About half of the converts are arb held and hedged.

Convertible bonds are bonds that convert into stock above a certain level and can be modeled as a corporate bond plus an equity option.

The option has ‘delta’ which indicates how much the bond moves like the stock, which varies from 0% (no exposure) to 100% (acts like stock). Most deltas are in the middle.

The equivalent exposure is the amount outstanding times conversion times the conversion ratio times the delta.

We calculated the total convert delta as percentage of the stock outlying which would be the total amount of stock shorted by arbitragers if they owned all the converts and shorted the appropriate amount of stock. Arbs buy converts and short stock to gain access to volatility without directional risk.

We found that the average cost paid by the market to short the stock is correlated to the percent of the float that the convert delta represents.

We found that the amount of stock shorted as a function of float is correlated to the percent of the float the convert delta represents.

This does not mean that all the shorts in the name are convert arbitrageurs, but that the borrow market is dominated by the convert shorts.

The cheapness of the converts, compared to neutral fair value, is also a function of the borrow cost, so for example if stock costs 1% per annum to borrow, it may trade 1% per year cheap compared to the model.

The convert arbitrageurs are in touch with the borrow market, and the borrow market should pay attention to the convert market.

When new converts are issued, or when the are redeemed, or when the delta changes, the borrow market should be affected.

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