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NIO Converts: The Chinese and the Greeks
An article by • Published Jan 12, 2021
Nio Inc. ($NIO), a Chinese-based electric vehicle manufacturer announced a
of $1.3 billion of convertible senior notes.
Proposed terms of the dual tranche deal:
$650 million Convertible Senior Notes due 2026 + $100mm greenshoe
0.00-0.50% coupon
45-50% conversion premium
3-year put
$650 million Convertible Senior Notes due 2027 + $100mm greenshoe
0.50-1.00% coupon
45-50% conversion premium
4-year put


Convertible Bonds Explained

Convertible bonds, or "converts," are hybrid instruments. Debt obligations, that have embedded options which allow them to be converted into common equity (or ADRs, as is the case in NIO). For some issuers, converts are the market of last resort when credit quality is poor (early stage or unable to get rated by the rating agencies). For others, they offer a means to raise equity-like financing at a higher equity price than the current price. Although unaware of the current mix, it was once the case that long-only investors purchased around 70% of convertible bond issuance, while arbitrage ("arb") accounts bought the remaining 30%.
Long-only investors simply look as converts as equity with a coupon and downside protection, whereas arb accounts use converts to get long or short the implied volatility of the equity of the underlying issuer and long or short the 'implied' credit spread. Given the embedded option in them, convert valuations are partially driven by option math and input variables:
Stock price relative to embedded option conversion price
Maturity
Risk-free rate
Dividend yield, if any
Implied volatility


Basic Convert Math

NIO is at $62.50 at the time of this writing
Assume the greenshoes get exercised so $1.5 billion of bonds
Up 47.5% (mid-point of 'price talk' above) equates into a $92.2 conversion price (62.5 x 1.475)
Each $1000 bond converts into 10.85 shares (the conversion ratio), calculated by dividing 1000 by the conversion price (1000 / 92.2)
If 30% of the converts are sold to arb accounts, one can calculated the volume of shares that need to be sold short, for 'delta-neutral' positioning (delta described below)
Convert funds have complex models to calculate these values (ie Kynex), but using an option calculator available online and the current stock price, conversion price, 1% for the risk-free rate, 1,095 days for the 2026 notes (to the put date, not maturity) and implied volatility of 70, the delta on the embedded option would be approximately 0.62
If 30% of the $750 million 2026 notes are sold to arb accounts, that is $225 million
$225 million divided by $1000 par per bond = 225,000 bonds
225,000 bonds each convert into 10.85 shares
$225 million bonds thus convert into around 2.4 million shares
The embedded stock exposure is 1.5 million shares (2.4mm x 0.62 delta)
30% of the 1.5 million shares, or around 450,000 shares would then be sold short to get arb accounts 'on delta'
The same math can be done for the 2027 converts


The Greeks

Delta (0-100%) is the change in the price of the bond relative to a percentage move in the underlying equity/ADR. It's not static. A higher delta means more equity sensitivity and a lower delta has less exposure to the stock
Gamma measures the rate of change in delta and gives an idea of convexity
Vega is the implied volatility
Rho is the exposure to interest rate changes
Omega is the exposure to the credit spread / credit quality
Theta is the time value of the embedded option


Gamma Trading

Arb accounts typically try to monetize gamma trading, which is one of the more complex concepts in all of finance. Broadly speaking, once in a delta-neutral position, convert arb accounts that are long the bond and short the stock really don't care whether the stock goes up or down. They just want it to be volatile and realize higher volatility than the implied volatility they got long. They want to trade the gamma and re-set deltas as that happens. If short the convertible bond, the opposite is true and one is short implied volatility. It would be easy to go down many rabbit holes around these concepts and its surely the case that if there is a solid bond floor (based on recovery value) arb accounts prefer that the stock goes lower, but to stay 'on-delta' these investors will short more stock as it goes higher or buy stock back to reduce the short stock position if it goes lower (unless in a negative gamma situation).

Example
Long $1 million NIO 2026 bond
Delta-neutral trading would mean you'd short 6,727 shares against the long bond position (same math as above)
Think about it this way, the option embedded in the bond is long 6,727 shares and the short common/ADR offsets that stock exposure
If you wake up tomorrow and the stock opens +$10 at 72.5, the delta of the embedded option is now 0.67, so I am now long 7,270 shares in the bond, but only short the 6,727 shares
Effectively one gets longer the stock via the change in gamma and can monetize those changes without taking market exposure by re-setting deltas after such moves
Most arb funds typically set a band at which to monetize gamma and re-set deltas, for example 10% moves up or down
In a long convert arb position one is long the credit spread and long implied volatility. All else being equal the position would make money if the credit spread tightened or the implied volatility went higher even if the stock didn't move
Typically credit spreads and implied volatility are positively correlated, however, with credit spreads moving higher as 'implied vol' goes higher
Despite the low coupons on converts, most funds think of convertible bonds in terms of what credit spread they are getting paid relative to the credit risk they are taking, just as most credit funds do. But because the coupon is so low, the implied credit spread is a combination of the coupon/spread and the value captured monetizing gamma


Other Notes

If a convert fund is long the convert, they need not report the short stock position anywhere, but if the fund is short the implied volatility via a short convert bond position, they must report the offsetting long stock position. Said differently, funds reporting long stock positions may actually be short the credit or short the volatility of the company and may not be expressing any view on the underlying equity.
Implied volatility is a difficult concept. Realized volatility can be calculated and measured. The job of a convertible bond analyst or trader is to use their judgment on whether realized volatility will be more or less than what the embedded option is implying.
Funds can target their desired exposure by isolating the volatility or credit spread. For example, if a trader was long a convertible bond, short the stock in delta-neutral position and was long credit default swaps (short the credit spread) on the same issuer, they are only long the implied volatility. Likewise, one can arb or reduce volatility exposure through listed options. If the embedded option in a convert implied 70 vol and similar maturity listed options imply 90 vol, one could buy the convert, sell the volatility in the options market and try to capture the difference.
Gamma trading doesn't need to be done in the convert market. The same exact manner of trading can be done using options, for example long a call option versus short the common equity on a delta-neutral basis is simply a long volatility trade
Negative gamma happens in distressed situations, whereby simplistically the short equity position in an arbitrage trade doesn't offset losses on the long bond leg of the trade. Rather than buy stock back as the delta goes lower, one must sell more stock.

Convertible bonds and convertible arbitrage trading are far from easy to understand. The concepts aren't for the faint of heart, but hopefully this helps. A decade or two ago there was significant inefficiencies in the market that allowed convert arb funds to derive outperformance with little, if any, market exposure. Those inefficiencies have been squeezed out of the market over the years, but the concepts and math remain true.