Risk-free interest rate
Encyclopedia
Risk-free interest rate is the theoretical rate of return
of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time.
s. For USD investments, usually US Treasury bills are used, while a common choice for EUR investments are German government bills or Euribor
rates. The mean real interest rate
of US treasury bills during the 20th century was 0.9% p.a. (Corresponding figures for Germany are inapplicable due to hyperinflation during the 1920s.)
These securities are considered to be relatively risk-free because the likelihood of these governments defaulting
is perceived to be extremely low and because the short maturity
of the bill protects the investor from interest-rate risk that is present in all fixed rate bond
s (if interest rates go up soon after the bill is purchased, the investor will miss out on a fairly small amount of interest before the bill matures and can be reinvested at the new interest rate).
Since this interest rate can be obtained with no risk, it is implied that any additional risk taken by an investor should be rewarded with an interest rate higher than the risk-free rate (on an after-tax basis, which may be achieved with preferential tax treatment; some local government US bonds give below the risk-free rate).
in general, and is an important assumption for rational pricing
. It is also a required input in financial calculations, such as the Black–Scholes formula for pricing stock options and the Sharpe Ratio
. Note that some finance and economic theories assume that market participants can borrow at the risk free rate; in practice, of course, very few borrowers have access to finance
at the risk free rate.
, because no individual government of the Eurozone
has the authority to print currency. Of course, many countries have other measures and institutions, such as theoretically independent central bank
s, to reduce the likelihood of such an occurrence.
An alternative interpretation is that, while no investment is truly free of risk, scenarios in which a major government with a long track record of stability defaults on its obligations are so far outside what is known that one cannot make quantitative statements about their chances of happening, and, therefore, it is simply not feasible to include them in financial planning. A German investor living circa 1904 trying to decide whether to purchase long-term bonds issued by the German government could scarcely have been able to anticipate a World War followed by hyperinflation
. The US Treasuries commonly used for risk free rates have not defaulted since 1933 http://spectator.org/archives/2009/01/21/was-there-ever-a-default-on-us/print.
Rate of return
In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...
of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time.
Risk-free assets
Risk-free assets usually refer to short-dated government bondBond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
s. For USD investments, usually US Treasury bills are used, while a common choice for EUR investments are German government bills or Euribor
Euribor
The Euro Interbank Offered Rate is a daily reference rate based on the averaged interest rates at which Eurozone banks offer to lend unsecured funds to other banks in the euro wholesale money market .-Scope:...
rates. The mean real interest rate
Real interest rate
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate...
of US treasury bills during the 20th century was 0.9% p.a. (Corresponding figures for Germany are inapplicable due to hyperinflation during the 1920s.)
These securities are considered to be relatively risk-free because the likelihood of these governments defaulting
Default (finance)
In finance, default occurs when a debtor has not met his or her legal obligations according to the debt contract, e.g. has not made a scheduled payment, or has violated a loan covenant of the debt contract. A default is the failure to pay back a loan. Default may occur if the debtor is either...
is perceived to be extremely low and because the short maturity
Maturity (finance)
In finance, maturity or maturity date refers to the final payment date of a loan or other financial instrument, at which point the principal is due to be paid....
of the bill protects the investor from interest-rate risk that is present in all fixed rate bond
Fixed rate bond
In finance, a fixed rate bond is a type of debt instrument bond with a fixed coupon rate, as opposed to a floating rate note. A fixed rate bond is a long term debt paper that carries a predetermined interest rate...
s (if interest rates go up soon after the bill is purchased, the investor will miss out on a fairly small amount of interest before the bill matures and can be reinvested at the new interest rate).
Since this interest rate can be obtained with no risk, it is implied that any additional risk taken by an investor should be rewarded with an interest rate higher than the risk-free rate (on an after-tax basis, which may be achieved with preferential tax treatment; some local government US bonds give below the risk-free rate).
Application
The risk-free interest rate is thus of significant importance to Modern Portfolio TheoryModern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
in general, and is an important assumption for rational pricing
Rational pricing
Rational pricing is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away"...
. It is also a required input in financial calculations, such as the Black–Scholes formula for pricing stock options and the Sharpe Ratio
Sharpe ratio
The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
. Note that some finance and economic theories assume that market participants can borrow at the risk free rate; in practice, of course, very few borrowers have access to finance
Access to finance
Access to finance refers to the possibility that individuals or enterprises can access financial services, including credit, deposit, payment, insurance, and other risk management services...
at the risk free rate.
Why risk-free?
One explanation for the assumption that no default risk exists is due to the nature of government debt. For a fiat currency, the government retains the theoretical capacity to print as much of that currency as will be required to pay its own debts (in that currency). In this case, true default is theoretically impossible: owners of government debt can always be paid, but with money that may have substantially lower value. Rather than reflecting the default risk of the government, the risk-free interest rate, therefore, reflects the likelihood that the government will print money to pay its debts, thereby debasing the currency. Note that this does not apply to some currencies, such as the EuroEuro
The euro is the official currency of the eurozone: 17 of the 27 member states of the European Union. It is also the currency used by the Institutions of the European Union. The eurozone consists of Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg,...
, because no individual government of the Eurozone
Eurozone
The eurozone , officially called the euro area, is an economic and monetary union of seventeen European Union member states that have adopted the euro as their common currency and sole legal tender...
has the authority to print currency. Of course, many countries have other measures and institutions, such as theoretically independent central bank
Central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...
s, to reduce the likelihood of such an occurrence.
An alternative interpretation is that, while no investment is truly free of risk, scenarios in which a major government with a long track record of stability defaults on its obligations are so far outside what is known that one cannot make quantitative statements about their chances of happening, and, therefore, it is simply not feasible to include them in financial planning. A German investor living circa 1904 trying to decide whether to purchase long-term bonds issued by the German government could scarcely have been able to anticipate a World War followed by hyperinflation
Hyperinflation
In economics, hyperinflation is inflation that is very high or out of control. While the real values of the specific economic items generally stay the same in terms of relatively stable foreign currencies, in hyperinflationary conditions the general price level within a specific economy increases...
. The US Treasuries commonly used for risk free rates have not defaulted since 1933 http://spectator.org/archives/2009/01/21/was-there-ever-a-default-on-us/print.