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Part 7 – Investors of convertibles: Hedging and arbitrage

• Investors’ perspectives on convertibles

• Convexity ratio: equity-like return with less risk

• Busted convertibles

• Hedging with stock and options

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Investors who are restricted in their equity holdings

Example Florida Department of Labor prohibits self-insurance funds from investing in any equities.

Convertibles, despite their equity component, are typically classified as fixed-income instruments.

These restricted investors will profit from the equity like payoffs available with convertibles and increase their diversification.

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Arbitrage specialists

They attempt to lock in profits due to misalignment between the equity market and the convertibles. They are less concerned with the positive outlook of the equity.

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Equity-like returns with less risk

Convertible securities are an appropriate investmentvehicle for long-term investors seeking a high rate oftotal return but with less risk than common stock.

Convertible investors hope to earn two-thirds of the upside return with only one-third of the downside risk.- In bull markets, convertibles have trailed global equity markets by only a few percentage point- In bear markets convertibles offer considerably

more downside support.

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Convexity ratio

• Classic “two-thirds upside, one-third downside”

• Convexity ratio is the ratio of upside and downside participation.

For example, suppose the convertible provides 64% of the upside participation with only 34% of the downside movement, then the convexity ratio is 1.85. That is, the convertible provides 85% more upside participation than downside risk.

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Insulation from volatility

The price movements of convertibles are generally far less volatile.

Convertible Closing Price Closing Price % Closing Price Closing Price %

Company 8/24/01 9/21/01 Change 8/24/01 9/21/01 ChangeAvon Products 45.89 44.04 4.03 51.13 51.25 0.24Bell Atlandtic/New Zealand Tel

17.85 14.15 -20.73 100.50 101.25 0.75

Diamond Offshare 27.90 26.35 -5.56 83.50 84.13 0.75Federal Realty Trust 23.62 20.32 -13.97 93.25 87.13 -6.57INCO 17.55 12.45 -29.06 99.38 97.25 -2.14Average -14.15 -2.78DJIA 10423.20 8235.81 -20.99 -20.99S& P 500 1184.90 965.80 -18.49 -18.49NASDAQ 1916.80 1423.19 -25.75 -25.75

Common Stock

Convertible Bond Price Changes,August 24, 2001-September 2001

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Risk-reward relationship

Performance of various asset classes, 1973-1995

Compound annual return standard deviation

Convertible bonds 11.70 % 12.47%

S&P 500 11.84% 17.27%

Long-term corporate bonds 9.66% 12.44%

Intermediate-term 9.91% 8.93% corporate bonds

Source: Goldman Sachs Global Convertible Research (1996) “Convertibles as an Asset Class.”

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Possible reasons for the better performance

Inefficient company timing in calling convertible issues If a deep-in-the-money convertible enjoys a significant yield advantage over the common stock but it is not called, it is likely to outperform the underlying stock. Companies may delay conversion for a number of reasons including balance sheet and rating agency considerations.

Attractive convertible pricing at issue Typically, convertible securities are initially priced several percentage points cheap to their theoretical value in order to insure a successful launch. The conversion option is undervalued.

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What is a busted convertible?

The underlying stock is far out-of-the-money – the convertible trades on its fixed income characteristics.

Busted convertibles are characterized by low equity price sensitivity (low delta), large conversion premium and high yield to maturity.

• delta < 4%

• conversion premium > 75%

• yield more than 10%

Average credit quality of the busted convertibles is BB- versus BB+ for the entire domestic universe.

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Advantages

• In contrast to junk bonds, the upside potential is not capped – may enjoy unlimited upside potential if the stock price recovers.

• With busted convertibles, the equity warrant (deep out-of-the-money) is often mispriced. Investors are effectively buying high yield debtwith a free equity kicker.

• Busted convertibles are more attractive investment than high-yield debts in a modern economy that has shifted from slow growth, cyclical companies to more volatile growth companies.

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Disadvantages

• Busted convertibles are often more illiquid. Traditional convertibleinvestors become sellers as equity sensitivity diminishes.

• Convertible securities are generally subordinate to other creditorsin the event of a liquidation or bankruptcy.

The biggest risk is continued credit deterioration.

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Arbitrage

• The process of making a riskfree profit by buying and selling the same asset in two different markets simultaneously.

• Suppose the convertible trades below parity, it can be purchased while simultaneously shorting an amount of stock equal to the conversion ratio. This is a rare occurrence (may only occur in markets where it is impossible or difficult to short the stock).

Recent market phenomenonVolatility generally benefits convertible bond arbitrage because a CB trade is inherently long volatility, but it can also cause problems if done without any delta hedges. For example, in recent Indian market, the index volatility shot up and some illiquid CBs collapsed when the equitymarket fell.

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Hedging with common stock

• Undervalued convertible bonds present opportunity conservative investors can take advantage of through hedging techniques.

• Hedgers can retain a portion of the stock’s potential by selling short a circumscribed quantity of common against a convertible whilereducing or even eliminating stock market risk.

• They can swap upside potential for downside profits by shorting more of the stock.

• Carefully balancing the use of margin and hedging ratios can further enhance the risk reward relationship.

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Bullish hedges

• Designed to allow investors to participate in upwardmarket moves at reduced risk.

• As an alternative to owning the underlying commonstock, the hedge offers about half the upside potential advantage while assuming a small fractionof the downside risk.

• Bullish hedges are a low-risk alternative to a mix ofstocks, non-investment grade bonds and cash.

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Example – Bullish posture

CurrentPrices

Stock $30.00 $15 $30 $45 $60Convertible Bond 122.00 81 122 180 240

Strategy: Buy 10 bonds and short 200 shares of stock ($6,000) Investment = $12,200

Profit or loss on bonds -4,100 0 5,800 11,800Profit or loss on stock 3,000 0 -3,000 -6,000Bond interest received 400 400 400 400Stock dividends paid -30 -30 -30 -30Total profit or loss -730 370 3,170 6,170Return on investment -6.0% 3.0% 26.0% 50.6%

Prices in Six Months

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Bullish posture with 50% margin• The convertible bond may be purchased on 50%

margin.

• The hedge position’s upside potential increases close to that of the underlying common stock whilelimiting the downside losses to only a fraction of the common’s loss.

• It is also a superior alternative to owning theconvertible bond outright. If the common were todrop 50% in 6 months, the hedge position would beexpected to lose only 15% versus 30% loss for the convertible bond.

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Example – Bullish posture with 50% margin

CurrentPrices

Stock $30.00 $15 $30 $45 $60Convertible Bond 122.00 81 122 180 240

Strategy: Buy 10 bonds and short 200 shares of stock ($6,000) Investment = $6,100

Profit or loss on bonds -4,100 0 5,800 11,800Profit or loss on stock 3,000 0 -3,000 -6,000Bond interest received 400 400 400 400Stock dividends paid -30 -30 -30 -30Margin interest paid at 6% -183 -183 -183 -183Total profit or loss -913 187 2,987 5,987Return on investment -15.0% 3.1% 49.0% 98.1%

Prices in Six Months

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Example – Neutral posture

CurrentPrices

Stock $30.00 $15 $30 $45 $60Convertible Bond 122.00 81 122 180 240

Strategy: Buy 10 bonds and short 300 shares of stock ($9,000) Investment = $12,200

Profit or loss on bonds -4,100 0 5,800 11,800Profit or loss on stock 4,500 0 -4,500 -9,000Bond interest received 400 400 400 400Stock dividends paid -45 -45 -45 -45Total profit or loss 755 355 1,655 3,155Return on investment 6.2% 2.9% 13.6% 25.9%

Prices in Six Months

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Convertible Bonds hedged by theshort sale of stock - Bearish Posture

CurrentPrices

Stock $30.00 $15 $30 $45 $60Convertible Bond 122.00 81 122 180 240

Strategy: Buy 10 bonds and short 400 shares of stock ($12,000) Investment = $12,200

Profit or loss on bonds -4,100 0 5,800 11,800Profit or loss on stock 6,000 0 -6,000 -12,000Bond interest received 400 400 400 400Stock dividends paid -60 -60 -60 -60Total profit or loss 2,240 340 140 140Return on investment 18.4% 2.8% 1.1% 1.1%

Prices in Six Months

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Hedging with put options

• A short stock position can be created through buying puts.

• The cost of purchasing downside protection with puts is greater than the accrued interest from the convertibles. This is in contrast to the neutral hedge with stock, which earns a positive stand-still of return.

• As stock price goes down, since the stock price moves down faster than the convertible price, the gain from putsaccelerates.

• As stock price goes up, once the put premium is recovered,the profits increases.

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Buy 1,000 bonds at 118.57%Buy 80 put struck at $100 for $975 per optionTotal investmentPut expire in 182 daysStock price % change -50% -33% -16% 0 +16% +33% +50%Assumed stock price 50.0 66.7 83.3 100.0 116.7 133.3 150.0Estmated cvt. price (%) 93.1 100.2 108.9 118.6 129.1 140.1 151.6Current yield (%) 5.4 5.0 4.6 4.2 3.9 3.6 3.3Conversion premium (%) 132.6 87.9 63.3 48.2 38.2 31.3 26.3Delta (%) 47.2 59.9 69.1 75.9 80.9 84.7 87.6P/I convertible ('000) -255 -183 -96 0 +105 +215 330P/I put ('000) +322 +189 +55 -78 -78 -78 -78Interest paid (@5.75) -2 -2 -2 -2 -2 -2 -2Bond interest ('000) +25 +25 +25 +25 +25 +25 +25Total P/I ('000) +90 +28 -18 -55 +49 +160 +275Amount investment ('000) 1,264 1,264 1,264 1,264 1,264 1,264 1,264ROI (annualized) +14.7 +4.5 -2.9 -8.6 +7.9 +27.0 +48.4

=$1,185,700=$ 78,000=$1,263,700

Buy 1,000 bonds at 118.57% and buy 80 puts struck at $100

Example

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Hedging with less number of puts

Buy 1,000 bonds at 118.57% and buy 50 puts struck at $100.

Stock price % change -50% -33% -16 0 16% 33% 50%ROI (annualized) -4.8% -6.7% -6.2% -4.0% 13.3% 33.3% 55.7%

Suppose we purchase only 55 puts for a hedge ratio of 62.5%, this strategy

• reduces the loss on a stand-still basis• permits modest losses on the downside• increases returns on the upside

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Long Stock Plus Long Puts

• outperforms on the upside, but provides little downside support.• expensive to implement

Buy 8,000 bonds at $100 and buy 80 puts struck at $100 for $9.75 eachBuy 8000 shares at $100Buy 80 puts struck at $100 for $9.75 per optionTotal investmentStock price % change -50% -33% -16% 0 +16% +33% +50%Assumed stock price 50.0 66.7 83.3 100.0 116.7 133.3 150.0Stock p/l -400 -267 -133 0 +133 +267 +400Put p/l +322 +189 +55 -78 -78 -78 -78Interest paid (@5.75) -2 -2 -2 -2 -2 -2 -2Total P/I ('000) -79 -79 -79 -79 +353 +187 +320ROI (annualized) -17.4 -17.4 -174 -17.4 +12.6 +47.2 +86.5

=$800,000=$ 78,000=$878,000

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Hedging with shorting calls

• Best scenario: The stock price remains unchanged and theoption premium enhances the income and reduces the initialinvestment.

• As the stock price moves up, we get squeezed as the loss onour short call position begins to catch up with the premiumearned, and the gain on the convertible.

• On the downside, the premium earned cushions the blowas the stock price falls, but provides no real support.

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Buy 1,000 bonds at 118.57Sell 50 calls struck at $110 for $8.49 per optionTotal investmentCalls expire in 182 daysStock price % change -50% -33% -16% 0 +16% +33% +50%Assumed stock price 50.0 66.7 83.3 100.0 116.7 133.3 150.0Estmated cvt. price (%) 93.1 100.2 108.9 118.6 129.1 140.1 151.6Current yield (%) 5.4 5.0 4.6 4.2 3.9 3.6 3.3Conversion premium (%) 132.6 87.9 63.3 48.2 38.2 31.3 26.3Delta (%) 47.2 59.9 69.1 75.9 80.9 84.7 87.6P/I convertible ('000) -255 -183 -96 0 +105 +215 330P/I calls ('000) +42 +42 +42 +42 -33 -117 -200Interest earned (@5.75) +1 +1 +1 +1 +1 +1 +1Bond interest ('000) +25 +25 +25 +25 +25 +25 +25Total P/I ('000) -187 -115 -28 +69 +97 +125 +156Amount investment ('000) 1,143 1,143 1,143 1,143 1,143 1,143 1,143ROI (annualized) -30 -19.1 -4.9 +12.4 +17.8 +23.1 +29.3

=$1,185,700=-$ 42,450=$1,143,250

Buy 1,000 bonds at 118.57% and sell 50 calls struck at $110

Example

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General strategies

• If we buy puts and pay a premium, we want the market to move.

• If we earn a premium by selling calls, we want the market to stand still.

• By buying puts and selling calls, we can combine the attributes of both.

• By altering the number of options and their strike prices, wecan modify the return profile to match our view of the market.

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Long Stock Plus Short Calls

Buy 8,000 shares at $100 and sell 80 calls struck at $110 for $8.49 eachStock price % change -50% -33% -16% 0 +16% +33% +50%Assumed stock price 50.0 66.7 83.3 100.0 116.7 133.3 150.0Stock p/l -400 -267 -133 0 +133 +267 +400Call p/l +68 +189 +55 -78 -78 -78 -78Interest earned (@5.75) +2 +2 +2 +2 +2 +2 +2Total P/I ('000) -330 -197 -63 +69 +82 +82 +82ROI (annualized) -70.1 -46.7 -16.7 +20.1 +23.8 +23.8 +23.8

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Bond market volatility risk

Bond market volatility is harmful to convertible hedgers

• Rapidly declining interest rates in 1992-93 encouraged many companies to call their convertibles sooner than usual – resulting premature loss of conversion premiums and accrued interest.

• Sudden interest rate up trend in 1994 caused additional problems as investment floors dropped.

• Declining interest rates in the years following 1994 once again saw an unusual number of convertibles redeemed.

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Risks of hedging – Event risk

• A bankruptcy may produce net losses depending on if the bond winds up with meaningful residual value.

• A cash takeover destroys a bond’s conversion premium.

• When a company calls a bonds, it usually announces the redemptionjust prior to an interest payment date – investors lose accrued interestin addition to conversion premium.

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Choices of convertible bonds for arbitrage

• Speculative bonds lean more towards under-valuation than investment grade issues.

• Expected to hold up better on the downside than non-investmentgrade convertible preferred, non-investment grade convertiblebonds make the best hedge candidates.

• A perfect hedge candidate is a high yielding bond trading nearpar at a modest conversion premium. It also has a volatile non-dividend-paying underlying stock that is readily borrowablefor short selling.

• Convertible hedge funds generally leverage their investments. The level of margin is governed by Regulation T (50% maximummargin).