### Trading Cash

Can you buy and sell cash? That sounds like a silly idea. Just like a cheesy mortgage agent trying to push a deal would say: "Cash is cash, you can't buy this $100 bill at any other price."

Really? You can't buy the $100 bill at a different price other than $100, but if you deposit the $100, one bank pays 5% interest, another pays 3.5%, that is certainly different prices in cash.

Interest rate obviously is the key factor in trading cash in ForEx market. In stock market, there is also opportunity for trading cash. Let's look at one example as it just happens today (6/23/06).

Anadarko Petroleum (APC), a natural gas, crude oil development and production company, announced this morning that it will acquire Kerr-McGee (KMG) and Western Gas Resources (WGR) in cash. We will look at the KMG part of the deal. APC will pay $70.5 per share in cash for all KMG shares. Furthermore, it is a friendly takeover and the KMG board already accepted the offer at the announcement. There is a very steep breakup fee if the deal doesn't go through. On Thursday KMG close at $50.3 so the offer price has a huge 40% in premium. The deal is expected to close at the end of third quarter.

So what do you expect KMG to trade today? $70.5?

Assuming there is no risk of the deal breakup (with the steep breakup fee), and no chance for any competing bids (with the steep premium), $70.5 seems to be right answer, but that's wrong. The correct answer is somewhere around $69.5. Here is how I come to this number:

Since the deal is to be close by the end of third quarter, there is about 110 calendar days from now. With bank interest rate around 5%, the interest incurred from now to deal close is about $1.0 per share. Thus the current fair price for the stock is $70.5 - $1 = $69.5. Otherwise if higher than that you might be better off just selling the cash to the bank. The fair price (or theoretical price) comes from the fact that you have to borrow $69.5 from the bank to buy 1 share of KMG, paying $1 interest until the deal close when you will sell the share for $70.5, resulting in no profit (thus no arbitrage).

In reality, the trading of such "future pseudo-cash" like KMG stock is not so simple. The breakup risk is tiny, but not zero (that would reduce the price slight); the chance of competing bid is almost none, but not absolutely impossible (thus would increase the price slightly). But the biggest factor is supply/demand. Many of the KMG shareholders can take profits now even selling at the price below the "theoretical price" of $69.5. In the mean time there is less incentive to buy the shares because the speculative upside is limited. Such imbalance in buy/sell action (much more sells than buys) will cause the share price to go down, until the price is low enough to attract enough capital for the arbitrage traders: the trade of buying the underpriced "pseudo-cash" and sell the real cash to profit on the difference.

That looks like what happens on the first day after the deal is announced: At pre-market after the news breaks, a few trades happened around $69 -- close but below the theoretical price. Then after the market open, all the investors pour in to take profit. The sell orders push the price down to $68.4. That's more than $1 of cash arbitrage money. That leaves enough gap for the arbitrage trades to come in to pick up the $1 risk-free money.

It is an easy "prediction" for how this stock should move next: after the profit-taking volume dies down in the next few days, the stocks should be trading around $69 to $69.5, and as the time goes by, the interests component slowly goes down (thus the theoretical price goes up) and eventually the stock price should reach the cash offer price of $70.5. Anyone who want to arbitrage the cash should use their financing interest rate of their banks or brokers (currently 4% to 5%), and calculate the theoretical price (with the estimated calendar days remaining to the deal closing date) and trade the price difference between the cash and the pseudo-cash.

So cash can be traded even in stock market. The opportunity arises from 1) Interest rate differences; 2) the supply/demand imbalance, and 3) from the people who know how to calculate the interests and those who don't. You might think that only the arbitrage professionals can trade cash, but in fact the supply/demand imbalance is typically quite large that it leaves lot of riskfree cash for small investors to pick up.

Here are a few recent close cash deal examples: HD buying HUG (Hughes Supply); SuperValu and CVS buying Albertson's (ABS); Danaher Corp (DHR) buying Sybron Dental (SYD).

How do you price the options in the cash takeout situation? You don't need Black-Scholes (which is wrong in these situations), just need some common sense and high school math. Rule#1: all out-of-money (relative to the cash offer price) options has 0 theoretical price. In the market place, this is typically represented by no-bid (0 bid price, but ask price can be any number). In the KMG cases, Aug 65 Put is price at 0 bid, 0.55 ask. July 65 Put actually has bid, priced at 0.15 bid, 0.2 ask (previous day prices: 14.6/14.7).

For in-the-money call option, you don't need to pay the full price for the stock until expiration (thus save you interests). So fair price should be: use the theoretical "present value" of cash offer price at the expiration as the stock price, then discount the interest it cost you for buying the options. Take the example of KMG July 55 Call. The cash offer price for stock is $70.5, the present value: $69.5, the present value at expiration is $69.2), the call option should be roughly 69.2 - 55 = 14.2. But paying $14.2 for the call would cost you 0.05 in interest payment, so the theoretical price of this call should be $14.2 - 0.05 = $14.15. In contrast, if you just take the cash offer price and put in the BS formula with 0 volatility, you get $15.73; If you use the present value of $69.5, you get $14.73. The market price of this call is 13.6/13.8. Thus if you have this call, you should continue holding it until expiration to realize $0.45 of riskfree value.

For in-the-money put option, it is always better to exercise it and earn interests, rather than sitting on the put. Thus the put price should be Strike - Cash Offer Price + Interest Earned on Strike from now to deal close. Note that the put price has nothing to do with expiration, namely all the puts of the same strike with different expirations should price the same. For example, for KMG July 75 Put, the theoretical price should be 75 - 70.5 + 1.0 = $5.5. In the market place, the bid/offer of the 75 put is all over the place: Jul: 4.3/9.0; Aug: 5.8/8.9; Oct: 6.1/6.7; Jan07: 5.8/6.9. It seems it is profitable to just sell these put (except Jul 75), but you might get immediately assignment and the profit of the price difference is about the same as the arbitrage cash/pseudo-cash difference already exists in the market (so would be easier just to buy the pseudo-cash -- i.e., the KMG stock -- on the market).

In summary, the theoretical option pricing for cash takeout stock (with absolute certainty of the deal) is:

1) OTM option (relative to cash offer price) = 0

2) ITM Call = (Present value of cash offer price at expiration) - Strike - (Interest Cost of Call from now to expiration)

3) ITM Put = Strike - (Cash Offer Price) + (Interest Earned on Strike from now to deal close)

(But should be exercised immediately if long).

The above takeover deal was completed at the end August 2006. The last traded KMG stock price was 70.47, or almost exactly the takeout price of 70.50, as it should be.

(The author can be contacted at huangxinw@gmail.com.)

Really? You can't buy the $100 bill at a different price other than $100, but if you deposit the $100, one bank pays 5% interest, another pays 3.5%, that is certainly different prices in cash.

Interest rate obviously is the key factor in trading cash in ForEx market. In stock market, there is also opportunity for trading cash. Let's look at one example as it just happens today (6/23/06).

**Pricing a Cash Takeout Stock**Anadarko Petroleum (APC), a natural gas, crude oil development and production company, announced this morning that it will acquire Kerr-McGee (KMG) and Western Gas Resources (WGR) in cash. We will look at the KMG part of the deal. APC will pay $70.5 per share in cash for all KMG shares. Furthermore, it is a friendly takeover and the KMG board already accepted the offer at the announcement. There is a very steep breakup fee if the deal doesn't go through. On Thursday KMG close at $50.3 so the offer price has a huge 40% in premium. The deal is expected to close at the end of third quarter.

So what do you expect KMG to trade today? $70.5?

Assuming there is no risk of the deal breakup (with the steep breakup fee), and no chance for any competing bids (with the steep premium), $70.5 seems to be right answer, but that's wrong. The correct answer is somewhere around $69.5. Here is how I come to this number:

Since the deal is to be close by the end of third quarter, there is about 110 calendar days from now. With bank interest rate around 5%, the interest incurred from now to deal close is about $1.0 per share. Thus the current fair price for the stock is $70.5 - $1 = $69.5. Otherwise if higher than that you might be better off just selling the cash to the bank. The fair price (or theoretical price) comes from the fact that you have to borrow $69.5 from the bank to buy 1 share of KMG, paying $1 interest until the deal close when you will sell the share for $70.5, resulting in no profit (thus no arbitrage).

**Pseudo-Cash vs Cash**In reality, the trading of such "future pseudo-cash" like KMG stock is not so simple. The breakup risk is tiny, but not zero (that would reduce the price slight); the chance of competing bid is almost none, but not absolutely impossible (thus would increase the price slightly). But the biggest factor is supply/demand. Many of the KMG shareholders can take profits now even selling at the price below the "theoretical price" of $69.5. In the mean time there is less incentive to buy the shares because the speculative upside is limited. Such imbalance in buy/sell action (much more sells than buys) will cause the share price to go down, until the price is low enough to attract enough capital for the arbitrage traders: the trade of buying the underpriced "pseudo-cash" and sell the real cash to profit on the difference.

That looks like what happens on the first day after the deal is announced: At pre-market after the news breaks, a few trades happened around $69 -- close but below the theoretical price. Then after the market open, all the investors pour in to take profit. The sell orders push the price down to $68.4. That's more than $1 of cash arbitrage money. That leaves enough gap for the arbitrage trades to come in to pick up the $1 risk-free money.

It is an easy "prediction" for how this stock should move next: after the profit-taking volume dies down in the next few days, the stocks should be trading around $69 to $69.5, and as the time goes by, the interests component slowly goes down (thus the theoretical price goes up) and eventually the stock price should reach the cash offer price of $70.5. Anyone who want to arbitrage the cash should use their financing interest rate of their banks or brokers (currently 4% to 5%), and calculate the theoretical price (with the estimated calendar days remaining to the deal closing date) and trade the price difference between the cash and the pseudo-cash.

So cash can be traded even in stock market. The opportunity arises from 1) Interest rate differences; 2) the supply/demand imbalance, and 3) from the people who know how to calculate the interests and those who don't. You might think that only the arbitrage professionals can trade cash, but in fact the supply/demand imbalance is typically quite large that it leaves lot of riskfree cash for small investors to pick up.

Here are a few recent close cash deal examples: HD buying HUG (Hughes Supply); SuperValu and CVS buying Albertson's (ABS); Danaher Corp (DHR) buying Sybron Dental (SYD).

**Option Pricing**How do you price the options in the cash takeout situation? You don't need Black-Scholes (which is wrong in these situations), just need some common sense and high school math. Rule#1: all out-of-money (relative to the cash offer price) options has 0 theoretical price. In the market place, this is typically represented by no-bid (0 bid price, but ask price can be any number). In the KMG cases, Aug 65 Put is price at 0 bid, 0.55 ask. July 65 Put actually has bid, priced at 0.15 bid, 0.2 ask (previous day prices: 14.6/14.7).

For in-the-money call option, you don't need to pay the full price for the stock until expiration (thus save you interests). So fair price should be: use the theoretical "present value" of cash offer price at the expiration as the stock price, then discount the interest it cost you for buying the options. Take the example of KMG July 55 Call. The cash offer price for stock is $70.5, the present value: $69.5, the present value at expiration is $69.2), the call option should be roughly 69.2 - 55 = 14.2. But paying $14.2 for the call would cost you 0.05 in interest payment, so the theoretical price of this call should be $14.2 - 0.05 = $14.15. In contrast, if you just take the cash offer price and put in the BS formula with 0 volatility, you get $15.73; If you use the present value of $69.5, you get $14.73. The market price of this call is 13.6/13.8. Thus if you have this call, you should continue holding it until expiration to realize $0.45 of riskfree value.

For in-the-money put option, it is always better to exercise it and earn interests, rather than sitting on the put. Thus the put price should be Strike - Cash Offer Price + Interest Earned on Strike from now to deal close. Note that the put price has nothing to do with expiration, namely all the puts of the same strike with different expirations should price the same. For example, for KMG July 75 Put, the theoretical price should be 75 - 70.5 + 1.0 = $5.5. In the market place, the bid/offer of the 75 put is all over the place: Jul: 4.3/9.0; Aug: 5.8/8.9; Oct: 6.1/6.7; Jan07: 5.8/6.9. It seems it is profitable to just sell these put (except Jul 75), but you might get immediately assignment and the profit of the price difference is about the same as the arbitrage cash/pseudo-cash difference already exists in the market (so would be easier just to buy the pseudo-cash -- i.e., the KMG stock -- on the market).

In summary, the theoretical option pricing for cash takeout stock (with absolute certainty of the deal) is:

1) OTM option (relative to cash offer price) = 0

2) ITM Call = (Present value of cash offer price at expiration) - Strike - (Interest Cost of Call from now to expiration)

3) ITM Put = Strike - (Cash Offer Price) + (Interest Earned on Strike from now to deal close)

(But should be exercised immediately if long).

**Postscript: KMG ceased to exist**The above takeover deal was completed at the end August 2006. The last traded KMG stock price was 70.47, or almost exactly the takeout price of 70.50, as it should be.

(The author can be contacted at huangxinw@gmail.com.)