# Funded equity collars and margin loans

There is an article in the Financial Times today concerning equity funded collars [1]. The equity collar structure is used by a counterparty $A$ which wants to build up a position in a stock $S_t$. Let $B$ be the investment bank arranging the transaction, then the structure is as follows:

• $A$ enters into an equity collar with $B$ on shares $S_t$, i.e. $B$ sells a put with strike $k$ to $A$ and buys a call with strike $(k+\varepsilon)$ from them;
• Given the collar has positive delta to $B$ (short put + long call), to delta-hedge it the bank borrows stock $S_t$ which it then sells to $A$.

Another way for $A$ to build a position in the stock would be a margin loan, in which $A$ buys stock $S_t$ with a loan from $B$ which is collateralized by the bought stock (i.e. a repo-like transaction). Cash margin calls ensue if the stock price starts falling below predefined levels.

Now, the article claims that

[...] banks like [collars] because instead of taking on the credit risk of the borrower [as in a margin loan] , they take on the market risk of the underlying stock, which they can hedge as the share price fluctuates.

I understand the delta-hedge on the collar is imperfect (partial hedge, discrete rebalancing) plus there is gamma exposure, hence I understand the market risk coming from the collar structure (although it could be argued a margin loan also has market risk given it is collateralized by the stock). I also understand the credit/counterparty risk coming from the margin loan transaction, as a counterparty defaulting in the midst of a fast depreciation of the stock would leave the bank exposed to the gap between the latest margin call and the value of the stock collateral.

However I struggle to understand why there is no credit/counterparty risk in the collar structure. Can anybody explain?

There is no credit risk because the client pledges the underlying shares as collateral to the funded collar. This is not explained in the article.

The structure is built in such a way that the value of the loan + derivative package is always less than the value of the shares.

This can be done by for example lending an amount equal to the discounted put strike minus the initial cost of the collar (minus bank pnl).

The counterparty credit risk disappears and the bank can concern itself solely with the risk management of the position wrt market risk factors.

• what loan are you referring to? – Daneel Olivaw Apr 19 '18 at 9:32
• The payoff to the client of the collar combined with the share can be written: $\Phi(S_T)=k1_{\{S_T<k\}}+S_T1_{\{k\leq S_T \leq k+\varepsilon\}}+(k+\varepsilon)1_{\{k+\varepsilon<S_T\}}$ thus it is always positive, meaning that the bank will never have positive exposure and hence any counterparty risk. – Daneel Olivaw Apr 19 '18 at 9:37
• The structure is a funded collar ie loan + collar. – Ivan Apr 19 '18 at 13:52