What is the Risk-Free Rate
in a risky environment ?
Chris Golden
EFFAS-EBC/DVFA Meeting
Frankfurt, February 2012
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
1
Summary
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•
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•
•
The purpose of this presentation
What is a Risk-Free Rate?
Why do we need one?
Why are we re-examining it now?
What would it look like?
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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The purpose of this presentation
• The Risk-Free Rate (Rf) is everywhere in finance
• Part of its definition is that it be default-risk
free
• That virtue is increasingly rare
• But there were always many other fundamental
problems
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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The purpose of this presentation
• In this presentation I want to
– Examine the problems that always existed
– Examine the problems which have come to the
fore
• As a result of the financial crisis
– Suggest some ways forward
– Ask for help!
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What is a Risk-Free Rate?
• A Risk-Free Rate is one in which
– Expected Returns and
– Actual Returns
– Are indeed and always will be
– Equal
• i.e. there is no variance around the expected return
• Generally this therefore means an asset that is
– Fixed-rate, and
– Default-free
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What is a Risk-Free Rate?
• The maturity of the Risk-Free Rate
– should match the horizon of the asset being
valued/matched/hedged
• This can be short-term
– E.g. Options
• Medium-term
– E.g. Building contracts
• Infinite
– E.g. Equity/Corporate valuations
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What is a Risk-Free Rate?
• So the Risk-Free Rate used in valuation
– will depend upon when the cash flow being
valued is expected to occur
– It may therefore vary across time
• Of both observation
• And Maturity
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What is a Risk-Free Rate?
• The maturity constraint means that we need to
add another condition to the Risk-Free Rate:
– For the expected value to have no variance
– There cannot be any reinvestment risk
• So the Risk-Free Rate must be a single payment
– i.e. it must have a zero-coupon format
• It also implies that there is not so much A single
Risk-Free Rate,
• but a whole Risk-Free Curve (Rfc)
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What is a Risk-Free Rate?
• In summary therefore :
– The Rf must be
• A single payment instrument
• Of the suitable maturity
• Free of any credit/default risk
– It may also need to be replicable
• But this is not an essential characteristic
• In ALL the uses of Rf
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why do we need one?
• The Risk-Free Rate is a variable used in numerous
areas of finance:
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Equity Valuation
Portfolio Performance Measurement
Option Valuation
Insurance (MCEV for liabilities)
• It generally serves the role of evaluating what
alternative return could be guaranteed
– In a given situation
• Some examples follow
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Rf in Equity Valuation Models
Model
CAPM
APM
Multi
factor
Expected Return
E(R) = Rf +  (Rm- Rf)
Inputs Needed
Risk-Free Rate
Beta relative to market portfolio
Market Risk Premium
E(R) = Rf + j=1j (Rj- Rf)
Risk-Free Rate; # of Factors;
Betas relative to each factor
Factor risk premiums
E(R) = Rf + j=1,,Nj (Rj- Rf) Risk-Free Rate; Macro factors
Betas relative to macro factors
Macro economic risk premiums
Chris Golden EFFAS-EBC/DVFA
Frankfurt Aswath
Source:
Feb 2012
Damodaran
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Rf in Option Valuation
• The Black-Scholes Formula:
A Call Option price C is given by
Where
and
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why are we re-examining it now?
• It has become readily apparent to anyone who
has noticed what is happening
– That assuming that government issues are default risk
free cannot be justified
• There has been increasing press and other
comments to that effect
– E.g. Press : Gillian Tett in the FT
– Official Institutions: The IMF
– Investment Managers : BlackRock
• And many others!
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why are we re-examining it now?
• But there were plenty of questions before too!
• E.g Some Govies were said to be TOO expensive
– To be simply the default-Risk-Free Rate
• Various Govies benefited from
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–
–
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Tax-exemptions
Eligibility for repo
Greater liquidity
Regulatory requirements:
• Holdings for solvency or reserve purposes
• Not all Govie markets have strips
– I.e. Zero-coupon cash flows values have to be derived
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why are we re-examining it now?
• Why not Govies, even then ?
– Govies frequently had added advantages
– Beyond simply being considered free of default risk
• A bond yield decomposes into
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–
–
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A Risk-Free Rate
A Default/Credit Risk
A Liquidity Premium/Discount
A Convenience Factor
• Govies may not have default risk, but they have a
liquidity discount and a convenience factor
• Both of these mean that Govies would underestimate
the Rf
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why are we re-examining it now?
• Note that there is an argument that governments
can (or need) never default
– On their domestic debt
– in their own currency
• This is probably practically true
– Though only reasonably certain (legally) if the issuer is
the same as the printer of currency
• But note that equally practically
– Even the ECB can lend to banks
– And accept only Govie debt in collateral
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why are we re-examining it now?
• Although this was not really the most satisfactory
method…..
• It is clear that in the past
– You simply looked up the relevant Risk-Free Rate
• A government bond yield (or better: a zero)
• LIBOR or some similar rate
• Even Swaps
• But in the present Govies no longer look so
default risk-free
• And we are increasingly aware of the problems
with LIBOR and Swaps
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Some Questions
• Can we really consider Govies an appropriate
Risk-Free Rate today?
• Is the concept of “risk free” even appropriate
or relevant in today’s world?
• If not, then what happens to CAPM, portfolio
theory, BS model?
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Some Considerations
• Horses for Courses:
– The Rf should be fit for purpose/use
– And there are many purposes/uses
• There is probably room for more than one Rf
curve
• Just as there is room for more than one yield
curve (across the same set of points)
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Some Considerations
• Some Rf uses require replicability
– The Rf therefore needs to be observable
• And TRADEABLE
• Other Rf uses may not have that requirement
– And therefore the Rf in those uses may be
unobservable
– But derived from observable data
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Some Considerations
• Spurious accuracy!
• Whatever method is chosen to obtain a Rf,
– Whether directly observed (replicable)
– Or derived (unobservable)
• The Rf (and the Rfc) will be changing more or less
constantly
• Even if based on observed rates most of the Rfc will
be unobserved
• And based on some curve-modeling technique
• So to what degree of accuracy do we need the Rf ?
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What would it look like?
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•
•
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I do not propose a specific solution
We are all looking for answers
But I can outline some necessary dimensions
And suggest some key parameters
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What would it look like?
• The key dimensions that have to be examined
in determining a Risk-Free Rate :
– Theoretically Sound Concept
– Computationally Tractable
– Based on clean data inputs
• Available in real time
– (Possibly) Replicable
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Some Suggestions
• Based on the swap curve
– adjusted for credit risk and a liquidity premium
• But the concept implies determining what the credit
risk is
• Which is self-referential
– i.e. if we know what the credit risk is……
• Implied by the Cash-CDS Arbitrage
– CDS is close to pure credit risk
– Especially if it is CCP settled
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Advantages of the Swap Curve
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•
•
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It exists in almost all currencies
It is easy to build
It is always current
It is mandated for insurance in Holland
– (Although this may be a disadvantage….)
• And it is proposed for Solvency II purposes
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Disadvantages of the Swap Curve
• Adjustment required for Credit Risk
– Academia uses spread between secured and
unsecured rates
• i.e. compares with the repo rate for equivalent maturity
– But this method has problems too
• Convenience
• Liquidity
– On the other hand do collateralised swaps need a
credit adjustment?
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Disadvantages of the Swap Curve
• The Floating leg (3-mo LIBOR)
– Is not extensively traded
– Could be (and probably has been) manipulated
• The current definition for LIBOR makes the
rate conceptual
• Rather than an actual rate which can be tested
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why Use CDS vs Cash?
• Inasmuch as CDS capture a credit risk spread
• That spread should be over the credit-risk free
curve
– Counterparty-risk can be mitigated
• Empirical observations show that this spread
• Is over neither the Swap, nor the Govie curve
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why Use CDS vs Cash?
• i.e. (With all other things being equal) =>
• CBY – SR < CDS < CBY – GBY
• Where
– CBY = Cash Bond Yield
– SR = Swap Rate
– GBY = Government Bond Yield
• In other words the implied risk-free curve
• Lies BETWEEN the Govie Curve and the Swap
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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Why Use CDS vs Cash?
• In principle there is only one Risk-Free Curve
– Irrespective of the reference names used
• So any CDS/Cash Bond pair should be usable
– And as “information valuable” as any other
• There are an extremely large number of
reference names in the CDS market
– But using those contained in the CDX and iTraxx
“Main” indices are the most liquid
– Europe iTraxx has 3, 5 ,7 and 10 year maturities
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What to do?
• The EBC will be examining the question
further
• Sergey Smirnoff and I will head that effort
• We will want help:
– Thoughts/suggestions
– Data
– Feedback
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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What to do?
• If you interested, please contact us by e-mail
– Chairman@EFFAS-EBC.org
– SergeySmirnoff@EFFAS-EBC.org
Thank you for listening !
Chris Golden EFFAS-EBC/DVFA Frankfurt
Feb 2012
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