FOR WHOM THE BELL CURVES
Jasper Moiseiwitsch looks at the options value in convertibles, and how they can affect the performance of an issue.
By Jasper Moiseiwitsch

Consider for a moment the unthinkable. You run finances for a major telecommunications company in Asia, and you're being hammered by the global down-turn in your business. But you still need to raise capital to succeed, and among the dwindling opportunities only one seems practicable: sell the large percent stake you own in another suffering telephone company in the region. Trouble is, the share price of this stake has been collapsing for months. How can you sell it without flooding the market with shares that will simply depress it more?

The answer, says your friendly investment banker, is to issue an exchangeable bond and concentrate on the options value of the deal - an element that can support the issue's price despite the poor expected performance of the underlying security. Sounds simple, but you can be forgiven for feeling a little dizzy. You've just entered into the arcane world of determining the options value of your company's stake and its power to attract investors.

The options value of an exchangeable deal is frequently its most overlooked aspect, and options' role as a hedging instrument affects the price of every exchangeable issue. The pricing of most options is fixed via a formula designed in the 1970s by Fischer Black and Myron Scholes, two University of Chicago quants who won the Nobel Prize for their efforts. Their insights fueled the phenomenal growth of the options market in the 1980s. Bankers will tell you that the Black-Scholes pricing is straightforward, but beware. Investors in a given deal have many different motivations, and too much of a reliance on the magic of Black-Scholes can endanger the success of the issue.

Top Down Option

Convertibles operate in three dimensions - investors have to gauge their risk according to where they expect interest rates to go, where they expect volatility to be, and whether the issuer is likely to default. Equity-linked paper is favored by hedge funds, which take extremely sophisticated, high-maintenance positions. Regular fund managers take a much more straightforward approach, concentrating on the value of the underlying security. From your point of view, sitting at your desk at the battered telecom, you have to carefully gauge the appetite of these two types of investor, and balance the issue's pricing between them.

This can be extremely difficult. A case in point is the Cable & Wireless exchangeable issued in April. This US$1.5 billion zero-coupon bond exchangeable into shares of Pacific Century CyberWorks (PCCW), managed and underwritten by UBS Warburg, was rumored to be largely undersubscribed. Few are certain what the final take-up was, but UBS Warburg will not deny the deal saw mediocre market response.

Fair enough: PCCW has possessed a basket-case stock for more than a year, its share price having plummeted 90 percent in the 12 months prior to the transaction. With an underlying security so seriously in the doghouse, UBS found itself in the middle of a deal that clearly needed some extra help in the guise of an exchangeable.

UBS Warburg, a first-rate bank with execellent investor credentials, knows how to price these transactions. Obviously, UBS Warburg thought that there would be investor appetite for the convertible despite the weakness of the underlying stock. Its confidence was based on the options value of the issue, as defined by Black-Scholes.

The Sweet Spot

According to this view of the deal, the sweet spot lay in the option to convert into PCCW shares at HK$3.60 over a period of slightly more than two years (PCCW's closing price at March 30, just prior to the deal issue, was HK$3.075). To get an understanding of the full worth of the issue, investors needed to know the value of the option to convert C&W debt into PCCW equity.

Black-Scholes carries two important assumptions. The first is that investors don't just hold their convertibles, they hedge them. Put simply, investors could hedge the C&W exchangeable by short selling PCCW shares.

By assuming that investors hedge, Black-Scholes reasons that risk is managed and therefore minimized. To the extent that greater risk demands a cheaper price, the formula overestimates the value of an option for an investor that doesn't hedge.

Fully hedged investors, holding positions on the buy and sell sides, would not care whether PCCW trades up or down. They would only care about the degree to which the share price fluctuates - the more volatile the better. A hedged investor could find a profitable exit if PCCW rose sharply upwards (by converting the C&W bonds into shares) or sharply downwards (by locking in the short position). This is why Black-Scholes calculations are discussed in terms of volatility. Investors find value in options according to the volatility implied by the terms of the deal, and they compare this figure with a stock's historic volatility.

There's a problem. To properly manage a position in the Cable & Wireless exchangeable, fund managers must continuously enter the market, buying and shorting the exchangeable and PCCW stock. But many investors are not equipped for that kind of trading, either because they lack the expertise or because they are restricted by mandate to hedge.

Most fund managers, for example, including the biggest such as Fidelity and Schroders, are forbidden to short sell. If such investors cannot hedge, they can only profitably convert into PCCW if the shares rise, which is why so many investors dwelled on PCCW's fundamentals when offered the Cable & Wireless exchangeable.

Volatile Mix

Anthony Muh, regional head of investment (Asia) at Citibank Global Asset Management, characterizes the very different motivations of these two types of exchangeable investors. "[The long investor] gets involved in buying a convertible note because they want exposure to the underlying security," says Muh. They fundamentally want to hold the stock. The type of investor that is only concerned with volatility, he continues, "is typically a hedge fund that is looking to arbitrage and find short-term opportunities. Their concern on a day-to-day basis is probing that volatility."

This leads to the second important assumption of Black-Scholes: share prices assume a kind of normal distribution. In plain English, this says that daily volatility in share prices over the long run assume a bell curve. A price rise one day is matched by a fall another. Extreme price swings are rare and fall at the sides, or Ôtail' of the curve, while small price movements are common. These fall in the middle, or the steep, fat part of the curve.

Since a short investor views the stock's volatility as detached from the underlying, the direction of the volatility is meaningless to the value of the option. It's the level of volatility that matters. And that's where the hedge-fund investor makes his bet. But there was nothing Ônormal' about PCCW's volatility to the long-term investor. Declines greatly led advances. And investors who took a poor view on the firm's finances or management saw this as part of a continuing trend - indeed, yesterday's share price is a predictor of tomorrow's.

To Andrew Ballingal, investment director at TAL CEF, a Hong Kong-based fund manager, the pricing of the option was incidental to the glaring fact that the underlying stock was greatly troubled. "Human nature being what it is," he says, "most investors' perceptions of a company tend to be strongly colored by its recent share price performance." He steered clear of the issue.

There is another complication. Because PCCW's share price has fallen so dramatically since March 2000, the security is highly volatile. This gives UBS Warburg, following their Black-Scholes calculations, room to charge a hefty premium on the option. As it was, the terms of the bank's issue implied a volatility of 27 percent (at the April 3 issue closing price of HK$3.10).

For the unhedged investor this proposed a kind of double hit. PCCW is volatile, yes, but the movement has been almost exclusively downwards. To the extent that such investors believed the share price would continue downwards, and that they were asked to pay extra for PCCW's volatility, the deal looked bad. In other words, they were asked to take a buy position in a stock that has performed abysmally, and pay a premium for the privilege. "The underlying stock has been extremely volatile over the past 18 months," says Julian Mayo, managing director at investing firm iRegent Group, of the C&W exchangeable. "If the pricing is based on historic volatility, then the option is likely to be expensive and therefore unattractive," he says.

The Unhedged Investor

The lesson for any prospective equity-linked issuer is simple. If a firm wants to reach a broad investor audience (that is, beyond the hedge funds) it has to dump certain assumptions implicit in Black-Scholes.

The unhedged investor is concerned about the direction of the share price, not just its volatility. Black-Scholes is agnostic about company fundamentals - investors are not. And finally, while Black-Scholes assumes fully random share price movement, the investor that takes a directional view based on a company's fundamentals tends to be guided by past price performance.

Issuers can remedy this several ways. They can lower the exercise price. They can sweeten the debt offering. And, just as importantly, they can reassure investors on the equity stake. Investors need to be sold on the equity fundamentals and will not be convinced by the terms of a Black-Scholes computation alone. In the end there's no magic that can get around the obvious. Investors want an investing story. They want to be assured that, in the last instance, they can comfortably take a stake in the company.

Jasper Moiseiwitsch is a freelance writer for CFO Asia based in Hong Kong.