds to match those cash ows very closely. Since they never have to trade the bonds they've bought, they have no inter-temporal price risk, unless the bond defaults. And again, since they are going to hold the bonds to maturity, they are of the opinion that they shouldn't have to mark them to market, they should be able to discount the promised cash ows at risk free, allowing for a historically derived probability of default on a well-diversi ed portfolio. Depending on the market and time period you look at, the di erence between this actuarial calculated value and the market value has historically been about 75 basis points running (probably higher at the moment).

Of course, bonds have a market value and hence can't be marked o -market by the actuaries, so instead they take the spare 75 bps and add that to the rate they discount the annuity cash ows at to value their liabilities. Equally obviously, the annuity writers can't just say that they think there is a 75 bps free lunch on corporate bonds which they will take up-front, thanks very much, instead they have to hide it behind some science, hence the impressive sounding "illiquidity premium ".

The issues I have with this are many and various, but mostly revolve around three points:

  • It's a risk premium. You can't take £100 of equities, project forward assuming a 3% equity risk premium and discount to get a value of £120 (not anymore, anyway. Older pensions actuaries would do well to look a bit embarrased and shu e their feet at this point.) The prices of corporate bonds move together, and they move together with the broader market for nancial instruments. More importantly, default events on bonds are not independent. One cannot assess the risk on a port-folio of bonds the way you can on a portfolio of term assurances. Default events cluster. And when defaults occur, the e ect is catastrophically different from, say, a downward price movement in equities. A default event results in a permanent loss of capital. On the other hand, a 40% annual fall in the value of the equity market can be followed by a similar gain, leaving a (passive) investor in a similar position at the end of the second year as at the start of the first. I can suggest that sceptical readers pick up Giesecke et al. (2011), which is a detailed study of 150 years of corporate bond defaults. An investor in the late 1800's could have seen one third of the bonds in his portfolio default. Again, to repeat, that is not a temporary price movement which may or may not be reversed, that is a permanent loss of one third of capital. Bond defaults cluster. Assets which tend to move together, particularly assets which move together in extreme ways, trade at a discount to their expected values. We call this a risk premium.

  • But let's assume that there is a premium associated with less liquid instruments. How do we measure it? I've seen studies which concluded that it could be zero. Or a couple of bps. The rules of thumb generally used or proposed to divide the corporate spread into buckets associated with default risk premium and illiquidity premium seem arbitrary: along the lines of half the spread minus 40 bps . Trying to calculate the premium using the CDS vs cash bond basis requires many assumptions and approximations and in the end gives an answer which is unstable, often showing a negative premium associated with illiquidity. Other methods which try to be scienti c about the issue come up with equally contradictory or contentious answers. One is left to rely on actuarial judgment.

  • Finally, even if there is such a thing as an illiquidity premium, and even if we could measure it somehow with con dence, why capitalise it upfront? If there is a premium that must be earned by holding these bonds, then annuity writers should realise it as it arises. By marking down the value of their liabilities in this way, they are booking pro ts now which will arise over the course of the next twenty or more years, if at all.

End of rant. Happy to hear that I'm wrong, and that there is some hard data to back up this practice - email me at phil.joubert{@}


Kay Giesecke, Francis A. Longsta , Stephen Schaefer, and Ilya Strebulaev. Cor-
porate bond default risk: A 150-year perspective. Journal of Financial Eco-
nomics, July 2011.