Interpreting Repo Rates in Equity Forward Pricing
Summary
The document examines the repo-rate term in an equity forward pricing expression that also includes the spot price, risk-free rate, dividend rate, and time to maturity. It contrasts this expression with a basic cost-of-carry argument: borrow cash, buy the stock, short a forward, and use the forward proceeds to repay the borrowing at maturity.
The question is how stock financing through repo should be interpreted, especially since the stated formula subtracts the repo rate from the risk-free rate. The accepted response points readers to a separate equity-repo discussion and cautions that its 2013 material may contain outdated conventions, including its reference to Libor. The excerpt does not itself explain the mechanics or settle the apparent tension between a high repo rate and lower financing cost, so it serves mainly as a pointer to further study.
Key ideas
- The forward expression shown subtracts repo and dividend rates from the risk-free rate in the carry term.
- A basic replication argument borrows cash to buy stock and shorts a forward against that position.
- The document asks how repo financing changes the cost of carrying the stock.
- The accepted response refers readers to older equity-repo material and notes that some conventions may be obsolete.
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Full text
# How to explain the repo rate in equity forward price formula?
# How to explain the repo rate in equity forward price formula?
The equity forward price formula is:
$F(T) = S_{t}\cdot e^{(r_{f} - r_{repo}-div)\cdot (T-t)}$
where $S_{t}$ is the spot price, $r_{f}$ is the risk-free rate and $r_{repo}$ is the repo rate and $T$ is the maturity $div$ is the dividend rate.
How to interpret the repo rate here? For example, in the no-arbitrage cost of carry model without repo and dividend:
- we will borrow fund at $S_{t}$ at $r_{f}$
- buy stock using the $S_{t}$ and short forward
- at $T$, sell forward at $F(T)$ and repay the loan of $S_{t}\cdot e^{r_{f}\cdot (T-t)}$
If we have repo here, first we say borrow fund $S_{t}$ at $r_{f}$ and then buy stock for $S_{t}$. Then use the stock to enter repo market? The $r_{repo}$ here has a negative sign which means a benefit. Should I comprehend as I can lend the stock at the $r_{repo}$ financing cash, save the cash and get again $r_{f}$, so the cost of financing is $r_{f} - r_{repo}$? Otherwise, how to interpret the $r_{repo}$ here?
If the equity is illiquid, meaning the high repo rate, then the cost of financing is $r_{f} - r_{repo}$ even lower?
## Answer by Frido (score 4, accepted)
https://quant.stackexchange.com/a/81742
I think your question has come up before, and I believe it's a valid question. Instead of explaining it myself, I will link a relevant document on equity repo/financing which I believe will answer your question:
BNP Paribas - A new normal in equity repo
Mind you, the document is from 2013, so you need to decide what parts are still relevant (eg Libor is obsolete) in current markets and regulations.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.