Case Study

1
Case Study

• Arbitrage in the Government Bond Market?

2
Pricing Discrepancy

• Callable 8.25 May 00-05
• bid 101.125
• ask 101.25
• Non-callable Synthetics How to construct the
  synthetic bonds?
• 8.25 May 05 bid 98.53, ask 98.78
• 8.25 May 00 bid 100.28, ask 100.43
• Conclusion Apparent price discrepancy.

3
Calculations

• 8.25 May 05 synthetic bond equals 0.6875 of
• 12 May 05 plus 0.3125 of May 05 STRIP
• Cost to Buy at ASK 0.6875129.91 0.312530.31
  98.78.
• Cost to Sell at BID 98.53.
• Similarly, 8.25 May 00 synthetic bond equals
  0.9296 of 8 7/8 May 00 plus 0.0704 of May 00
  STRIP

4
Pricing Relation

• The price of the callable bond should be lower
  than the synthetic bonds.
• When interest rates drop, a callable 00-05 bond
  can be called and the govt can refinance at a
  lower rate. Obviously a 05 bond should be worth
  more because it offers the govt an option.
• A callable 00-05 is also worth less than a 00
  bond. This can be seen when interest rates up,
  the Treasury will not call the bond and enjoy a
  lower financing cost.
• Option prices can never be negative.

5
When should the bonds be called?

• If the price of the bonds is greater than par,
  and the call protection expired, then the
  Treasury should call them in order to lower its
  financing costs.
• Did the Treasury call the bonds optimally? No! In
  14 of 42 instances, the Treasury failed to call a
  bond, see Exhibit 1.

6
Profiting from Discrepancy

• If investors already owned the callable bond,
  then they should sell the callable bond at the
  101.125 and buy the synthetic bond (1) at
  98.78.
• If investors do not own the callable bond, they
  can short sell the bond and profit from the
  transaction. However, short sales in bonds is not
  common.

7
Repo Markets

• If you own a security, you could enter into a
  sale-and-repurchase-agreement (repo) by
  simultaneously selling the security and agreeing
  to repurchase it at later date, effectively
  obtaining a collateralised short-term loan.
• The single most important source of financing for
  government securities dealers is the repo market.
• Government securities are liquid and default
  free. Hence they are excellent collateral.

8
Reverse Repo

• The reverse repo is similar to borrowing a
  security now and agree to resell it at a pre-set
  price in the future.
• The reverse repo is similar to borrowing a
  security and providing cash collateral for a
  fixed term.
• You receive interest on the cash collateral and
  pay an interest fee for the privilege of
  borrowing the security. The resulting net
  interest rate is called the repo rate.

9
Reverse Repo and Short Sale

• The parallel example for the repo is the pawn
  shop business.
• Combining a reverse repo with a sale of the
  security results in a short sale.
• Term frames for repos are one day (overnight),
  term repos up to a few months, or open repos that
  roll over daily unless terminated by either party.

10
Risks Involved

• Thompson would like to close out the position at
  a profit when the price of the 00-05 is below
  that of her synthetic position. So she needs to
  either roll overnight repos or enter into an open
  repo.
• She may need to cover the entire maturity if the
  convergence never realises.
• Furthermore, if the callable bond rose in price
  relative to her synthetic, and she was required
  to deliver the callable, she could lose money on
  her position.

11
Liquidity

• Why does this pricing anomaly exist?
• First, think about the liquidity. People may pay
  more (demand a lower yield) on more liquid
  instruments.
• How do we check the liquidity? Use the bid-ask
  spread. If the bid-ask spread is smaller for the
  callable bonds, then there exists a premium for
  the callable bond.

12
Taxes

• As long as there are non-taxable holders of the
  00-05, or non-taxable investors can carry out
  the arbitrage, prices should be set by these
  marginal investors.
• Since some pension funds are not paying taxes, we
  should consider arbitrage based on the positions
  of these non-taxable investors.

13
Unique Demand

• Is there a unique demand for this particular
  00-05 bond?
• This is essentially the segmented markets
  hypothesis. It is not easy for us to imagine that
  this callable bond is so unique that some
  investors are willing to pay a premium to hold
  it.
• All Treasury bonds are essentially substitutes.

14
Other Transaction Costs

• Short-selling and reverse repos can involve risks
  and transaction costs.
• However, any owner of the 00-05 can merely sell
  it and replace it with another synthetic, not
  requiring any short-selling.
• After considering these factors, we may conclude
  that there indeed exists an arbitrage opportunity.

15
Why Issue Callable Debt?

• Flexibility
• It can call the debt and replace it with a lower
  coupon debt when the interest rate drops. It can
  continue to serve the debt when the interest rate
  goes up.
• Budgetary flexibility. The govt can retire debt
  easily if it has budget surplus.
• Does government have better information about the
  future interest rate? The Federal government may
  value the call option more than investors do.
  Probably not.

16
Holders of Callable Bonds

• Investors demand a higher coupon payments (higher
  yield) to compensate for the call options they
  sold to the issuers.
• The implication of higher coupon bonds, which
  leads to shorter duration should not be ignored.