Zero-Coupon Bond Arbitrage and the Mechanics of a Short Sale
Summary
The document presents a possible price inconsistency in a zero-coupon bond term structure: a four-year bond is priced above a three-year bond despite paying its face value later. It sketches a trade that shorts the four-year bond and buys the three-year bond, then asks how the short position is actually settled. The example highlights that proceeds from selling a borrowed bond do not by themselves explain how to return the security or meet the obligation at maturity.
The discussion is a conceptual prompt rather than a complete arbitrage analysis. It does not establish the securities’ cash flows, short-sale terms, financing costs, collateral requirements, or whether the displayed prices are tradable. In particular, the suggested comparison relies on mismatched maturities, so the investor’s obligations and reinvestment or funding needs must be specified before concluding that the apparent price difference is a risk-free profit.
Key ideas
- A short sale requires borrowing the bond and eventually returning an equivalent security or settling the obligation.
- The example compares zero-coupon bonds with different maturities, so their maturity payments do not occur at the same time.
- A quoted price discrepancy alone does not establish an executable arbitrage after funding and borrowing terms are considered.
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Full text
# Bond arbitrage in practice
# Bond arbitrage in practice
If we have the following term structure for riskless bonds:
\begin{array} {|c|c|} \hline \text{Maturity} & \text{\$1 Zero-Bond price}\\ \hline \text{0 years} & \$ 1.00 \\ \hline \text{1 years} & \$ 0.97 \\ \hline \text{2 years} & \$ 0.93 \\ \hline \text{3 years} & \$ 0.89 \\ \hline \text{4 years} & \$ 0.90 \\ \hline \end{array} an arbitrage profit is possible by "shorting the 4-year zero-bond and longing the 3-year zero-bond".
Yet the question remains how this maneuver should work out in reality?
If we argue like this:
> The trader writes a 4-year zero-bond of $\$ 1{,}000{,}000$ nominal value. By selling this bond he gains $\$ 900{,}000$. With this money he can buy the 3-year zero-bond for $\$ 890{,}000$, leaving him $\$ 10{,}000$. After three years, the 3-year ZB matures, paying him $\$ 1{,}000{,}000$. This money is exactly what's needed to pay the obligations resulting from the 4-year zero-bond. So the net profit is $\$ 10{,}000$.
...the question arises why the trader can sell riskless bonds?
If we argue like this:
> Second idea: The trader borrows a 4-year zero-bond of $\$ 1{,}000{,}000$ nominal value. By selling this bond he gains $\$ 900{,}000$. With this money he can buy the 3-year zero-bond for $\$ 890{,}000$, leaving him $\$ 10{,}000$. After three years, the 3-year ZB matures, paying him $\$ 1{,}000{,}000$.
... how does the story end? We have to get the 4-year zero-bond back, right? So we assume it's availabe for $\$ 1{,}000{,}000$? Or can we hold on to the $\$ 1{,}000{,}000$ for the year and then say that paying the borrower back the nominal value is good enough?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.