3: Repo Pricing

Mini Chapter Three

Repo determines forward prices of cash instruments

Repo cash flows can be mimicked by going long a bond in spot and selling futures on it (with the bond to be delivered on maturity). Difference between the futures and the spot price would imply the repo rate or interpreted the other way, given a repo rate and a spot price the future/forward price of the bond can be determined.

\[ \text{Future/Forward price} = \text{Current price} \times ( 1 + \text{Repo rate} \times \dfrac{n}{ 365} ) \]

Cash Futures Basis as a risk barometer

The notation above calculates futures/forward price of a security/bond using the market repo rate, but for securities/bonds that have a deep futures market an implied repo rate can be calculated. Any basis between the implied repo and market repo (former lower than latter) would reflect the ‘special-ness’ of the security/bond on repo

Trivia. BoJ’s YCC and ‘Special-ness’ implied by JGB futures prices – market-wide bets on BoJ doing away with YCC (early 2023) triggered a wave of shorts on the cheapest to deliver bonds (those that would be delivered on the futures contracts) also part of the YCC operations. As the central bank bought more and more of the bonds under its operations it ended up being the sole lender to those who wanted to short them (short forwards) and in turn the sole buyer of the same in the cash market. This created more than a 100% beneficial ownership for BoJ on some of these bonds with large short forwards positions with the market. Basis between the implied repo rate on certain bonds (as calculated by JGB futures that built large short positions and their cash prices) and the market repo rate reflected by the JGB yield curve was a reflection of the ‘special-ness’ of those bonds; implied repo rates dropped to as low as -5%. Negative carry on the ‘special on repo bonds’ finally realised at the time of futures settlement as prices converged to cash markets.

Cross Currency Repos

When the currency of the cash lent is different from the currency of the underlying asset it is understood as a cross currency repo.

• Pricing/Hedging can be broken down into two components – cross currency swap on the currency of the underlying versus the currency of the cash lent and the repo rate on the underlying.
• As an example think of a local Indian Bank that’s surplus in INR cash and is in need of USD. If the bank could borrow dollars from a USD investor by lending its local sovereign bond (IGB), the investor would lend its dollar cash at the local repo rate equivalent USD interest. Assuming the same tenor India repo rate at 6%, and USDINR Cross currency swap at 5% vs USD SOFR, the cross currency repo rate for borrowing USD cash would be USD SOFR + 100bps.