I'd like to carve out a space for a more theoretical discussion of how options theory can help us understand the implications of taking Tesla private. The offer to exchange a common share for the shareholder's choice of a private share or $420 cash is itself an option. Once shareholders approve the transaction a common share actually becomes a defacto option with the private share as the underlying. This metamorphosis from stock to option is subtle and complex. Many of our expectations about how a stock should behave fly out the window because it starts to behave more like an option. Likewise commonly traded options on Tesla will morph from being an option on a stock to an option on an option on a private company. So conventional behavior around trades option can break down over the course of this transaction. Trading strategies will adapt. So with all this in play, I think it will benefit us all to gain an option theoretic understanding into what this transaction implies.
Put-Call Parity
Under normal conditions, put-call parity holds when for stock at price X, strike K, and put and call option with the same expiration
X = K + Call(X, K) - Put(X, K)
So usually prices of options and the underlying will tend to trade near parity subject to illiquidity or bid/ask spreads. So basically there is a small transaction cost to trade.
Put-call parity also implies that the implied volatility of a call is identical to the that of the paired put option. We think of implied volatility as a measure of demand for an option as it relates to the premium an option buyer is willing to pay. It there is stronger demand for a put option than for its paired call option, the implied volatility of the put goes higher than that for the call. This imbalance means the price of the put option becomes higher than parity. It is usually short lived through traders who seek arbitrage opportunities. But in extreme markets it can become pronounced and sustain. This happens when shares become extraordinarily hard to borrow for shorting. Basically shorts are willing to pay a premium to keep adding to their short position when the supply of shares to borrow is exhausted. This imbalance also motivates sophisticated longs to write put options as a way to harvest the premium bears are willing to pay them.
Taking Tesla private has the potential to violate put-call parity. Specifically shorts have expanded the supply of long position from 170M shares to 205M. 35M shares shorted will be forced out of circulation by the time all shares have converted. Redeemable shares will be scarce, and shorts will need them to close their positions. In the event of a short squeeze, shorts may pay a premium for call options so as to limit their losses. Other traders may pay a premium for call options so as to speculate on the short squeeze. Meanwhile, put options will lose value. The cash out offer of $420 put a floor on the value of a share at conversion and this floor will decrease the implied volatility of put options. So the question is whether implied volatility for call options will collapse with puts or remain high through a speculation and hedging in a short squeeze. I believe there is a substantial risk of imbalance. I expect calls to trade above parity as we approach the take-private transaction.
Synthetic Longs
Put-call parity suggests a way to synthesize having a long position from a portfolio of cash and options. Specifically, the synthetic long portfolio consists of:
Long 1 call strike K expiring T
Short 1 put strike K expiring T
Cash $K × exp(-r(T-t))
The cash earns the risk free rate r. At time T, this portfolio has the equivalent value as a share of stock, $X(T). Therefore, under conditions of put-call parity the value of the stock and the synthetic long portfolio are equivalent.
Let's consider how an institutional investor might use this. Suppose also that this investor is unable to hold private shares. The investor believes that Tesla will be taken private in or before Merch. It must then find some reasonable way to exit a large holding of Tesla shares, say 1M. One option is to convert shares into synthetic long positions. Consider this trade.
Sell 1M shares Tesla at $355/sh for $355M
Buy 10k Merch call contracts strike $420 for $23M
Sell 10k Merch put contracts strike $420 for $85M
The cash out proceeds are $417M which can earn $3M or more interest by Merch. So cash is worth $420M in Merch. Thus, the investor has realized the cash out value well in advance of the completion of the take-private transaction.
Now the investor is also short puts and long calls. If the transaction fails and the price of Tesla is below $420 in Merch, then the investor can use the cash to buy shares back at strike. Likewise if the transaction fails but Tesla is above $420, it uses the call option plus $420M cash to repurchase all the shares. So in the event of a failed take-private attempt, the investor continues to own 1M shares of Tesla as if nothing had happened.
If the take-private transaction happens as planned, then the puts expire worthless. Now the investor is sitting on $420M cash plus 10k call contract. This is clearly better than waiting to cash out shares in Merch. At the outset of this trade the call options are worth $23M. This is essentially the value that the take-private offer is transferring to a cash out shareholder. The cash option is actually worth $443 = $420 + $23. The investor can decide how to trade this call option. In the event that demand for private shares is high or there is a short squeeze, the value of the call option can appreciate.
Let's consider the case where demand for private shares is high enough that the price of private shares is above $420. In this case, the price of Tesla shares will converge to the price of private shares. The Merch call option is actually an option on the private shares, since at expiration above strike common share and private share are swapped. Suppose the price of the private share is around $450 plus random noise. That random noise is key. It is based on the implied volatility of an option on private shares. The bigger the IV, the more valuable the call option. Even if the expected price is just $30 over the strike, the option could see valuations twice this high or more. Thus, it is attractive to hold onto this call option long enough to be sure that the market has priced it well. Certainly the market cannot price it well until there is a prospectus for private Tesla and the shareholders have approved the transaction.
Shareholder Dynamics
I believe institutional and other sophisticated investors (especially those not planning to continue with private Tesla) will see value in converting shares into synthetic long portfolios. It gives them exposure to upside value beyond the $420 cash out value. But this strategy also impacts how actual shares circulate.
First, when a synthetic long is created, effectively a synthetic short is also created for the counterparties in options trade. This supply of synthetic short positions can become an attractive alternative to borrowing shares to short. So as longs go synthetic, it becomes cheaper for shorts to go synthetic as well. Specifically a cheap DTM put should be quite attractive to shorts. The irony here is that shorts may be encouraged to stay in the game because puts become so cheap. Meanwhile, brokers may want to rein in borrowed shares as this trade exposes them to complex credit exposure through a take-private transaction. Brokers may elect to restrict the supply of shares available to be shorted. This would only push shorts harder into puts and synthetic short positions.
Both longs cashing out and shorts have motivation to gravitate to synthetic positions. This can derisk the potential for a short squeeze. We could see short interest (borrowed shares) decline even while shorts maintain a very large short position via synthetic shorts. If this is orderly it could appear that shorts are closing though the share price remains relatively stable. It's just a migration from borrowed shares to synthetic short positions with no real impact on price. It only appears that shorts are covering when they are not. This does not mean there won't be fireworks, but simply that things can appear to be mild on the surface while massive wealth transfer happens in the options market. Once shorts have peacefully migrated into puts, the value of those puts will implode.
Funding the Cash Out Offer
Finally, I would point out that Musk and friends who put up the cash out money have an opportunity to raise that cash through writing out options to expire in Merch. Investment bankers can customize this for them. But the essence of what they are doing is granting a massive put option to Tesla shareholders in exchange for the privilege of taking Tesla private.
Increasing the strike on this massive out option decreases the value of the call option on private shares that shareholders receive in the transaction. Specifically, where Y is the price of a private share and X the price of a common share, the offer is
K + Call(Y, K, t, T)
in exchange for a common share. We do not really know how to price this because private shares are not in circulation to be traded just yet. What we can observe, however, is
K + Call(X, K, t, T)
That is we can think of common shares as a proxy for private shares. After all, they are both instruments of equity in Tesla, though they are not identical instruments. Private equity should be less volatile than common equity, which would have implications for implied volatility. Nevertheless, at the time of exchange T,
X(T) = max(K*, Y(T))
where K* is the cash out level, now $420. So these converge
Call(X, K*, t, T) -> Call(Y, K*, T, T)
as t -> T. This is why it is important not to sell the call option too soon.
At any rate the value of the offer, K + Call(Y, K, t, T), is not as sensitive to the cash out strike K. Increasing K by one dollar decreases value of the call by a fraction of a dollar. If one believes that the value of private Tesla is substantially greater than what one has with public Tesla, then you want to capture that value in the call option. We can all watch Call(X, K*, t, T) trade in the meantime. All shareholders will want that to go very high.
In negotiating around the cash out level, whether it should be higher than $420, we need to appreciate fact that the cost of the put option to raise the funds is a cost that will be borne by all private shareholders. If that cost is too high, the transaction will become uneconomical to do and could cancel the whole deal. So there is an unbound to how much the non-private shareholders can get in concessions from private shareholders. But short of this the more value is extracted the less valuable private shares become. That is, increasing K decreases Y. So the total value of the transaction, K + Call(X, K, t, T), is optimized at some value of K where both non-private and private shareholders can share optimally in this transaction. Some value midway between current share prices (around $355) and the value of a private share ($525, my totally subjective impression) is likely where the deal creates the most value for all current shareholders. So $420 is in the ballpark, maybe $440 or $460 is in the cards, but going to far could undermine any value in the transaction for all shareholders.
Conclusion
I hope this illustrates some of ways option theoretic analysis can provide clarity into the value, dynamics and opportunities in the take-private transaction. I do believe this transaction is in the benefit of all shareholders. Tesla will definitely not want to burn bridges. I believe there may be future opportunities to invest in Tesla that could be attractive non-private investors. For example, bonds or even preferred stock may be offered. At this point, however, it is import to think through the strategic options one has to personally benefit from the deal. Going synthetic may be worth considering if you need to cash out.
All the best.
Put-Call Parity
Under normal conditions, put-call parity holds when for stock at price X, strike K, and put and call option with the same expiration
X = K + Call(X, K) - Put(X, K)
So usually prices of options and the underlying will tend to trade near parity subject to illiquidity or bid/ask spreads. So basically there is a small transaction cost to trade.
Put-call parity also implies that the implied volatility of a call is identical to the that of the paired put option. We think of implied volatility as a measure of demand for an option as it relates to the premium an option buyer is willing to pay. It there is stronger demand for a put option than for its paired call option, the implied volatility of the put goes higher than that for the call. This imbalance means the price of the put option becomes higher than parity. It is usually short lived through traders who seek arbitrage opportunities. But in extreme markets it can become pronounced and sustain. This happens when shares become extraordinarily hard to borrow for shorting. Basically shorts are willing to pay a premium to keep adding to their short position when the supply of shares to borrow is exhausted. This imbalance also motivates sophisticated longs to write put options as a way to harvest the premium bears are willing to pay them.
Taking Tesla private has the potential to violate put-call parity. Specifically shorts have expanded the supply of long position from 170M shares to 205M. 35M shares shorted will be forced out of circulation by the time all shares have converted. Redeemable shares will be scarce, and shorts will need them to close their positions. In the event of a short squeeze, shorts may pay a premium for call options so as to limit their losses. Other traders may pay a premium for call options so as to speculate on the short squeeze. Meanwhile, put options will lose value. The cash out offer of $420 put a floor on the value of a share at conversion and this floor will decrease the implied volatility of put options. So the question is whether implied volatility for call options will collapse with puts or remain high through a speculation and hedging in a short squeeze. I believe there is a substantial risk of imbalance. I expect calls to trade above parity as we approach the take-private transaction.
Synthetic Longs
Put-call parity suggests a way to synthesize having a long position from a portfolio of cash and options. Specifically, the synthetic long portfolio consists of:
Long 1 call strike K expiring T
Short 1 put strike K expiring T
Cash $K × exp(-r(T-t))
The cash earns the risk free rate r. At time T, this portfolio has the equivalent value as a share of stock, $X(T). Therefore, under conditions of put-call parity the value of the stock and the synthetic long portfolio are equivalent.
Let's consider how an institutional investor might use this. Suppose also that this investor is unable to hold private shares. The investor believes that Tesla will be taken private in or before Merch. It must then find some reasonable way to exit a large holding of Tesla shares, say 1M. One option is to convert shares into synthetic long positions. Consider this trade.
Sell 1M shares Tesla at $355/sh for $355M
Buy 10k Merch call contracts strike $420 for $23M
Sell 10k Merch put contracts strike $420 for $85M
The cash out proceeds are $417M which can earn $3M or more interest by Merch. So cash is worth $420M in Merch. Thus, the investor has realized the cash out value well in advance of the completion of the take-private transaction.
Now the investor is also short puts and long calls. If the transaction fails and the price of Tesla is below $420 in Merch, then the investor can use the cash to buy shares back at strike. Likewise if the transaction fails but Tesla is above $420, it uses the call option plus $420M cash to repurchase all the shares. So in the event of a failed take-private attempt, the investor continues to own 1M shares of Tesla as if nothing had happened.
If the take-private transaction happens as planned, then the puts expire worthless. Now the investor is sitting on $420M cash plus 10k call contract. This is clearly better than waiting to cash out shares in Merch. At the outset of this trade the call options are worth $23M. This is essentially the value that the take-private offer is transferring to a cash out shareholder. The cash option is actually worth $443 = $420 + $23. The investor can decide how to trade this call option. In the event that demand for private shares is high or there is a short squeeze, the value of the call option can appreciate.
Let's consider the case where demand for private shares is high enough that the price of private shares is above $420. In this case, the price of Tesla shares will converge to the price of private shares. The Merch call option is actually an option on the private shares, since at expiration above strike common share and private share are swapped. Suppose the price of the private share is around $450 plus random noise. That random noise is key. It is based on the implied volatility of an option on private shares. The bigger the IV, the more valuable the call option. Even if the expected price is just $30 over the strike, the option could see valuations twice this high or more. Thus, it is attractive to hold onto this call option long enough to be sure that the market has priced it well. Certainly the market cannot price it well until there is a prospectus for private Tesla and the shareholders have approved the transaction.
Shareholder Dynamics
I believe institutional and other sophisticated investors (especially those not planning to continue with private Tesla) will see value in converting shares into synthetic long portfolios. It gives them exposure to upside value beyond the $420 cash out value. But this strategy also impacts how actual shares circulate.
First, when a synthetic long is created, effectively a synthetic short is also created for the counterparties in options trade. This supply of synthetic short positions can become an attractive alternative to borrowing shares to short. So as longs go synthetic, it becomes cheaper for shorts to go synthetic as well. Specifically a cheap DTM put should be quite attractive to shorts. The irony here is that shorts may be encouraged to stay in the game because puts become so cheap. Meanwhile, brokers may want to rein in borrowed shares as this trade exposes them to complex credit exposure through a take-private transaction. Brokers may elect to restrict the supply of shares available to be shorted. This would only push shorts harder into puts and synthetic short positions.
Both longs cashing out and shorts have motivation to gravitate to synthetic positions. This can derisk the potential for a short squeeze. We could see short interest (borrowed shares) decline even while shorts maintain a very large short position via synthetic shorts. If this is orderly it could appear that shorts are closing though the share price remains relatively stable. It's just a migration from borrowed shares to synthetic short positions with no real impact on price. It only appears that shorts are covering when they are not. This does not mean there won't be fireworks, but simply that things can appear to be mild on the surface while massive wealth transfer happens in the options market. Once shorts have peacefully migrated into puts, the value of those puts will implode.
Funding the Cash Out Offer
Finally, I would point out that Musk and friends who put up the cash out money have an opportunity to raise that cash through writing out options to expire in Merch. Investment bankers can customize this for them. But the essence of what they are doing is granting a massive put option to Tesla shareholders in exchange for the privilege of taking Tesla private.
Increasing the strike on this massive out option decreases the value of the call option on private shares that shareholders receive in the transaction. Specifically, where Y is the price of a private share and X the price of a common share, the offer is
K + Call(Y, K, t, T)
in exchange for a common share. We do not really know how to price this because private shares are not in circulation to be traded just yet. What we can observe, however, is
K + Call(X, K, t, T)
That is we can think of common shares as a proxy for private shares. After all, they are both instruments of equity in Tesla, though they are not identical instruments. Private equity should be less volatile than common equity, which would have implications for implied volatility. Nevertheless, at the time of exchange T,
X(T) = max(K*, Y(T))
where K* is the cash out level, now $420. So these converge
Call(X, K*, t, T) -> Call(Y, K*, T, T)
as t -> T. This is why it is important not to sell the call option too soon.
At any rate the value of the offer, K + Call(Y, K, t, T), is not as sensitive to the cash out strike K. Increasing K by one dollar decreases value of the call by a fraction of a dollar. If one believes that the value of private Tesla is substantially greater than what one has with public Tesla, then you want to capture that value in the call option. We can all watch Call(X, K*, t, T) trade in the meantime. All shareholders will want that to go very high.
In negotiating around the cash out level, whether it should be higher than $420, we need to appreciate fact that the cost of the put option to raise the funds is a cost that will be borne by all private shareholders. If that cost is too high, the transaction will become uneconomical to do and could cancel the whole deal. So there is an unbound to how much the non-private shareholders can get in concessions from private shareholders. But short of this the more value is extracted the less valuable private shares become. That is, increasing K decreases Y. So the total value of the transaction, K + Call(X, K, t, T), is optimized at some value of K where both non-private and private shareholders can share optimally in this transaction. Some value midway between current share prices (around $355) and the value of a private share ($525, my totally subjective impression) is likely where the deal creates the most value for all current shareholders. So $420 is in the ballpark, maybe $440 or $460 is in the cards, but going to far could undermine any value in the transaction for all shareholders.
Conclusion
I hope this illustrates some of ways option theoretic analysis can provide clarity into the value, dynamics and opportunities in the take-private transaction. I do believe this transaction is in the benefit of all shareholders. Tesla will definitely not want to burn bridges. I believe there may be future opportunities to invest in Tesla that could be attractive non-private investors. For example, bonds or even preferred stock may be offered. At this point, however, it is import to think through the strategic options one has to personally benefit from the deal. Going synthetic may be worth considering if you need to cash out.
All the best.
