Accounting for Repo Rates in Self-Financing Stock Strategies

Summary

The document examines how stock-secured borrowing affects the self-financing condition for a trading strategy. It sets out the standard setup with a risk-free money account and a risky stock, where portfolio value changes through holdings in each asset. It then considers borrowing against stock collateral, with financing interest adjusted by the stock’s repo rate.

The central question is how to represent the borrowing and collateral positions in the strategy and where the repo rate should enter the model. The author proposes that the repo rate might affect the stock’s drift under a risk-neutral measure, or that a separate funding account may be needed. The document presents this as an unresolved modeling question and does not establish a definitive accounting convention or derivation. Its value is in identifying that secured funding terms may need explicit representation in self-financing portfolio dynamics.

Key ideas

• The standard self-financing condition tracks changes in cash and risky-asset holdings.
• Stock-secured borrowing introduces financing costs that depend on the repo rate.
• The document asks whether the repo rate belongs in the stock drift under the risk-neutral measure.
• A separate funding account is raised as a possible way to model stock-secured borrowing.
• The discussion poses the modeling issue without resolving it.

Tags

# Self financing strategy and repo rate


# Self financing strategy and repo rate












I was wondering how to adjust the self financing condition when cash borrowing cas be secured by the stock.

Suppose the risk-free money account is $B_t$ and there is a risky asset $S_t$. One have that $dB_t=r_tB_tdt$ where $r_t$ is the risk free instantaneous rate.

In the classical seeting, the strategy $\pi_t = b_tB_t +\varphi_tS_t$ is self financed if $d\pi_t = b_t dB_t + \varphi_t dS_t=b_tr_tB_tdt + \varphi_t dS_t$.

Suppose now that I start from $t=0$ with an empty portfolio, I then borrow $S_t$, buy a stock and pledge stock to secure the loan. At $t+dt$, I would have to pay $(r_t - q_t)S_t dt$ worth of interests on the loan, where $q_t$ is the stock's repo rate.

What would be $(b_t,\varphi_t)$ in that case and where should I account for the repo rate (my guess is that it is in the stock's drift : $dS_t=(r_t - q_t)dt + \sigma_t dW^Q_t$) ? Should one add a new money account for stock secured funding ?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.