001-calculation-of-the-term-structure-of-liquidity-premium.pdf

Calculation of the Term Structure of Liquidity Premium

Article published with permission from IPS-Sendero. of 5

Calculation of the Term Structure of Liquidity PremiumBy Suresh Sankaran

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 isalso indisputable that we probably spend less time thinking about it than any other riskcategory. From an enterprise wide risk management point of view, the need for theintegration of liquidity, market and credit risk was recognised after the Russian crisis (August1998) and the “flight to quality" that followed.

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

The term premium liquidity preference theory postulates that investors demand a riskpremium for holding long term instruments, owing to risk aversion against the undiversifiablerisk of interest rate changes, which compounds over time and hence affects longer terminstruments most. This does not imply that longer term holdings are any less liquid whencompared to other investments. Yield to maturity on long term instruments of differentmaturities 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 onthe 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 potentialloss of principal.

Differing lengths in the lending period correspond to different degrees of uncertainty aboutfuture events. Very little change takes place in the political or economic structure of a nationor the world in any given year--the short-term. However, over a long period of time typicalfor some types of structural Government borrowing (T-Bonds) and private borrowing (homemortgages), massive changes may take place in rates of inflation, political conflict, and theglobal balance of power. In the long-term tremendous uncertainty exists and yet there areinstitutional lenders that actively seek the long term. For example, pension funds and lifeinsurance companies that need to plan for exact financial obligations well into the future, arenot surprisingly, key players in the longer-term instruments arena.



An important consideration with respect to the liquidity premium is that lenders have moreflexibility with regards to the length of the lending period relative to borrowers. Manyborrowers enter the long term market precisely because the nature of their project is longterm. For these projects to be financially feasible the borrower needs to rely on a longcontinuous stream of revenues to repay the debt. Such projects are just not possible in a oneto ten year horizon. Many home owners find that housing is affordable only if they canstretch 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 canmake six sequential six-month loans. The 5 year loan locks in an interest rate for the durationof the loan at the prevailing long-term rate whereas the sequence of six medium-term loansexposes 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 themedium term sequence which allows the lender to react to changing economic conditions.There is a balancing act taking place between uncertainty about future economic conditionsand 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 theprocess of buying and selling financial instruments, and this paper seeks to explore amethodology 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 thepossible future rates that the lender may use to manage interest rate risks.Therefore:

Thus,

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



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

The revised equation is now:



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

Period RiskyCurve (A)

ImpliedForward Rate

for (A)

Risk FreeCurve (B)

ImpliedForward

Rate for (B)

Difference CreditSpread

LiquidityPremium

(1) (2) (1) - (2) CS/(1+{B}1

1 4.6695 4.229

2 4.841 0.05012781 4.416 0.04603336 0.00409445 0.00019124 0.0039033 4.9255 0.152461834 4.535 0.14008984 0.01237199 0.00019124 0.0121814 4.9675 0.213856986 4.606 0.19725285 0.01660414 0.00019124 0.0164135 4.9948 0.275957793 4.64 0.25454632 0.02141147 0.00019124 0.021226 5.013915 0.341161144 4.653 0.31374175 0.0274194 0.00019124 0.0272287 5.0375 0.410621923 4.687 0.37800019 0.03262173 0.00019124 0.032438 5.057686 0.483961542 4.706 0.44468296 0.03927858 0.00019124 0.0390879 5.070712 0.560756229 4.721 0.51462118 0.04613505 0.00019124 0.04594410 5.0775 0.640957432 4.751 0.59067617 0.05028126 0.00019124 0.0500911 5.080058 0.724738834 4.777103 0.67082225 0.05391658 0.00019124 0.05372512 5.079879 0.812319521 4.785314 0.75228616 0.06003337 0.00019124 0.05984213 5.077846 0.903904237 4.776875 0.8342171 0.06968714 0.00019124 0.06949614 5.074461 0.999679491 4.759578 0.91739842 0.08228107 0.00019124 0.0820915 5.07 1.099814759 4.742 1.00360882 0.09620594 0.00019124 0.09601516 5.064597 1.204460819 4.729927 1.09475296 0.10970786 0.00019124 0.10951717 5.058311 1.313753272 4.724944 1.19205944 0.12169384 0.00019124 0.12150318 5.051174 1.427819438 4.725653 1.29591278 0.13190665 0.00019124 0.13171519 5.043216 1.546784412 4.729311 1.40600586 0.14077855 0.00019124 0.14058720 5.0345 1.670788194 4.733 1.52156911 0.14921909 0.00019124 0.14902821 5.025128 1.799997282 4.734465 1.64169084 0.15830644 0.00019124 0.15811522 5.01525 1.934621892 4.732521 1.76563119 0.1689907 0.00019124 0.16879923 5.005047 2.074921224 4.726883 1.89293109 0.18199014 0.00019124 0.18179924 4.99471 2.221202596 4.717862 2.02341944 0.19778315 0.00019124 0.19759225 4.984422 2.373817125 4.706127 2.15720216 0.21661496 0.00019124 0.21642426 4.974352 2.533159663 4.692517 2.29463016 0.2385295 0.00019124 0.23833827 4.96464 2.699657803 4.677904 2.43625581 0.263402 0.00019124 0.26321128 4.955391 2.873762805 4.663076 2.58276102 0.29100178 0.00019124 0.29081129 4.94667 3.055937192 4.648649 2.73486712 0.32107007 0.00019124 0.32087930 4.9385 3.246641132 4.635 2.89322371 0.35341742 0.00019124 0.35322631 4.930855 3.446308168 4.622218 3.05827627 0.38803189 0.00019124 0.387841



Liquidity Premium

This approach takes into account the fact that borrowers are expected to pay a premium overand above the market price and over and above the spread the lending organisation chooses toincorporate as a measure of effective provisioning against bad and doubtful debts occurring.This approach models liquidity premium effectively as a spectrum by taking cognisance ofthe 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 risingstructure.

The revolutionary idea that defines the boundary between modern times and the past is themastery of risk: the notion that the future is more than a whim of the gods and that menand 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 ashas been used for pricing and valuation in the market risk world.

Suresh Sankaran is the Vice president and Director, Strategic Consulting Services, IPS-Sendero, UK.

001-calculation-of-the-term-structure-of-liquidity-premium.pdf

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