Calculation of the Term Structure of Liquidity Premium

10/15/2014 02:59 AM

Traditionally, liquidity has been defined as:

  • A Russian problem;
  • An Asian problem;
  • Someone else’s problem;
  • A broker’s problem;
  • Not something to worry about since it is guaranteed by the Central Bank; or,
  • All of the above.

Even the Bard has commented on liquidity with the rather pithy ‘put money in thy purse’!

The fact is that most of us are in agreement that liquidity is an important risk element but it is also indisputable that we probably spend less time thinking about it than any other risk category. From an enterprise wide risk management point of view, the need for the integration of liquidity, market and credit risk was recognised after the Russian crisis (August 1998) and the “flight to quality” that followed.

In this context, liquidity risks can be defined as the risks arising when an institution is unable to raise cash to fund its business activities ( funding liquidity), or can not execute a transaction at the prevailing market prices due to a temporary lack of appetite for the transaction by other market players (trading liquidity). It is the former that we seek to comprehend and compute in the sections that follow.

The term premium liquidity preference theory postulates that investors demand a risk premium for holding long term instruments, owing to risk aversion against the undiversifiable risk of interest rate changes, which compounds over time and hence affects longer term instruments most. This does not imply that longer term holdings are any less liquid when compared to other investments. Yield to maturity on long term instruments of different maturities depends on investment horizon, which may be specific for individual investors. This is due to the fact that different borrowers have different risk ratings and depending on the organisation’s risk appetite, credit spreads are added to the interbank rates to structure a ‘risky’ yield curve, and this results in the addition of a reserve against foreseeable potential loss of principal.

Differing lengths in the lending period correspond to different degrees of uncertainty about future events. Very little change takes place in the political or economic structure of a nation or the world in any given year–the short-term. However, over a long period of time typical for some types of structural Government borrowing (T-Bonds) and private borrowing (home mortgages), massive changes may take place in rates of inflation, political conflict, and the global balance of power. In the long-term tremendous uncertainty exists and yet there are institutional lenders that actively seek the long term. For example, pension funds and life insurance companies that need to plan for exact financial obligations well into the future, are not surprisingly, key players in the longer-term instruments arena.

An important consideration with respect to the liquidity premium is that lenders have more flexibility with regards to the length of the lending period relative to borrowers. Many borrowers enter the long term market precisely because the nature of their project is long term. For these projects to be financially feasible the borrower needs to rely on a long continuous stream of revenues to repay the debt. Such projects are just not possible in a one to ten year horizon. Many home owners find that housing is affordable only if they can stretch the loan payments over a 20-30 year period of time given their annual income.

Lenders, however, have a choice. A lender can make a loan for 5 years or that individual can make six sequential six-month loans. The 5 year loan locks in an interest rate for the duration of the loan at the prevailing long-term rate whereas the sequence of six medium-term loans exposes the lender to changes in nominal rates each time the funds are reinvested. The long-term loan exposes the lender to the uncertainty of distant future events in contrast to the medium term sequence which allows the lender to react to changing economic conditions. There is a balancing act taking place between uncertainty about future economic conditions and the direction of future interest rates.

The liquidity premium will be directly influenced by expectations of future short-term rates. The actual derivation of liquidity and risk premia take place in financial markets through the process of buying and selling financial instruments, and this paper seeks to explore a methodology for the computation of a term structure for this premia.

Implied forward computations of interest rates can be used as a starting point to arrive at the possible future rates that the lender may use to manage interest rate risks. Therefore:


I(r)t = Estimation of forward rates for time t

r = Interest rates

ti2 = Interest rates for time-period 2

ti1 = Interest rates for time-period 1

The difference between the implied forward rates in a risk-free curve and in a ‘risky’ curve is a difference on account of the credit risk inherent in the lending and the term structure of the liquidity premium. Therefore:

LP(t) = Liquidity Premium at time t;

IF(rfree)(t) = Implied forward rate of the risk-free curve at time t;

IF(risky)(t) = Implied forward rate of the risky curve at time t;

cs(t) = credit spread at time t.

Obviously, the equation is flawed since the credit spread at time t is not a constant but changes according to the credit risk of the borrower, and therefore, the stipulated liquidity premium will not be a constant but a variable. To eliminate this problem, it can be stipulated that the risky curve is the curve that the lending organisation faces when it has a borrowing decision to make. In other words, we substitute the variable credit spreads value with a constant, which is the credit risk of the lending organisation, which makes this a constant across time-buckets, and for all counterparties, since this is the premium that the lending organisation will have to pay in order to borrow the funds if it were in need.

The revised equation is now:

CSt = credit spread of the lending organisation for each time period, a constant

Taking the sterling risk free curve and a triple A-rated organisation as an example, the following term structure for the liquidity premium can be easily constructed:

This approach takes into account the fact that borrowers are expected to pay a premium over and above the market price and over and above the spread the lending organisation chooses to incorporate as a measure of effective provisioning against bad and doubtful debts occurring. This approach models liquidity premium effectively as a spectrum by taking cognisance of the fact that as lending tenor increases, so does the premium. As can be seen from the table, even if the long term rates taper off, or indeed fall, the liquidity premium exhibits a rising structure.

The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.

Peter Bernstein, Against the Gods.

The advantage of this approach is that it uses the same non-arbitrage theory for liquidity as has been used for pricing and valuation in the market risk world.

Copyright ©2014 Suresh Sankaran