How Repo Rates Affect Delta-One Forward and Futures Pricing
Summary
The document explains why repo rates matter to delta-one trading alongside interest rates and dividend yields. For an individual stock, the repo rate can serve as the financing rate in the cost-of-carry relationship between spot and forward prices. Replicating a forward by holding the stock requires financing that purchase; pledging the stock as collateral through a repo is one way to obtain that financing.
The answers also distinguish a broad portfolio approximation from stock-specific funding: a generic rate may stand in for repo across a portfolio, but individual repo rates need not equal it. A separate explanation describes the fee earned by lending a scarce security as a convenience yield. That benefit can make holding the cash security more attractive than holding its future and, if unreflected in futures pricing, can create an arbitrage opportunity. The discussion is conceptual and does not quantify funding effects or address all contract-specific details.
Key ideas
- For an individual stock, repo can provide the financing rate used in forward pricing.
- A generic interest rate may approximate repo across a broad portfolio, but rates can differ by security.
- A security-lending fee acts like a convenience yield for holding the cash asset.
- Futures pricing must reflect financing and lending economics to avoid the described arbitrage.
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Full text
# Delta one trading: dependence on repo rate?
# Delta one trading: dependence on repo rate?
I have heard a delta-one trader mentioning the dependency of its activity on interest rates, dividend yields and repo rates.
While I can understand the exposure he has to interest rates and dividend yields through the trading of futures contract, as per the formula of the futures price:
$$F(t,T) = S_t \times e^{(r-q)(T-t)} $$
where $S_t$ is the spot price at time $t$, $r$ is the interest rate, $q$ is the continuous dividend yield and $T$ the maturity of the contract, I can't see where the repo rate dependence is coming from.
Is it coming from the margin requirements? Like for example if you were to post margins on this position, you would earn the interest rate (the repo rate?) on the margins you have posted at the broker's?
## Answer by dm63 (score 1)
https://quant.stackexchange.com/a/49017
For an individual stock, the repo rate IS the interest rate r contained in the formula for the forward price. For example, suppose you are trying to replicate a forward contract by holding the stock. You need to finance the purchase of the stock, but the easiest way of doing that for most market participants is to pledge the stock as collateral against a loan- which is a repo contract.
It’s true that repo rates across a large stock portfolio may be approximated by a generic interest rate r (say Fed Funds) but it need not be the case in theory.
## Answer by Charles Fox (score 0)
https://quant.stackexchange.com/a/49007
It is a form of convenience yield. If someone is willing to pay you a fee to borrow your bond, that increases your desire to own the bond rather than the futures contract. If the future's price was not adjusted lower for this yield, you could make an arbitrage profit by buying the bond/stock, lending it to collect the fee, and shorting the future.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.