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Questions about Grosvenor Group Case

Please prepare a brief report addressing the questions below.

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Questions about SOFR Term Structure

Global regulators are pressuring users of floating-rate debt and swaps to reference only in- terest rates that are determined by a large and liquid underlying market. In the U.S., only the overnight government bond repo market was deemed sufficiently reliable. Hence SOFR

· a volume-weighted average rate in this market computed by the N.Y. Federal Reserve – has emerged as a new benchmark.

However, market participants need floating rates of all tenors – not just an overnight rate At the very least, they would like to have 1-month, 3-month, 6-month, and 12-month “SOFR” to replace LIBOR term rates in existing swaps. The trouble is, there is almost no trading in long-term repos.

The simplest solution would be if there were a market for SOFR-based OIS to any maturity T because the OIS rate to T corresponds to a claim to overnight SOFR compounded every day until T . Hence, if a term-repo rate did exist, it would have this value by absence of arbitrage. But the SOFR OIS market isn’t developed enough yet. So using OIS data to infer reference rates would defeat the goal of only relying on deep markets.

This case asks you to consider the relationship between different short-term interest rates in order to understand what term-SOFR should “look like.”

· Question 1. First, verify the statement above that if there was a 1-year SOFR OIS and also a 1-year term repo, and if we have

( 1 ) ( 1 )Rrepo ̸= ROIS

then there is an arbitrage opportunity. Do this by constructing a table showing all of the cash-flows at each date from all the arbitrage transactions that you will undertake. Be sure to specify precisely what securities you are trading and the quantities in each transaction. You may ignore repo haircuts, and all transactions costs. Don’t worry

about counting days precisely. (It suffices to assume either Rrepo > ROIS

or Rrepo <

1 1 1

( R )OIS

1

since, if you demonstrate the arbitrage in one direction, you can reverse the

trades to establish the other.)

· Question 2. The CME has introduced 3-month SOFR futures contracts, whose set- tlement value is the daily-compounded value of SOFR over the prior quarter. (See the formula for “final settlement price” on the contract specification page, whose link is on the Canvas site.) This payout formula is exactly the same as the payout for a SOFR-OIS covering the same period. So, the nearest term contract, maturing at T1 say, is literally an OIS to T1 and the second contract, maturing at T2, is effectively a forward-starting OIS for the period T1 to T2, and so on. So from these contracts we

can build term interest rates to any of the maturity dates. (Currently there is active trading in contracts up to about 12 quarters ahead).

We want to show that, under some assumptions, these futures rates can define a term- structure of OIS rates. Then, from Question 1, these also must equal term repo rates.

( 6 mo )So let’s make the assumption that the futures are actually forwards and pay all of their cashflows at the end (with no marking to market). Now also assume that we are at one of the the CME quarterly expiration dates. Show that, if you could do a 6-month OIS with someone at the rate ROIS, you would have an arbitrage opportunity if

( 2 ) ( 6 mo )1 + 1 ROIS

(1 + 1 Rf )(1 + 1 Rf )

( n ) ( 4 ) ( 1 ) ( 4 ) ( 2 )where Rf

are the rates on the nth quarterly SOFR futures contract. (The contract

( − )actually trades in units of 100 (1 Rf ).) As in Question 1, specify precisely each transaction that you will undertake to create the arbitrage. (Hint: At time zero you will need to execute trades in both contracts – but for different amounts.)

· ( 1 ) ( 1 )Question 3. Now consider another 1-year rate: the rate on one-year T-bills. Call this rate RT B. It is just related to the price of the (zero-coupon) T-bill via B0,1 = 1/(1 + RT B). Is it true that if we observe

( R ) ( R )repo TB

1 1

we also have an arbitrage opportunity? Are any new assumptions required to complete this argument?

· Question 4. The CME uses its futures to interpolate and report term-SOFR rates every day. Regulators in 2021 have approved these term rates for use in floating-rate loans. From the links on Canvas, compare these term rates to the Treasury rates for the same maturities. Which do you think is a better measure of the “true” riskless rate?

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