The impact of rising and falling stock prices

In last weeks column I looked at the cash flow characteristics of a one to one convertible hedge. The example included $100,000 worth of 6% XYZ convertible debentures that were convertible into 2,000 shares of XYZ common at $50 per share (XYZ common was trading at $40 per share at the time the hedge was initiated). In the example, the hedge fund manager sold short 2,000 shares of XYZ common against a long position in the convertible debentures.

We examined the cash flow advantages of this strategy. There is a cost to implementing the short sale, say depending on the deal the Hedge fund has with its primary broker, $800 per year interest to borrow the shares that would be delivered to the buyer of XYZ common, plus an additional $2,000 per year to fund the cost of the XYZ common stock dividend (XYZ common paid a $1.00 per share annual dividend). On the positive side, the hedge fund earns $6,000 interest income from the convertible debenture, which nets the fund positive cash flow in the amount of $3,200 ($6,000 interest income less $2,800 in annual expenses).

The hedge fund need only put up $20,000 in order to carry the position (the difference between the money received from the short sale and the cost of buying the convertible debentures). That is a much better deal than the average retail investor is likely to get with their broker, as Mr. D.T. pointed out in response to my column last week.

Mr. D.T. writes, “I understand when you borrow stock to sell short, you need to put up much more margin than the 1% you mention. As a retail investor, I don’t think I can sell short on those terms. Significantly more margin is required from what I have seen.”

He is right of course, although two things make the convertible hedge different; 1) the hedge fund owns the convertible debenture and links it to the short sale. Since the short sale is hedged there is substantially less risk in the position. 2) The hedge fund is a much larger account and in a much better position to negotiate with the broker to receive more attractive terms.

Back to the strategy. At this point, the hedge fund has created a fully leveraged position, with the $2,800 in positive cash flow representing a 14% cash on cash return (readers who want to review the entire transcript of last week’s column, they can retrieve it at www.croftgroup.com and then click articles).

However, while a fully hedged position delivers positive cash flow, it is not a neutral strategy. In fact it is a slightly bearish strategy.

I say that because I would expect XYZ common shares to move more dramatically up or down then the XYZ convertible debenture. Analysts use past performance to assess how closely the two securities will interact, and a mathematical function referred to as delta is used to approximate this relative movement.

To keep this example as simple as possible we’ll assume that historically, XYZ convertible debenture had a delta of 0.70. That is, we would expect the convertible debenture – assuming interest rates remain static — to move about 70% as much as the underlying common shares up or down. Of course delta is not a static number. Delta will increase in a rising market and decrease in a declining market.

It is a bearish bias because the fund profits if the underlying common shares decline and will lose money if the underlying common shares rise. Here’s how.

If XYZ common were to decline, I would expect the convertible debenture to fall about 30% less than the common shares. Using what we know about delta, if XYZ common falls 25% to $30 per share, the XYZ convertible bonds might decline 17.5% to $82.50 (based on delta, the convertible’s decline was about 70% of the decline in the underlying common).

At this point, the hedge fund has a long bond convertible debenture that lost $17,500, and a short position in the underlying common shares that was ahead by $20,000. Net profit for the fund is $2,500, plus any cash flow advantage that we discussed previously.

In percentage terms, the 2.5% profit is one the overall position, which is really a 12.5% profit on the actual capital being employed (remember only $20,000 was actually invested in the strategy).

On the other side, if XYZ common were to rise to $50 per share, the XYZ convertible debenture will rise approximately 70% (based on the delta) as much, and might trade at say $114. In this example, the $100,000 face value of XYZ convertible debentures is now worth $114,000. The hedge fund has made $14,000 on the convertible debenture position, but has lost $20,000 on the short XYZ common stock position. Net loss to the fund is $6,000 less any excess cash flow that was received over the course of this trade.

Now you might say that is not a significant loss. After all, we began with a $100,000 portfolio, and $6,000 represents only a 6% loss. But again, like the upside move, this loss is really 30% of the $20,000 capital employed.

Some would say that given the limited risk assumption, these returns are reasonable. However, you can look at limited risk in one of two ways. You can say that the fund can only lose $20,000 on this highly leveraged position. Or you can say that the fund can lose all of the capital committed to a particular position.

With most hedge funds, the real risk is not the strategy. It is often the result of using too much leverage in a particular strategy. And in defense of convertible hedge funds, most would not leverage 100% of their capital.

Convertible hedge managers use delta to put a bullish or bearish slant to any hedge. We already know that a one to one hedge is bearish. But if the manager sold short only 1,000 shares of XYZ, equal to just 50% of the conversion value of the convertible, the hedge would not have as strong a cash flow advantage, but would take on a bullish bias.

For a market neutral trade, the manager might sell 70% of the common shares short, using 0.70 as the delta. At that rate, both securities should move about the same amount over short periods, and the position would make most of its money on the cash flow.

What this implies, as it does with most hedge funds, is that it all comes down to the managers ability to pick stocks or market direction. The convertible hedge strategy simply brings with it more risks than appear on the surface. A rating change on the debt of XYZ, for example, will result in the market demanding a higher yield on the convertible bonds which by extension, means lower bond prices, and that will impact the conversion premium.

If for some reason the broker is not able to continue borrowing the stock in order to cover the short sale – a short squeeze, which to be fair is a highly unlikely occurrence — the convertible hedger would be forced to prematurely close out the short by re-purchasing the shares.

A more likely possibility is to have another company offer to buy out the common shares via a takeover. That could result in a sharp increase in the price of the common which would not be fully reflected in the convertible. Because the acquiring company may have a stronger credit rating, and the management may want to eliminate the convertible debentures. The acquiring company could redeem the debentures through a forced conversion, which would effectively eliminate the conversion premium.

There is also the normal ongoing decay of the conversion premium over time. As the convertible debenture moves closer to maturity, the conversion premium shrinks. Convertible hedgers need to be sure that the premium decay is in line with the cash flow advantage. If it is not, then the hedge doesn’t work very well, particularly on a risk adjusted basis.

Another factor that is often overlooked is the limited number of decent convertible debentures in the market. A convertible debenture is a bond issued by companies that want to reduce their cost of borrowing. You entice investors to buy your debt at a lower interest rate – i.e. a lower rate than it would cost if the company were to issue traditional corporate bonds — in exchange for an equity kicker.

During the last few years, as the spread between corporate bond yields and government bond yields narrowed, convertible debentures became less popular, again limiting the supply of decent convertible debentures.