Risk-free bond (Ofer Abarbanel online library)

risk-free bond is a theoretical bond that repays interest and principal with absolute certainty. The rate of return would be the risk-free interest rate. It is primary security, which pays off 1 unit no matter state of economy is realized at time {\displaystyle t+1}. So its payoff is the same regardless of what state occurs. Thus, an investor experiences no risk by investing in such an asset.

In practice, government bonds of financially stable countries are treated as risk-free bonds, as governments can raise taxes or indeed print money to repay their domestic currency debt.[1]

For instance, United States Treasury notes and United States Treasury bonds are often assumed to be risk-free bonds.[2] Even though investors in United States Treasury securities do in fact face a small amount of credit risk,[3] this risk is often considered to be negligible. An example of this credit risk was shown by Russia, which defaulted on its domestic debt during the 1998 Russian financial crisis.

Risk-free bond vs. Arrow-Debreu security[5]

The risk-free bond can be replicated by a portfolio of two Arrow-Debreu securities. This portfolio exactly matches the payoff of the risk-free bond since the portfolio too pays 1 unit regardless of which state occurs. This is because if its price were different from that of the risk-free bond, we would have an arbitrage opportunity present in the economy. When an arbitrage opportunity is present, it means that riskless profits can be made through some trading strategy. In this specific case, if portfolio of Arrow-Debreu securities differs in price from the price of the risk-free bond, then the arbitrage strategy would be to buy the lower priced one and sell short the higher priced one. Since each has exactly the same payoff profile, this trade would leave us with zero net risk (the risk of one cancels the other’s risk because we have bought and sold in equal quantities the same payoff profile). However, we would make a profit because we are buying at a low price and selling at a high price. Since arbitrage conditions cannot exist in an economy, the price of the risk-free bond equals the price of the portfolio.

References

  1. ^“Belgium’s KBC scraps ‘risk-free’ practice on sovereign bonds – FT.com”.
  2. ^“Risk-Free Asset”. Investopedia. investopedia.com. Retrieved 1 March 2016.
  3. ^Mattia, Laura (February 25, 2014). “Think Bonds Are Risk-Free? Think Again”. abcnews.go.com. ABC. Retrieved 1 March 2016.
  4. ^Musiela, Marek; Rutkowski, Marek (2006-01-21). Martingale Methods in Financial Modelling. Springer Science & Business Media. ISBN 9783540266532.
  5. ^ Jump up to:ab c Baz, Jamil; Chacko, George (2004-01-12). Financial Derivatives: Pricing, Applications, and Mathematics. Cambridge University Press. ISBN 9780521815109.

 

Ofer Abarbanel online library