Using Bond Yields and OIS as Proxies for GC Repo in CIP Analysis

# Availability of GC Repo Rates for Different Maturities


# Availability of GC Repo Rates for Different Maturities












I am trying to replicate a Covered Interest Rate Parity arbitrage trade using General Collateral Repo rates for my Bachelor Thesis. My problem is that I do not have the necessary knowledge of what information will be available to me, once I have access to a Bloomberg Terminal (At my university, one needs to make an appointment to gain access, hence I want to prepare beforehand to be time-efficient).

The CIP trade I am referring to can be envisaged as follows and is commonly done using Libor rates in the literature.

Step 1: Borrow \$1,000,000 at the cost of $r_\$=2.5\%$

Step 2(a): Convert the fund in \$ to € at the spot exchange rate $S_0 = \$1.1237/€$, leading to $\$1,000,000/\$1.1237/€ = €889917.2$

Step 2(b): Enter into a forward contract simultaneously to sell € at the forward exchange rate $F_{0,360} = \$1.1128/€$, the size of the contract, €923289.1, is decided below;

Step 3: Invest the amount of € 889917.2 for one year in the euroland at the rate of $r_€=3.75\%$ . At the end of one year, the investment return is $€889917.2\times(1+0.0375) = €923289.1$, all of which is to be converted back into \$. So €923289.1 is also the size of the forward contract in step 2(b);

Step 4: Convert €923289.1 to \$ with the forward contract in step 2(b), resulting in $€923289.1\times\$1.1128/€ = \$1,027,436$;

Step 5: Repay the lender at the future value of the borrowing (principal plus interest), which is $\$1,000,000\times(1+0.025) = \$1,025,000$.

Thus the arbitrageur in this example makes a riskless profit of \$ 2,436.

What I am looking to do now is to compute past weekly monthly and quarterly CIP arbitrage trades for G11 currencies (USD, GBP, JPY, AUD, NZD, CAD, CHF, NOK,DKK and SEK), however since some people argue that there is a difference in default risk among LIBOR panels, I want to use fully collateralized repo rates, to eliminate/mitigate differences in risk.

Essentially, I would be grateful for information of which data on different maturities will be available on Bloomberg. I know that most of the volume in Repo Markets is overnight, however, I would be interested in one-week, one-month, and three-month rates. Otherwise, I would have to roll over the overnight rate and introduce roll-over risk. I have already tried to gather information on data-availability via google but unfortunately was not successful.

Thanks in advance!

## Answer by Attack68 (score 4, accepted)

https://quant.stackexchange.com/a/47002

Imagine you are an Asset Manager with Eur 1bn and you would like to retain this in as riskless and liquid means possible. What can you do?

There are practically 2 things worth doing:

- Buy short dated AAA (German) EUR Government Bonds. These are essentially treated as riskless investments with an active and liquid secondary market. You can sell the bonds at any time but you are exposed to interest rate risk in the interim.

- Reverse Repo short dated AAA (German) EUR Government Debt for a particular period. This is essentially a riskless agreement since you hold the collateral which is expected to have low volatility. If the Repo market is liquid you can exit the trade at any time but are exposed to repo rate risk in the interim.

(You would not typically deposit the funds in a bank since you then expose yourself to the bank's credit risk.)

You will observe that both 1 and 2 are very similar. Indeed for short term bonds and repo rates these rates tend to converge. They also converge due to a no arbitrage argument in their specific nature. If you can buy a short term bond at 2% yield and repo it for 1% you would enact as much of this trade as is capitally viable, until the rates converged.

So we establish that short term government bond yields can be thought of in terms of either their out right yields or by nature of their repo rate to term. Every bond is different and has a specific reaason why it may be 'expensive' or 'cheap' relative to surrounding bonds and indeed repo rates on individual bonds can be similar but I would suggest that constructing a bond yield curve from the knowledge of various bond prices (out to 1Y) will be a reasonable proxy for GC rates over similar maturities. Note that there are also different GC baskets for bonds of different maturities which can have price variants.

Now, instead, imagine you are a Global Bank with 1bn EUR that you want to deposit in as riskless and liquid means as possible. You would deposit the funds with the central bank and earn the central deposit rate. The best proxy for these rates is the OIS (overnight index swap) rate which in almost all currencies is within a few basis points of the central deposit rate.

### Answering you question

In bank trading floors CIR parity arbitrage is calculated with OIS rates as a basis for pricing, but if you want to use GC then I suggest you will need to source historical short dated bond yield prices and construct a curve. Both OIS rates and bond prices should be available in Bloomberg historical.

### Not Riskless

You cannot borrow money at Libor - its just not available anymore so any practical scenario that begins with "borrow money at Libor for 3M or 6M" can be discredited immediately. As I commented borrowing at Libor and buying government bonds is not a consistent type of trade, nor is it symmetrical - you might find an arbitrage both ways; either borrowing LIBOR in USD or EUR and then buying bonds in EUR/USD respectively, due to the dislocation of swap spreads in either currency. The FX swap you execute with a dealer is not risk free. What if half way through the period FX rates have moved significantly so your FX swap has considerable value (a large asset) and your bank counterparty goes bankrupt? If you have collateralised the FX swap this mitigates the loss but you are still exposed to margin period of risk and potentially new transaction costs which rise with market volatility.